diff --git "a/data/train/cpp-000.jsonl" "b/data/train/cpp-000.jsonl" --- "a/data/train/cpp-000.jsonl" +++ "b/data/train/cpp-000.jsonl" @@ -22,7 +22,7 @@ {"question_id": 32, "task_id": "longest-valid-parentheses", "difficulty": "Hard", "problem_description": "Given a string containing just the characters '(' and ')', return the length of the longest valid (well-formed) parentheses substring.\n\nExample 1:\n\nInput: s = \"(()\"\nOutput: 2\nExplanation: The longest valid parentheses substring is \"()\".\n\nExample 2:\n\nInput: s = \")()())\"\nOutput: 4\nExplanation: The longest valid parentheses substring is \"()()\".\n\nExample 3:\n\nInput: s = \"\"\nOutput: 0\n\nConstraints:\n\n- 0 <= s.length <= 3 * 10^4\n- s[i] is '(', or ')'.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"(()())\") == 6\n assert candidate(s = \"())\") == 2\n assert candidate(s = \"())(()\") == 2\n assert candidate(s = \"((((((()))))))\") == 14\n assert candidate(s = \"((())()())()\") == 12\n assert candidate(s = \")()(()(()))\") == 10\n assert candidate(s = \"(()(()(()(()))))\") == 16\n assert candidate(s = \")()())\") == 4\n assert candidate(s = \"()()()()()()()()\") == 16\n assert candidate(s = \"()(()(()))\") == 10\n assert candidate(s = \"()()(())\") == 8\n assert candidate(s = \"\") == 0\n assert candidate(s = \"(()))()\") == 4\n assert candidate(s = \"(()))(()))\") == 4\n assert candidate(s = \"(()))\") == 4\n assert candidate(s = \"(()(()))\") == 8\n assert candidate(s = \"((()))(())()()\") == 14\n assert candidate(s = \"((())()())\") == 10\n assert candidate(s = \"(()(())())()()\") == 14\n assert candidate(s = \"()(()(()(()(()(()))))\") == 18\n assert candidate(s = \"((((((((((()))))))))))\") == 22\n assert candidate(s = \"())()(()\") == 2\n assert candidate(s = \"()(()\") == 2\n assert candidate(s = \"(()\") == 2\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 72\n assert candidate(s = \"(((())))()()()\") == 14\n assert candidate(s = \"(()((())()())())\") == 16\n assert candidate(s = \"()()()()()()()()()\") == 18\n assert candidate(s = \"((())((()))\") == 10\n assert candidate(s = \"((()))\") == 6\n assert candidate(s = \"(()))(()())\") == 6\n assert candidate(s = \"()()\") == 4\n assert candidate(s = \"()()()()\") == 8\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()\") == 36\n assert candidate(s = \"()()()()()()()()()()()()()()()()()\") == 34\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 80\n assert candidate(s = \"(()(()(()(()(())))))\") == 20\n assert candidate(s = \"()(()(()))()()\") == 14\n assert candidate(s = \"(()((())()()))\") == 14\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 60\n assert candidate(s = \"((((()))))((((()))))((((()))))\") == 30\n assert candidate(s = \"(()((((())))))\") == 14\n assert candidate(s = \"(((((((((((((())))))))))()))))))))))))))))))()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 60\n assert candidate(s = \"((())()(()))\") == 12\n assert candidate(s = \"(((((())))))\") == 12\n assert candidate(s = \"(()((())())())\") == 14\n assert candidate(s = \"()((((((()))))))()\") == 18\n assert candidate(s = \"(((()(()(()(()(()(()()))))))))\") == 30\n assert candidate(s = \"((((()))))(((())))\") == 18\n assert candidate(s = \"(((())))(((())))(((())))(((())))\") == 32\n assert candidate(s = \"((((((((((())))))))))))\") == 22\n assert candidate(s = \"()(()(((()))()))\") == 16\n assert candidate(s = \"(((((())))))(((((())))))\") == 24\n assert candidate(s = \"()()(()(()))(()(()))()()\") == 24\n assert candidate(s = \"(()(()(()(()(()))))())\") == 22\n assert candidate(s = \"(()())(()())(()())\") == 18\n assert candidate(s = \"()()()(()(()(()(()(()()))))\") == 20\n assert candidate(s = \"(()(()))(()(()))(()(()))(()(()))\") == 32\n assert candidate(s = \"((((((((()))))))))\") == 18\n assert candidate(s = \"((()()()()()()))((()()()()()()))\") == 32\n assert candidate(s = \"()((()))()(()(()))()\") == 20\n assert candidate(s = \"(((((()(()(()(()(()(()()))))))))))()()()\") == 40\n assert candidate(s = \"(()(()(()(()(()(()(()(())))))))()()\") == 34\n assert candidate(s = \"(()(()(()(()))()))\") == 18\n assert candidate(s = \"()(()())(()(()))\") == 16\n assert candidate(s = \"(()(()(()(()(()(()(()(())))))))))\") == 32\n assert candidate(s = \"()(()(()(()(()(()(()(()(()))()))))))()()\") == 40\n assert candidate(s = \"()(()(()))()()()\") == 16\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(()))))))))))))))\") == 44\n assert candidate(s = \"((()))((()))\") == 12\n assert candidate(s = \"((()()(()())))()()\") == 18\n assert candidate(s = \"()(()(()(()(()(()(()(()))))))))))))()(()(()(()))()()()()()()()()\") == 30\n assert candidate(s = \"(()((())((()))(((())))))\") == 24\n assert candidate(s = \"()()()()()()()()()()\") == 20\n assert candidate(s = \"((((((((()))))))(()(()(()(()(()(()(()))))))))()()\") == 48\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(())))))()))))))))\") == 46\n assert candidate(s = \"(()(()(()(()(()(()()))))))\") == 26\n assert candidate(s = \"(()(()(()(()(()(()))))))\") == 24\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(()()))))))))))()())\") == 50\n assert candidate(s = \"()(()(()(()(()(())))))\") == 22\n assert candidate(s = \"(((()(()))(()(()))))\") == 20\n assert candidate(s = \"()((((()))))()(()(()))\") == 22\n assert candidate(s = \"(()((((()))))))()()\") == 14\n assert candidate(s = \"((((()))))(()(()))\") == 18\n assert candidate(s = \"(()(()(()(()(()(()))))())()()\") == 28\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(()(()(()))()))))))))))))))))))\") == 54\n assert candidate(s = \"(()(()(()(()(()(()(()))))))))))))()(()(()(()))\") == 28\n assert candidate(s = \"(()(()(()))(()(())))\") == 20\n assert candidate(s = \"(()(()))(()(()))\") == 16\n assert candidate(s = \"(((()()(()())()(()(())))))()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 126\n assert candidate(s = \"(()(()(()(()(()(()(()(()(())))))))))\") == 36\n assert candidate(s = \"(()(()))()(()())\") == 16\n assert candidate(s = \"()((((((((())))))))))()()\") == 20\n assert candidate(s = \"()(()(()(()(()(()(())))))()()()\") == 28\n assert candidate(s = \"(()(()(()(()(()(()(()()))))))))\") == 30\n assert candidate(s = \"((())())(()(()(()())))\") == 22\n assert candidate(s = \"((()))((()))((()))((()))\") == 24\n assert candidate(s = \"((()))()((()))()((()))\") == 22\n assert candidate(s = \"(()(()(()(()(()(()(()))))))))))))()\") == 28\n assert candidate(s = \"(()(())((())))\") == 14\n assert candidate(s = \"((((((((()))))))))))))))\") == 18\n assert candidate(s = \"(()(()(()(()(()(()(())))))))\") == 28\n assert candidate(s = \"(()(()(()(()(()(()(()))))))())\") == 30\n assert candidate(s = \"()()(()(()(()(()()))))\") == 22\n assert candidate(s = \"()(()))(()(()))\") == 8\n assert candidate(s = \"(()(()(()(()(()(()(()(())))))())))\") == 34\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()))))))))))))()(()(()(()))()()()()()()()()(()(()(())))\") == 38\n assert candidate(s = \"()(()(()(()(()(()(()(())))))))\") == 30\n assert candidate(s = \"(()()(()))((())())\") == 18\n assert candidate(s = \"(((((())))))(((()(()))(()))(()(()))(()(()))(()(()))(()(())))\") == 60\n assert candidate(s = \"(()(()(()(()(()(()(())))))())()()()\") == 34\n assert candidate(s = \"()(()(()(()(()(())))))()()\") == 26\n assert candidate(s = \"((()))(()(()))\") == 14\n assert candidate(s = \"())(()())(()(()()(())))\") == 20\n assert candidate(s = \"((())())(()(()(()(()))))\") == 24\n assert candidate(s = \"(((()))(()))(()())\") == 18\n assert candidate(s = \"((())())(()(()))\") == 16\n assert candidate(s = \"(()(()))(()(()))(()(()))\") == 24\n assert candidate(s = \"(()(()(())))()()()(()(()))\") == 26\n assert candidate(s = \"()()()()()()()()()()()()\") == 24\n assert candidate(s = \"(((((()(()))(()(())))))())\") == 26\n assert candidate(s = \"()(()(()(()(()(()(()(()))))))))\") == 30\n assert candidate(s = \"((())((()))(()(()))(()))\") == 24\n assert candidate(s = \"()(()()(()(()())))\") == 18\n assert candidate(s = \"((()(()())))()((()(())))\") == 24\n assert candidate(s = \"((((()))()()()(()))\") == 18\n assert candidate(s = \"((((((()))))))(()(()(())))\") == 26\n assert candidate(s = \"(((()(()(()(()())))))()())\") == 26\n assert candidate(s = \"()(()(()(()(()(()(())))))\") == 22\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()\") == 40\n assert candidate(s = \"()()()()()()()()()()()()()()()\") == 30\n assert candidate(s = \"((((((()))))))(()(()(()(()))))\") == 30\n assert candidate(s = \"(()())(())(()(()(()(())))())\") == 28\n", "comparison": "exact"}, "public_tests": ["\"(()\"", "\")()())\"", "\"\""], "hints": [], "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().longestValidParentheses", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:40+00:00", "tests_total": 133, "tests_dropped": 0, "flags": [], "topic_tags": ["string", "dynamic-programming", "stack", "bracket-sequences"]}, "language": "cpp", "interface": {"raw_signature": "int longestValidParentheses(string s) {", "container": "Solution", "callable": "longestValidParentheses", "parameters": [{"name": "s", "type": "string"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 33, "task_id": "search-in-rotated-sorted-array", "difficulty": "Medium", "problem_description": "There is an integer array nums sorted in ascending order (with distinct values).\n\nPrior to being passed to your function, nums is possibly left rotated at an unknown index k (1 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed). For example, [0,1,2,4,5,6,7] might be left rotated by 3 indices and become [4,5,6,7,0,1,2].\n\nGiven the array nums after the possible rotation and an integer target, return the index of target if it is in nums, or -1 if it is not in nums.\n\nYou must write an algorithm with O(log n) runtime complexity.\n\nExample 1:\n\nInput: nums = [4,5,6,7,0,1,2], target = 0\nOutput: 4\n\nExample 2:\n\nInput: nums = [4,5,6,7,0,1,2], target = 3\nOutput: -1\n\nExample 3:\n\nInput: nums = [1], target = 0\nOutput: -1\n\nConstraints:\n\n- 1 <= nums.length <= 5000\n- -10^4 <= nums[i] <= 10^4\n- All values of nums are unique.\n- nums is an ascending array that is possibly rotated.\n- -10^4 <= target <= 10^4\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3],target = 3) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 10) == 9\n assert candidate(nums = [5, 1, 3],target = 1) == 1\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 3) == -1\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 0) == 4\n assert candidate(nums = [6, 7, 8, 9, 1, 2, 3, 4, 5],target = 6) == 0\n assert candidate(nums = [2, 5, 6, 0, 1, 3, 4],target = 1) == -1\n assert candidate(nums = [3, 5, 1],target = 3) == 0\n assert candidate(nums = [11, 13, 15, 17],target = 11) == 0\n assert candidate(nums = [15, 1, 3, 5, 7, 9, 11, 13],target = 7) == 4\n assert candidate(nums = [5, 1, 2, 3, 4],target = 1) == 1\n assert candidate(nums = [5, 1, 2, 3, 4],target = 6) == -1\n assert candidate(nums = [3, 1],target = 1) == 1\n assert candidate(nums = [15, 17, 11, 13],target = 11) == 2\n assert candidate(nums = [5, 1, 3],target = 3) == 2\n assert candidate(nums = [11, 13, 15, 17],target = 10) == -1\n assert candidate(nums = [4, 5, 6, 7, 8, 1, 2, 3],target = 8) == 4\n assert candidate(nums = [2, 1],target = 1) == 1\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 0, 1],target = 5) == 3\n assert candidate(nums = [3, 5, 1],target = 1) == 2\n assert candidate(nums = [7, 0, 1, 2, 3, 4, 5, 6],target = 5) == 6\n assert candidate(nums = [11, 13, 15, 17],target = 13) == 1\n assert candidate(nums = [11, 13, 15, 17],target = 18) == -1\n assert candidate(nums = [5, 1, 3],target = 5) == 0\n assert candidate(nums = [1, 3, 5],target = 1) == 0\n assert candidate(nums = [1],target = 0) == -1\n assert candidate(nums = [6, 7, 8, 9, 1, 2, 3, 4, 5],target = 5) == 8\n assert candidate(nums = [1, 3, 5],target = 5) == 2\n assert candidate(nums = [11, 13, 15, 17],target = 17) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 3) == 2\n assert candidate(nums = [99, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98],target = 50) == 50\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 65) == -1\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 1019) == 19\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0, 1, 2, 3, 4],target = 49) == 44\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 90) == 75\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 3) == 15\n assert candidate(nums = [999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 1095) == 96\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 29) == 19\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 29) == 14\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 145) == 45\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 47) == 2\n assert candidate(nums = [6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5],target = 0) == 5\n assert candidate(nums = [20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 19) == 19\n assert candidate(nums = [47, 48, 49, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46],target = 45) == 48\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 1, 2],target = 2) == 10\n assert candidate(nums = [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7],target = 29) == 21\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 0],target = 0) == 99\n assert candidate(nums = [15, 16, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 20) == 4\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4],target = 1) == 26\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 0],target = 15) == 13\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3],target = 1) == 11\n assert candidate(nums = [6, 7, 8, 9, 10, 1, 2, 3, 4, 5],target = 10) == 4\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3],target = 10) == 6\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2],target = 11) == -1\n assert candidate(nums = [11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 1, 3, 5, 7, 9],target = 25) == 7\n assert candidate(nums = [11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 20) == -1\n assert candidate(nums = [11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 1, 3, 5, 7, 9],target = 29) == 9\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 29) == 14\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 18) == -1\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 43) == 78\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 70) == 25\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39],target = 0) == 0\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3],target = 11) == -1\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 100) == -1\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2],target = 15) == 12\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3],target = 0) == 16\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 198) == 98\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2],target = 19) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 15) == 14\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 16) == 7\n assert candidate(nums = [47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46],target = 97) == 50\n assert candidate(nums = [11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 15) == 4\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3],target = 3) == 30\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98],target = 99) == 49\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 0) == 11\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28],target = 25) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 31) == -1\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 1, 2],target = 10) == -1\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3],target = 19) == 15\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 20) == 5\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 1014) == 14\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1],target = 0) == 18\n assert candidate(nums = [30, 40, 50, 60, 70, 80, 90, 10, 20],target = 50) == 2\n assert candidate(nums = [15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 19) == 4\n assert candidate(nums = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5],target = 0) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == 9\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 9) == 19\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8, 10],target = 19) == 4\n assert candidate(nums = [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 49) == 15\n assert candidate(nums = [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 50) == -1\n assert candidate(nums = [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 0) == 11\n assert candidate(nums = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 25) == -1\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 35) == 15\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150],target = 75) == 75\n assert candidate(nums = [29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28],target = 14) == 15\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 50) == 50\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 0) == 51\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 2) == 13\n assert candidate(nums = [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7],target = 30) == 22\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6],target = 1) == 25\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3],target = 10) == 6\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 105) == 5\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2],target = 0) == 15\n assert candidate(nums = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5],target = 18) == -1\n assert candidate(nums = [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49],target = 35) == 85\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 2, 4, 6, 8],target = 97) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 0],target = 0) == 50\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3],target = 7) == 3\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 151) == -1\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 1) == 77\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 1) == -1\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1, 2, 3],target = 99) == 95\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 3, 5, 7],target = 15) == 2\n assert candidate(nums = [15, 16, 19, 20, 25, 1, 3, 4, 5, 7, 10, 14],target = 5) == 8\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 37) == 17\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 0) == 31\n assert candidate(nums = [33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],target = 61) == 14\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 5) == 16\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 5, 7, 9],target = 17) == 3\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8],target = 7) == -1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38],target = 39) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 0],target = 50) == 49\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2],target = 2) == 29\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 1, 2],target = 0) == -1\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 0, 1, 2],target = 30) == 27\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 0) == 6\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49],target = 25) == 25\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2],target = 21) == -1\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 110) == 10\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 999) == -1\n", "comparison": "exact"}, "public_tests": ["[4,5,6,7,0,1,2]\n0", "[4,5,6,7,0,1,2]\n3", "[1]\n0"], "hints": [], "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().search", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:42+00:00", "tests_total": 131, "tests_dropped": 1, "flags": [], "topic_tags": ["array", "binary-search"]}, "language": "cpp", "interface": {"raw_signature": "int search(vector& nums, int target) {", "container": "Solution", "callable": "search", "parameters": [{"name": "nums", "type": "vector&"}, {"name": "target", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 34, "task_id": "find-first-and-last-position-of-element-in-sorted-array", "difficulty": "Medium", "problem_description": "Given an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value.\n\nIf target is not found in the array, return [-1, -1].\n\nYou must write an algorithm with O(log n) runtime complexity.\n\nExample 1:\n\nInput: nums = [5,7,7,8,8,10], target = 8\nOutput: [3,4]\n\nExample 2:\n\nInput: nums = [5,7,7,8,8,10], target = 6\nOutput: [-1,-1]\n\nExample 3:\n\nInput: nums = [], target = 0\nOutput: [-1,-1]\n\nConstraints:\n\n- 0 <= nums.length <= 10^5\n- -10^9 <= nums[i] <= 10^9\n- nums is a non-decreasing array.\n- -10^9 <= target <= 10^9\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 6]\n assert candidate(nums = [2, 2, 2, 2, 3, 3, 4, 4, 4, 4],target = 2) == [0, 3]\n assert candidate(nums = [1, 2, 3, 4, 5],target = 5) == [4, 4]\n assert candidate(nums = [5, 7, 7, 8, 8, 10],target = 8) == [3, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 1) == [0, 0]\n assert candidate(nums = [-10, -5, -3, 0, 3, 5, 9, 10],target = 3) == [4, 4]\n assert candidate(nums = [1, 3, 5, 7, 9],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 5],target = 2) == [1, 3]\n assert candidate(nums = [1],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 5, 6],target = 4) == [4, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 7) == [6, 6]\n assert candidate(nums = [5, 7, 7, 8, 8, 10],target = 6) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 5) == [4, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == [4, 4]\n assert candidate(nums = [1, 1, 1, 1, 1],target = 1) == [0, 4]\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5],target = 2) == [1, 4]\n assert candidate(nums = [1, 3, 5, 7, 9],target = 2) == [-1, -1]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 9]\n assert candidate(nums = [],target = 0) == [-1, -1]\n assert candidate(nums = [1],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5],target = 1) == [0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9],target = 10) == [-1, -1]\n assert candidate(nums = [1],target = 2) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 20) == [19, 19]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 4) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 6) == [5, 5]\n assert candidate(nums = [-10, -8, -5, -3, -1, 0, 1, 3, 5, 7, 9, 11, 13],target = 15) == [-1, -1]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 5) == [9, 11]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 5],target = 2) == [1, 3]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = 5) == [6, 8]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 7) == [11, 12]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 9, 10],target = 5) == [6, 9]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 0) == [-1, -1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 4) == [-1, -1]\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10],target = 4) == [15, 19]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [0, 9]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5],target = 3) == [4, 7]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [0, 7]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 3) == [3, 4]\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],target = -100) == [0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 19]\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9],target = 4) == [4, 9]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 21) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 16) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7],target = 5) == [7, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 1) == [0, 0]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 2) == [2, 4]\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 10],target = 3) == [2, 5]\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5],target = 2) == [1, 4]\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 6],target = 2) == [1, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 4) == [5, 6]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 10) == [22, 22]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = -6) == [-1, -1]\n assert candidate(nums = [1, 3, 3, 3, 3, 5, 7, 9],target = 3) == [1, 4]\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 10],target = 5) == [7, 9]\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 22) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7],target = 4) == [4, 6]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -1) == [-1, -1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 15) == [7, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 2) == [1, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10],target = 7) == [18, 19]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = -5) == [1, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == [9, 9]\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],target = -90) == [10, 10]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10],target = 1) == [0, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 0) == [-1, -1]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = 20) == [6, 6]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 1) == [0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 13) == [6, 6]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 2) == [1, 2]\n assert candidate(nums = [-10, -5, -5, -1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = -5) == [1, 2]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8],target = 5) == [8, 11]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 5) == [7, 8]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10, 10, 10],target = 10) == [12, 15]\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [1, 20]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 10) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 8) == [13, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == [9, 9]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 10) == [9, 9]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 19]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [0, 31]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == [-1, -1]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = 0) == [4, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 15) == [14, 14]\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [1, 12]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 10) == [17, 18]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 6) == [9, 10]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -10) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 7) == [6, 6]\n assert candidate(nums = [-10, -8, -5, -3, -1, 0, 1, 3, 5, 7, 9, 11, 13],target = -3) == [3, 3]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 29) == [14, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 5) == [4, 4]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = 0) == [2, 2]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 21) == [10, 10]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 2) == [1, 2]\n assert candidate(nums = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5],target = 3) == [1, 21]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4],target = 3) == [6, 8]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 14]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 0) == [-1, -1]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = 25) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 8, 9],target = 5) == [7, 10]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 25) == [12, 12]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 7) == [6, 6]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 9) == [8, 8]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 8, 9],target = 8) == [13, 16]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],target = 10) == [0, 14]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 5) == [8, 12]\n assert candidate(nums = [-10, -5, -5, -5, 0, 0, 0, 1, 2, 3, 3, 3, 3, 4, 5, 6],target = -5) == [1, 3]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 0) == [-1, -1]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [0, 9]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10],target = 5) == [12, 16]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 21) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 6],target = 3) == [2, 5]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 6) == [10, 11]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = 9) == [9, 9]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 29]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 25) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 10) == [9, 9]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 11) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 11) == [10, 10]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 3) == [-1, -1]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = -10) == [0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 0) == [0, 4]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5],target = 3) == [3, 8]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 7) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == [4, 4]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 10]\n", "comparison": "exact"}, "public_tests": ["[5,7,7,8,8,10]\n8", "[5,7,7,8,8,10]\n6", "[]\n0"], "hints": [], "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().searchRange", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:44+00:00", "tests_total": 137, "tests_dropped": 0, "flags": [], "topic_tags": ["array", "binary-search"]}, "language": "cpp", "interface": {"raw_signature": "vector searchRange(vector& nums, int target) {", "container": "Solution", "callable": "searchRange", "parameters": [{"name": "nums", "type": "vector&"}, {"name": "target", "type": "int"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} -{"question_id": 35, "task_id": "search-insert-position", "difficulty": "Easy", "problem_description": "Given a sorted array of distinct integers and a target value, return the index if the target is found. If not, return the index where it would be if it were inserted in order.\n\nYou must write an algorithm with O(log n) runtime complexity.\n\nExample 1:\n\nInput: nums = [1,3,5,6], target = 5\nOutput: 2\n\nExample 2:\n\nInput: nums = [1,3,5,6], target = 2\nOutput: 1\n\nExample 3:\n\nInput: nums = [1,3,5,6], target = 7\nOutput: 4\n\nConstraints:\n\n- 1 <= nums.length <= 10^4\n- -10^4 <= nums[i] <= 10^4\n- nums contains distinct values sorted in ascending order.\n- -10^4 <= target <= 10^4\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-10, 0, 5, 10],target = 0) == 1\n assert candidate(nums = [1, 2, 4, 6, 7, 9],target = 3) == 2\n assert candidate(nums = [1, 3, 5],target = 4) == 2\n assert candidate(nums = [1, 3, 5, 6],target = 2) == 1\n assert candidate(nums = [-10, -5, -3, 2, 3, 4, 5],target = -4) == 2\n assert candidate(nums = [-10, 0, 10, 20, 30, 40, 50],target = -5) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11],target = 10) == 5\n assert candidate(nums = [1],target = 1) == 0\n assert candidate(nums = [-10, 0, 10, 20, 30, 40, 50],target = 25) == 4\n assert candidate(nums = [1, 3],target = 2) == 1\n assert candidate(nums = [-10, 0, 5, 10],target = 15) == 4\n assert candidate(nums = [1, 3, 5, 6],target = 7) == 4\n assert candidate(nums = [1, 3, 5, 6],target = 5) == 2\n assert candidate(nums = [1, 3],target = 4) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == 4\n assert candidate(nums = [1, 3, 4, 5, 6, 8, 9, 11, 13, 15],target = 7) == 5\n assert candidate(nums = [1, 2, 4, 6, 8, 10],target = 5) == 3\n assert candidate(nums = [1],target = 0) == 0\n assert candidate(nums = [1],target = 2) == 1\n assert candidate(nums = [-10, -5, -3, 2, 3, 4, 5],target = 3) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == 10\n assert candidate(nums = [1, 3, 5, 6],target = 0) == 0\n assert candidate(nums = [-10, 0, 5, 10],target = -5) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 256) == 8\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 5) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],target = 14) == 7\n assert candidate(nums = [10000],target = 9999) == 0\n assert candidate(nums = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100],target = -550) == 5\n assert candidate(nums = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 15) == 7\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10],target = -85) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 12) == 11\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 20) == 10\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 29) == 29\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 155) == 15\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 15) == 7\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],target = 27) == 5\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41],target = 39) == 13\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5.5) == 5\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 27) == 8\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = 200) == 14\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 33) == 6\n assert candidate(nums = [-10000, 10000],target = 10000) == 1\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24],target = 11) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 19) == 18\n assert candidate(nums = [-10000, 10000],target = 0) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 10) == 5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 20) == 10\n assert candidate(nums = [-10, -5, -3, -1, 0, 2, 4, 6, 8, 10],target = -6) == 1\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],target = 26) == 9\n assert candidate(nums = [50, 60, 70, 80, 90, 100, 110, 120, 130, 140],target = 145) == 10\n assert candidate(nums = [-10, -5, -3, 0, 4, 8, 12],target = 3) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],target = 12) == 6\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 512) == 9\n assert candidate(nums = [-10, -5, 0, 3, 9, 12, 15],target = 1) == 3\n assert candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500],target = -350) == 2\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256],target = 64) == 6\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100],target = 50) == 7\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80],target = 67) == 13\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 10) == 5\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58],target = 59) == 20\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 1) == 0\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],target = 100) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 500) == 4\n assert candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500],target = -250) == 3\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5.5) == 6\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20, 25, 30],target = 12) == 5\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 5500) == 5\n assert candidate(nums = [-1000, -500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500, 1000],target = -750) == 1\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -3) == 2\n assert candidate(nums = [1, 3, 5, 7, 9],target = 6) == 3\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 100) == 0\n assert candidate(nums = [1, 10, 100, 1000, 10000],target = 500) == 3\n assert candidate(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50],target = -35) == 2\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59],target = 3) == 1\n assert candidate(nums = [-10, -5, 0, 5, 10],target = -7) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 8) == 7\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 1500) == 1\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19],target = 18) == 6\n assert candidate(nums = [-10000, 10000],target = -10000) == 0\n assert candidate(nums = [-999, -998, -997, -996, -995, -994, -993, -992, -991, -990],target = -993) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 20) == 10\n assert candidate(nums = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = 1024) == 32\n assert candidate(nums = [-1000, -500, -250, -125, -62, -31, -15, -7, -3, -1],target = -10) == 7\n assert candidate(nums = [-10000, -9000, -8000, -7000, -6000, -5000, -4000, -3000, -2000, -1000],target = -7500) == 3\n assert candidate(nums = [2, 4, 6, 8, 10],target = 5) == 2\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == 11\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 29) == 9\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 93) == 18\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 550) == 5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 20) == 10\n assert candidate(nums = [1, 10, 100, 1000, 10000],target = 5000) == 4\n assert candidate(nums = [-10000, -9000, -8000, -7000, -6000, -5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 5000) == 15\n assert candidate(nums = [-10, -5, -3, -1, 0, 2, 4, 6, 8, 10],target = -4) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 14) == 7\n assert candidate(nums = [-5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000],target = -2500) == 3\n assert candidate(nums = [-10, -5, 0, 2, 5, 9, 11, 20],target = 3) == 4\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58],target = 26) == 9\n assert candidate(nums = [-500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500],target = -75) == 3\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],target = 31) == 15\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = -45) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],target = 44) == 22\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25],target = 15) == 5\n assert candidate(nums = [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023],target = 1024) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],target = 1150) == 11\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],target = 15) == 5\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 100) == 6\n assert candidate(nums = [100, 200, 300, 400, 500],target = 250) == 2\n assert candidate(nums = [-100, -50, 0, 50, 100],target = -75) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 15) == 14\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 19) == 9\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 257) == 9\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90],target = 5) == 0\n assert candidate(nums = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = -1) == 0\n", "comparison": "exact"}, "public_tests": ["[1,3,5,6]\n5", "[1,3,5,6]\n2", "[1,3,5,6]\n7"], "hints": [], "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().searchInsert", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:47+00:00", "tests_total": 119, "tests_dropped": 4, "flags": [], "topic_tags": ["array", "binary-search"]}, "language": "cpp", "interface": {"raw_signature": "int searchInsert(vector& nums, int target) {", "container": "Solution", "callable": "searchInsert", "parameters": [{"name": "nums", "type": "vector&"}, {"name": "target", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 35, "task_id": "search-insert-position", "difficulty": "Easy", "problem_description": "Given a sorted array of distinct integers and a target value, return the index if the target is found. If not, return the index where it would be if it were inserted in order.\n\nYou must write an algorithm with O(log n) runtime complexity.\n\nExample 1:\n\nInput: nums = [1,3,5,6], target = 5\nOutput: 2\n\nExample 2:\n\nInput: nums = [1,3,5,6], target = 2\nOutput: 1\n\nExample 3:\n\nInput: nums = [1,3,5,6], target = 7\nOutput: 4\n\nConstraints:\n\n- 1 <= nums.length <= 10^4\n- -10^4 <= nums[i] <= 10^4\n- nums contains distinct values sorted in ascending order.\n- -10^4 <= target <= 10^4\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-10, 0, 5, 10],target = 0) == 1\n assert candidate(nums = [1, 2, 4, 6, 7, 9],target = 3) == 2\n assert candidate(nums = [1, 3, 5],target = 4) == 2\n assert candidate(nums = [1, 3, 5, 6],target = 2) == 1\n assert candidate(nums = [-10, -5, -3, 2, 3, 4, 5],target = -4) == 2\n assert candidate(nums = [-10, 0, 10, 20, 30, 40, 50],target = -5) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11],target = 10) == 5\n assert candidate(nums = [1],target = 1) == 0\n assert candidate(nums = [-10, 0, 10, 20, 30, 40, 50],target = 25) == 4\n assert candidate(nums = [1, 3],target = 2) == 1\n assert candidate(nums = [-10, 0, 5, 10],target = 15) == 4\n assert candidate(nums = [1, 3, 5, 6],target = 7) == 4\n assert candidate(nums = [1, 3, 5, 6],target = 5) == 2\n assert candidate(nums = [1, 3],target = 4) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == 4\n assert candidate(nums = [1, 3, 4, 5, 6, 8, 9, 11, 13, 15],target = 7) == 5\n assert candidate(nums = [1, 2, 4, 6, 8, 10],target = 5) == 3\n assert candidate(nums = [1],target = 0) == 0\n assert candidate(nums = [1],target = 2) == 1\n assert candidate(nums = [-10, -5, -3, 2, 3, 4, 5],target = 3) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == 10\n assert candidate(nums = [1, 3, 5, 6],target = 0) == 0\n assert candidate(nums = [-10, 0, 5, 10],target = -5) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 256) == 8\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 5) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],target = 14) == 7\n assert candidate(nums = [10000],target = 9999) == 0\n assert candidate(nums = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100],target = -550) == 5\n assert candidate(nums = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 15) == 7\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10],target = -85) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 12) == 11\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 20) == 10\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 29) == 29\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 155) == 15\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 15) == 7\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],target = 27) == 5\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41],target = 39) == 13\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 27) == 8\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = 200) == 14\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 33) == 6\n assert candidate(nums = [-10000, 10000],target = 10000) == 1\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24],target = 11) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 19) == 18\n assert candidate(nums = [-10000, 10000],target = 0) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 10) == 5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 20) == 10\n assert candidate(nums = [-10, -5, -3, -1, 0, 2, 4, 6, 8, 10],target = -6) == 1\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],target = 26) == 9\n assert candidate(nums = [50, 60, 70, 80, 90, 100, 110, 120, 130, 140],target = 145) == 10\n assert candidate(nums = [-10, -5, -3, 0, 4, 8, 12],target = 3) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],target = 12) == 6\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 512) == 9\n assert candidate(nums = [-10, -5, 0, 3, 9, 12, 15],target = 1) == 3\n assert candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500],target = -350) == 2\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256],target = 64) == 6\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100],target = 50) == 7\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80],target = 67) == 13\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 10) == 5\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58],target = 59) == 20\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 1) == 0\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],target = 100) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 500) == 4\n assert candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500],target = -250) == 3\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20, 25, 30],target = 12) == 5\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 5500) == 5\n assert candidate(nums = [-1000, -500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500, 1000],target = -750) == 1\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -3) == 2\n assert candidate(nums = [1, 3, 5, 7, 9],target = 6) == 3\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 100) == 0\n assert candidate(nums = [1, 10, 100, 1000, 10000],target = 500) == 3\n assert candidate(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50],target = -35) == 2\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59],target = 3) == 1\n assert candidate(nums = [-10, -5, 0, 5, 10],target = -7) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 8) == 7\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 1500) == 1\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19],target = 18) == 6\n assert candidate(nums = [-10000, 10000],target = -10000) == 0\n assert candidate(nums = [-999, -998, -997, -996, -995, -994, -993, -992, -991, -990],target = -993) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 20) == 10\n assert candidate(nums = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = 1024) == 32\n assert candidate(nums = [-1000, -500, -250, -125, -62, -31, -15, -7, -3, -1],target = -10) == 7\n assert candidate(nums = [-10000, -9000, -8000, -7000, -6000, -5000, -4000, -3000, -2000, -1000],target = -7500) == 3\n assert candidate(nums = [2, 4, 6, 8, 10],target = 5) == 2\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == 11\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 29) == 9\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 93) == 18\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 550) == 5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 20) == 10\n assert candidate(nums = [1, 10, 100, 1000, 10000],target = 5000) == 4\n assert candidate(nums = [-10000, -9000, -8000, -7000, -6000, -5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 5000) == 15\n assert candidate(nums = [-10, -5, -3, -1, 0, 2, 4, 6, 8, 10],target = -4) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 14) == 7\n assert candidate(nums = [-5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000],target = -2500) == 3\n assert candidate(nums = [-10, -5, 0, 2, 5, 9, 11, 20],target = 3) == 4\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58],target = 26) == 9\n assert candidate(nums = [-500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500],target = -75) == 3\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],target = 31) == 15\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = -45) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],target = 44) == 22\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25],target = 15) == 5\n assert candidate(nums = [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023],target = 1024) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],target = 1150) == 11\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],target = 15) == 5\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 100) == 6\n assert candidate(nums = [100, 200, 300, 400, 500],target = 250) == 2\n assert candidate(nums = [-100, -50, 0, 50, 100],target = -75) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 15) == 14\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 19) == 9\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 257) == 9\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90],target = 5) == 0\n assert candidate(nums = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = -1) == 0\n", "comparison": "exact"}, "public_tests": ["[1,3,5,6]\n5", "[1,3,5,6]\n2", "[1,3,5,6]\n7"], "hints": [], "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().searchInsert", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:47+00:00", "tests_total": 119, "tests_dropped": 6, "flags": [], "topic_tags": ["array", "binary-search"]}, "language": "cpp", "interface": {"raw_signature": "int searchInsert(vector& nums, int target) {", "container": "Solution", "callable": "searchInsert", "parameters": [{"name": "nums", "type": "vector&"}, {"name": "target", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 36, "task_id": "valid-sudoku", "difficulty": "Medium", "problem_description": "Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:\n\n1. Each row must contain the digits 1-9 without repetition.\n2. Each column must contain the digits 1-9 without repetition.\n3. Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.\n\nNote:\n\n- A Sudoku board (partially filled) could be valid but is not necessarily solvable.\n- Only the filled cells need to be validated according to the mentioned rules.\n\nExample 1:\n\nInput: board =\n[[\"5\",\"3\",\".\",\".\",\"7\",\".\",\".\",\".\",\".\"]\n,[\"6\",\".\",\".\",\"1\",\"9\",\"5\",\".\",\".\",\".\"]\n,[\".\",\"9\",\"8\",\".\",\".\",\".\",\".\",\"6\",\".\"]\n,[\"8\",\".\",\".\",\".\",\"6\",\".\",\".\",\".\",\"3\"]\n,[\"4\",\".\",\".\",\"8\",\".\",\"3\",\".\",\".\",\"1\"]\n,[\"7\",\".\",\".\",\".\",\"2\",\".\",\".\",\".\",\"6\"]\n,[\".\",\"6\",\".\",\".\",\".\",\".\",\"2\",\"8\",\".\"]\n,[\".\",\".\",\".\",\"4\",\"1\",\"9\",\".\",\".\",\"5\"]\n,[\".\",\".\",\".\",\".\",\"8\",\".\",\".\",\"7\",\"9\"]]\nOutput: true\n\nExample 2:\n\nInput: board =\n[[\"8\",\"3\",\".\",\".\",\"7\",\".\",\".\",\".\",\".\"]\n,[\"6\",\".\",\".\",\"1\",\"9\",\"5\",\".\",\".\",\".\"]\n,[\".\",\"9\",\"8\",\".\",\".\",\".\",\".\",\"6\",\".\"]\n,[\"8\",\".\",\".\",\".\",\"6\",\".\",\".\",\".\",\"3\"]\n,[\"4\",\".\",\".\",\"8\",\".\",\"3\",\".\",\".\",\"1\"]\n,[\"7\",\".\",\".\",\".\",\"2\",\".\",\".\",\".\",\"6\"]\n,[\".\",\"6\",\".\",\".\",\".\",\".\",\"2\",\"8\",\".\"]\n,[\".\",\".\",\".\",\"4\",\"1\",\"9\",\".\",\".\",\"5\"]\n,[\".\",\".\",\".\",\".\",\"8\",\".\",\".\",\"7\",\"9\"]]\nOutput: false\nExplanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.\n\nConstraints:\n\n- board.length == 9\n- board[i].length == 9\n- board[i][j] is a digit 1-9 or '.'.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = [['8', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '5', '1', '9'], ['.', '9', '.', '.', '5', '.', '.', '.', '.'], ['.', '.', '.', '2', '.', '4', '.', '.', '.'], ['4', '.', '.', '.', '.', '.', '1', '.', '.'], ['.', '.', '.', '.', '.', '.', '7', '.', '3'], ['.', '.', '2', '.', '.', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '.', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '5', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['1', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '2', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '3', '.', '.', '.', '.', '.', '.'], ['4', '.', '.', '5', '.', '.', '.', '.', '.'], ['.', '5', '.', '.', '6', '.', '.', '.', '.'], ['.', '.', '6', '.', '.', '7', '.', '.', '.'], ['7', '.', '.', '.', '.', '.', '8', '.', '.'], ['.', '8', '.', '.', '.', '.', '.', '9', '.'], ['.', '.', '9', '.', '.', '.', '.', '.', '1']]) == True\n assert candidate(board = [['.', '.', '.', '.', '5', '.', '.', '1', '.'], ['.', '4', '.', '3', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '3', '.', '.', '1'], ['8', '.', '.', '.', '.', '.', '.', '2', '.'], ['.', '.', '2', '.', '7', '.', '4', '.', '.'], ['.', '1', '.', '.', '.', '.', '.', '.', '8'], ['9', '.', '.', '1', '.', '.', '.', '.', '.'], ['.', '.', '8', '.', '.', '8', '.', '7', '.'], ['.', '5', '.', '.', '9', '.', '.', '.', '.']]) == False\n assert candidate(board = [['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['4', '5', '6', '7', '8', '9', '1', '2', '3'], ['7', '8', '9', '1', '2', '3', '4', '5', '6'], ['2', '3', '4', '5', '6', '7', '8', '9', '1'], ['5', '6', '7', '8', '9', '1', '2', '3', '4'], ['8', '9', '1', '2', '3', '4', '5', '6', '7'], ['3', '4', '5', '6', '7', '8', '9', '1', '2'], ['6', '7', '8', '9', '1', '2', '3', '4', '5'], ['9', '1', '2', '3', '4', '5', '6', '7', '8']]) == True\n assert candidate(board = [['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['9', '8', '7', '6', '5', '4', '3', '2', '1'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == False\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['2', '3', '4', '5', '6', '7', '8', '9', '1'], ['3', '4', '5', '6', '7', '8', '9', '1', '2'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == False\n assert candidate(board = [['.', '.', '9', '7', '4', '8', '.', '.', '.'], ['7', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '2', '.', '1', '.', '9', '.', '.', '.'], ['.', '.', '7', '.', '.', '.', '2', '4', '.'], ['.', '6', '4', '.', '1', '.', '5', '9', '.'], ['.', '9', '8', '.', '.', '.', '3', '.', '.'], ['.', '.', '.', '8', '.', '3', '.', '2', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '6'], ['.', '.', '.', '2', '7', '5', '9', '.', '.']]) == True\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '5']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '9', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '4', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['5', '3', '4', '6', '7', '8', '9', '1', '2'], ['6', '7', '2', '1', '9', '5', '3', '4', '8'], ['1', '9', '8', '3', '4', '2', '5', '6', '7'], ['8', '5', '9', '7', '6', '1', '4', '2', '3'], ['4', '2', '6', '8', '5', '3', '7', '9', '1'], ['7', '1', '3', '9', '2', '4', '8', '5', '6'], ['9', '6', '1', '5', '3', '7', '2', '8', '4'], ['2', '8', '7', '4', '1', '9', '6', '3', '5'], ['3', '4', '5', '2', '8', '6', '1', '7', '9']]) == True\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == True\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '9'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['2', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '5', '7', '9']]) == False\n assert candidate(board = [['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9']]) == False\n", "comparison": "exact"}, "public_tests": ["[[\"5\",\"3\",\".\",\".\",\"7\",\".\",\".\",\".\",\".\"],[\"6\",\".\",\".\",\"1\",\"9\",\"5\",\".\",\".\",\".\"],[\".\",\"9\",\"8\",\".\",\".\",\".\",\".\",\"6\",\".\"],[\"8\",\".\",\".\",\".\",\"6\",\".\",\".\",\".\",\"3\"],[\"4\",\".\",\".\",\"8\",\".\",\"3\",\".\",\".\",\"1\"],[\"7\",\".\",\".\",\".\",\"2\",\".\",\".\",\".\",\"6\"],[\".\",\"6\",\".\",\".\",\".\",\".\",\"2\",\"8\",\".\"],[\".\",\".\",\".\",\"4\",\"1\",\"9\",\".\",\".\",\"5\"],[\".\",\".\",\".\",\".\",\"8\",\".\",\".\",\"7\",\"9\"]]", "[[\"8\",\"3\",\".\",\".\",\"7\",\".\",\".\",\".\",\".\"],[\"6\",\".\",\".\",\"1\",\"9\",\"5\",\".\",\".\",\".\"],[\".\",\"9\",\"8\",\".\",\".\",\".\",\".\",\"6\",\".\"],[\"8\",\".\",\".\",\".\",\"6\",\".\",\".\",\".\",\"3\"],[\"4\",\".\",\".\",\"8\",\".\",\"3\",\".\",\".\",\"1\"],[\"7\",\".\",\".\",\".\",\"2\",\".\",\".\",\".\",\"6\"],[\".\",\"6\",\".\",\".\",\".\",\".\",\"2\",\"8\",\".\"],[\".\",\".\",\".\",\"4\",\"1\",\"9\",\".\",\".\",\"5\"],[\".\",\".\",\".\",\".\",\"8\",\".\",\".\",\"7\",\"9\"]]"], "hints": [], "metadata": {"canonical_parameter_names": ["board"], "leetcode_dataset_entry_point": "Solution().isValidSudoku", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:49+00:00", "tests_total": 19, "tests_dropped": 0, "flags": ["has_images"], "topic_tags": ["array", "hash-table", "matrix"]}, "language": "cpp", "interface": {"raw_signature": "bool isValidSudoku(vector>& board) {", "container": "Solution", "callable": "isValidSudoku", "parameters": [{"name": "board", "type": "vector>&"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 38, "task_id": "count-and-say", "difficulty": "Medium", "problem_description": "The count-and-say sequence is a sequence of digit strings defined by the recursive formula:\n\n- countAndSay(1) = \"1\"\n- countAndSay(n) is the run-length encoding of countAndSay(n - 1).\n\nRun-length encoding (RLE) is a string compression method that works by replacing each maximal group of consecutive identical characters with the concatenation of the length of the group followed by the character itself. For example, to compress the string \"3322251\" we replace \"33\" with \"23\", replace \"222\" with \"32\", replace \"5\" with \"15\", and replace \"1\" with \"11\". Thus the compressed string becomes \"23321511\".\n\nGiven a positive integer n, return the n^th element of the count-and-say sequence.\n\nExample 1:\n\nInput: n = 4\nOutput: \"1211\"\nExplanation:\n\ncountAndSay(1) = \"1\"\ncountAndSay(2) = RLE of \"1\" = \"11\"\ncountAndSay(3) = RLE of \"11\" = \"21\"\ncountAndSay(4) = RLE of \"21\" = \"1211\"\n\nExample 2:\n\nInput: n = 1\nOutput: \"1\"\nExplanation:\nThis is the base case.\n\nConstraints:\n\n- 1 <= n <= 30\n\nFollow up: Could you solve it iteratively?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == \"1113213211\"\n assert candidate(n = 3) == \"21\"\n assert candidate(n = 30) == \"3113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321223112111311222112132113213221133122211311221122111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331222113321112131122211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112112322211322311311222113111231133211121312211231131112311211232221121113122113121113222123211211131221132211131221121321131211132221123113112211121312211231131122113221122112133221121321132132211331121321231231121113121113122122311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312211322311211133112111312211213211311123113223112111321322123122113222122211211232221121113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123112221221321132132211231131122211331121321232221121113122113121113222123211211131211121332211213111213122112132113121113222112132113213221232112111312111213322112132113213221133112132123123112111311222112132113311213211221121332211231131122211311123113321112131221123113112221132231131122211211131221131112311332211213211321223112111311222112132113212221132221222112112322211211131221131211132221232112111312111213111213211231131112311311221122132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132122311211131122211213211321222113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213213211221113122113121113222112132113213221232112111312111213322112132113213221133112132123123112111312211322311211133112111312212221121123222112132113213221133112132123222113223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211\"\n assert candidate(n = 15) == \"311311222113111231131112132112311321322112111312211312111322212311322113212221\"\n assert candidate(n = 4) == \"1211\"\n assert candidate(n = 9) == \"31131211131221\"\n assert candidate(n = 6) == \"312211\"\n assert candidate(n = 20) == \"11131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113121113123112112322111213211322211312113211\"\n assert candidate(n = 2) == \"11\"\n assert candidate(n = 25) == \"132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113212231121113112221121321132132211231232112311321322112311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312111312212231131122211311123113322112111312211312111322111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312212221121123222112132113213221133112132123123112111311222112132113213221132213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121132211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321231231121113112221121321132122311211131122211211131221131211322113322112111312211322132113213221123113112221131112311311121321122112132231121113122113322113111221131221\"\n assert candidate(n = 1) == \"1\"\n assert candidate(n = 7) == \"13112221\"\n assert candidate(n = 10) == \"13211311123113112211\"\n assert candidate(n = 5) == \"111221\"\n assert candidate(n = 29) == \"11131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211132221121311121312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221231122212213211321322112311311222113311213212322211211131221131211132221232112111312111213322112131112131221121321131211132221121321132132212321121113121112133221121321132132211331121321231231121113112221121321133112132112211213322112311311222113111231133211121312211231131122211322311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122111213122112311311222113111221131221221321132132211331121321231231121113112221121321133112132112211213322112311311222113111231133211121312211231131122211322311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122111213122112311311222112111331121113112221121113122113121113222112132113213221232112111312111213322112311311222113111221221113122112132113121113222112311311222113111221132221231221132221222112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312111322212321121113121112133221132211131221131211132221232112111312111213322112132113213221133112132113221321123113213221121113122123211211131221222112112322211231131122211311123113321112132132112211131221131211132221121321132132212321121113121112133221123113112221131112311332111213211322111213111213211231131211132211121311222113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131211131221223113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112211213322112312321123113213221123113112221133112132123222112311311222113111231132231121113112221121321133112132112211213322112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312111322212311222122132113213221123113112221133112132123222112311311222113111231133211121321132211121311121321122112133221123113112221131112311332211322111312211312111322212321121113121112133221121321132132211331121321231231121113112221121321132122311211131122211211131221131211322113322112111312211322132113213221123113112221131112311311121321122112132231121113122113322113111221131221\"\n assert candidate(n = 11) == \"11131221133112132113212221\"\n assert candidate(n = 22) == \"132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113213221133122112231131122211211131221131112311332211211131221131211132221232112111312111213322112132113213221133112132113221321123113213221121113122123211211131221222112112322211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211\"\n assert candidate(n = 12) == \"3113112221232112111312211312113211\"\n assert candidate(n = 27) == \"31131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321322123211211131211121332211231131122211311122122111312211213211312111322211231131122211311123113322112111331121113112221121113122113111231133221121113122113121113222123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221123113112221131112311332111213122112311311123112111331121113122112132113311213211321222122111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311123113322113223113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331221122311311222112111312211311123113322112132113213221133122211332111213112221133211322112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122211331121321232221121113122113121122132112311321322112111312211312111322211213111213122112132113121113222112132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212321121113121112133221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213212312311211131122211213211331121321122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311222113111221221113122112132113121113222112132113213221133122211332111213322112132113213221132231131122211311123113322112111312211312111322212321121113122123211231131122113221123113221113122112132113213211121332212311322113212221\"\n assert candidate(n = 26) == \"1113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123211211131211121311121321123113111231131122112213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122113221122112133221121113122113121113222123211211131211121311121321123113213221121113122113121113222113221113122113121113222112132113213221232112111312111213322112311311222113111221221113122112132113121113222112311311222113111221132221231221132221222112112322211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211\"\n assert candidate(n = 14) == \"11131221131211131231121113112221121321132132211331222113112211\"\n assert candidate(n = 21) == \"311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311122122111312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221131112311311121321122112132231121113122113322113111221131221\"\n assert candidate(n = 17) == \"11131221131211132221232112111312212321123113112221121113122113111231133221121321132132211331121321231231121113122113322113111221131221\"\n assert candidate(n = 18) == \"31131122211311123113321112131221123113112211121312211213211321322112311311222113311213212322211211131221131211132221232112111312111213111213211231131122212322211331222113112211\"\n assert candidate(n = 13) == \"1321132132111213122112311311222113111221131221\"\n assert candidate(n = 23) == \"111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122211331121321232221121113122113121113222123112221221321132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322212321121113122123211231131122113221123113221113122112132113213211121332212311322113212221\"\n assert candidate(n = 19) == \"1321132132211331121321231231121113112221121321132122311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112111331121113122112132113213211121332212311322113212221\"\n assert candidate(n = 28) == \"13211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221232112111312211312113211223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321322113311213212322211322132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212311322123123112111321322123122113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132132211331221122311311222112111312211311123113322112111312211312111322212311322123123112112322211211131221131211132221132213211321322113311213212322211231131122211311123113321112131221123113112211121312211213211321222113222112132113223113112221121113122113121113123112112322111213211322211312113211\"\n", "comparison": "exact"}, "public_tests": ["1", "4"], "hints": ["Create a helper function that maps an integer to pairs of its digits and their frequencies. For example, if you call this function with \"223314444411\", then it maps it to an array of pairs [[2,2], [3,2], [1,1], [4,5], [1, 2]].", "Create another helper function that takes the array of pairs and creates a new integer. For example, if you call this function with [[2,2], [3,2], [1,1], [4,5], [1, 2]], it should create \"22\"+\"23\"+\"11\"+\"54\"+\"21\" = \"2223115421\".", "Now, with the two helper functions, you can start with \"1\" and call the two functions alternatively n-1 times. The answer is the last integer you will obtain."], "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countAndSay", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:53+00:00", "tests_total": 28, "tests_dropped": 0, "flags": [], "topic_tags": ["string"]}, "language": "cpp", "interface": {"raw_signature": "string countAndSay(int n) {", "container": "Solution", "callable": "countAndSay", "parameters": [{"name": "n", "type": "int"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 39, "task_id": "combination-sum", "difficulty": "Medium", "problem_description": "Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.\n\nThe same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.\n\nThe test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.\n\nExample 1:\n\nInput: candidates = [2,3,6,7], target = 7\nOutput: [[2,2,3],[7]]\nExplanation:\n2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times.\n7 is a candidate, and 7 = 7.\nThese are the only two combinations.\n\nExample 2:\n\nInput: candidates = [2,3,5], target = 8\nOutput: [[2,2,2,2],[2,3,3],[3,5]]\n\nExample 3:\n\nInput: candidates = [2], target = 1\nOutput: []\n\nConstraints:\n\n- 1 <= candidates.length <= 30\n- 2 <= candidates[i] <= 40\n- All elements of candidates are distinct.\n- 1 <= target <= 40\n", "canonical_tests": {"language": "python", "source": "def answers_match(result, expected):\n \"\"\"The answer may list its items in any order (only the top-level order is free).\"\"\"\n if isinstance(result, list) and isinstance(expected, list):\n return sorted(result, key=repr) == sorted(expected, key=repr)\n return result == expected\n\n\ndef check(candidate):\n assert answers_match(candidate(candidates=[8, 7, 4, 3], target=11), [[3, 4, 4], [3, 8], [4, 7]])\n assert answers_match(candidate(candidates=[2, 5, 10], target=10), [[2, 2, 2, 2, 2], [5, 5], [10]])\n assert answers_match(candidate(candidates=[2, 5, 10], target=15), [[2, 2, 2, 2, 2, 5], [5, 5, 5], [5, 10]])\n assert answers_match(candidate(candidates=[3, 5, 7], target=10), [[3, 7], [5, 5]])\n assert answers_match(candidate(candidates=[2, 3, 5], target=8), [[2, 2, 2, 2], [2, 3, 3], [3, 5]])\n assert answers_match(candidate(candidates=[8, 2, 3], target=11), [[2, 2, 2, 2, 3], [2, 3, 3, 3], [3, 8]])\n assert answers_match(candidate(candidates=[3, 5, 8], target=11), [[3, 3, 5], [3, 8]])\n assert answers_match(candidate(candidates=[3, 5, 7, 8, 9], target=15), [[3, 3, 3, 3, 3], [3, 3, 9], [3, 5, 7], [5, 5, 5], [7, 8]])\n assert answers_match(candidate(candidates=[10, 20, 30], target=20), [[10, 10], [20]])\n assert answers_match(candidate(candidates=[3, 12, 9, 11, 6, 7, 8, 5, 4], target=15), [[3, 3, 3, 3, 3], [3, 3, 3, 6], [3, 3, 4, 5], [3, 3, 9], [3, 4, 4, 4], [3, 4, 8], [3, 5, 7], [3, 6, 6], [3, 12], [4, 4, 7], [4, 5, 6], [4, 11], [5, 5, 5], [6, 9], [7, 8]])\n assert answers_match(candidate(candidates=[7, 6, 5], target=17), [[5, 5, 7], [5, 6, 6]])\n assert answers_match(candidate(candidates=[10, 15, 3, 7], target=25), [[3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 10], [3, 7, 15], [10, 15]])\n assert answers_match(candidate(candidates=[7, 14], target=30), [])\n assert answers_match(candidate(candidates=[4, 6, 8], target=12), [[4, 4, 4], [4, 8], [6, 6]])\n assert answers_match(candidate(candidates=[2], target=1), [])\n assert answers_match(candidate(candidates=[3, 5, 7], target=11), [[3, 3, 5]])\n assert answers_match(candidate(candidates=[2, 3, 6, 7], target=7), [[2, 2, 3], [7]])\n assert answers_match(candidate(candidates=[2, 5, 10, 15, 20, 25], target=40), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 5, 5, 5, 15], [2, 2, 2, 2, 2, 5, 5, 10, 10], [2, 2, 2, 2, 2, 5, 5, 20], [2, 2, 2, 2, 2, 5, 10, 15], [2, 2, 2, 2, 2, 5, 25], [2, 2, 2, 2, 2, 10, 10, 10], [2, 2, 2, 2, 2, 10, 20], [2, 2, 2, 2, 2, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 20], [5, 5, 5, 10, 15], [5, 5, 5, 25], [5, 5, 10, 10, 10], [5, 5, 10, 20], [5, 5, 15, 15], [5, 10, 10, 15], [5, 10, 25], [5, 15, 20], [10, 10, 10, 10], [10, 10, 20], [10, 15, 15], [15, 25], [20, 20]])\n assert answers_match(candidate(candidates=[2, 5, 10, 15], target=20), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 10], [5, 5, 5, 5], [5, 5, 10], [5, 15], [10, 10]])\n assert answers_match(candidate(candidates=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29], target=40), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 5, 19], [2, 2, 2, 2, 2, 2, 2, 2, 7, 17], [2, 2, 2, 2, 2, 2, 2, 2, 11, 13], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 17], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 13], [2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 13], [2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 11], [2, 2, 2, 2, 2, 2, 2, 3, 23], [2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 5, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 7, 19], [2, 2, 2, 2, 2, 2, 2, 13, 13], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 11], [2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 7, 7], [2, 2, 2, 2, 2, 2, 3, 3, 3, 19], [2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 3, 3, 5, 17], [2, 2, 2, 2, 2, 2, 3, 3, 11, 11], [2, 2, 2, 2, 2, 2, 3, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 3, 5, 7, 13], [2, 2, 2, 2, 2, 2, 3, 7, 7, 11], [2, 2, 2, 2, 2, 2, 5, 5, 5, 13], [2, 2, 2, 2, 2, 2, 5, 5, 7, 11], [2, 2, 2, 2, 2, 2, 5, 23], [2, 2, 2, 2, 2, 2, 7, 7, 7, 7], [2, 2, 2, 2, 2, 2, 11, 17], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 7], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5], [2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 13], [2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 11], [2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 11], [2, 2, 2, 2, 2, 3, 3, 3, 7, 7, 7], [2, 2, 2, 2, 2, 3, 3, 5, 5, 7, 7], [2, 2, 2, 2, 2, 3, 3, 5, 19], [2, 2, 2, 2, 2, 3, 3, 7, 17], [2, 2, 2, 2, 2, 3, 3, 11, 13], [2, 2, 2, 2, 2, 3, 5, 5, 5, 5, 7], [2, 2, 2, 2, 2, 3, 5, 5, 17], [2, 2, 2, 2, 2, 3, 5, 11, 11], [2, 2, 2, 2, 2, 3, 7, 7, 13], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 7, 13], [2, 2, 2, 2, 2, 5, 7, 7, 11], [2, 2, 2, 2, 2, 7, 23], [2, 2, 2, 2, 2, 11, 19], [2, 2, 2, 2, 2, 13, 17], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 11], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7], [2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 7], [2, 2, 2, 2, 3, 3, 3, 3, 3, 17], [2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5], [2, 2, 2, 2, 3, 3, 3, 3, 7, 13], [2, 2, 2, 2, 3, 3, 3, 5, 5, 13], [2, 2, 2, 2, 3, 3, 3, 5, 7, 11], [2, 2, 2, 2, 3, 3, 3, 23], [2, 2, 2, 2, 3, 3, 5, 5, 5, 11], [2, 2, 2, 2, 3, 3, 5, 7, 7, 7], [2, 2, 2, 2, 3, 3, 7, 19], [2, 2, 2, 2, 3, 3, 13, 13], [2, 2, 2, 2, 3, 5, 5, 5, 7, 7], [2, 2, 2, 2, 3, 5, 5, 19], [2, 2, 2, 2, 3, 5, 7, 17], [2, 2, 2, 2, 3, 5, 11, 13], [2, 2, 2, 2, 3, 7, 11, 11], [2, 2, 2, 2, 3, 29], [2, 2, 2, 2, 5, 5, 5, 5, 5, 7], [2, 2, 2, 2, 5, 5, 5, 17], [2, 2, 2, 2, 5, 5, 11, 11], [2, 2, 2, 2, 5, 7, 7, 13], [2, 2, 2, 2, 7, 7, 7, 11], [2, 2, 2, 2, 13, 19], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 13], [2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 11], [2, 2, 2, 3, 3, 3, 3, 3, 5, 7, 7], [2, 2, 2, 3, 3, 3, 3, 3, 19], [2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 7], [2, 2, 2, 3, 3, 3, 3, 5, 17], [2, 2, 2, 3, 3, 3, 3, 11, 11], [2, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5], [2, 2, 2, 3, 3, 3, 5, 7, 13], [2, 2, 2, 3, 3, 3, 7, 7, 11], [2, 2, 2, 3, 3, 5, 5, 5, 13], [2, 2, 2, 3, 3, 5, 5, 7, 11], [2, 2, 2, 3, 3, 5, 23], [2, 2, 2, 3, 3, 7, 7, 7, 7], [2, 2, 2, 3, 3, 11, 17], [2, 2, 2, 3, 5, 5, 5, 5, 11], [2, 2, 2, 3, 5, 5, 7, 7, 7], [2, 2, 2, 3, 5, 7, 19], [2, 2, 2, 3, 5, 13, 13], [2, 2, 2, 3, 7, 7, 17], [2, 2, 2, 3, 7, 11, 13], [2, 2, 2, 5, 5, 5, 5, 7, 7], [2, 2, 2, 5, 5, 5, 19], [2, 2, 2, 5, 5, 7, 17], [2, 2, 2, 5, 5, 11, 13], [2, 2, 2, 5, 7, 11, 11], [2, 2, 2, 5, 29], [2, 2, 2, 7, 7, 7, 13], [2, 2, 2, 11, 23], [2, 2, 2, 17, 17], [2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 7], [2, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [2, 2, 3, 3, 3, 3, 3, 3, 5, 13], [2, 2, 3, 3, 3, 3, 3, 3, 7, 11], [2, 2, 3, 3, 3, 3, 3, 5, 5, 11], [2, 2, 3, 3, 3, 3, 3, 7, 7, 7], [2, 2, 3, 3, 3, 3, 5, 5, 7, 7], [2, 2, 3, 3, 3, 3, 5, 19], [2, 2, 3, 3, 3, 3, 7, 17], [2, 2, 3, 3, 3, 3, 11, 13], [2, 2, 3, 3, 3, 5, 5, 5, 5, 7], [2, 2, 3, 3, 3, 5, 5, 17], [2, 2, 3, 3, 3, 5, 11, 11], [2, 2, 3, 3, 3, 7, 7, 13], [2, 2, 3, 3, 5, 5, 5, 5, 5, 5], [2, 2, 3, 3, 5, 5, 7, 13], [2, 2, 3, 3, 5, 7, 7, 11], [2, 2, 3, 3, 7, 23], [2, 2, 3, 3, 11, 19], [2, 2, 3, 3, 13, 17], [2, 2, 3, 5, 5, 5, 5, 13], [2, 2, 3, 5, 5, 5, 7, 11], [2, 2, 3, 5, 5, 23], [2, 2, 3, 5, 7, 7, 7, 7], [2, 2, 3, 5, 11, 17], [2, 2, 3, 7, 7, 19], [2, 2, 3, 7, 13, 13], [2, 2, 3, 11, 11, 11], [2, 2, 5, 5, 5, 5, 5, 11], [2, 2, 5, 5, 5, 7, 7, 7], [2, 2, 5, 5, 7, 19], [2, 2, 5, 5, 13, 13], [2, 2, 5, 7, 7, 17], [2, 2, 5, 7, 11, 13], [2, 2, 7, 7, 11, 11], [2, 2, 7, 29], [2, 2, 13, 23], [2, 2, 17, 19], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [2, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 7], [2, 3, 3, 3, 3, 3, 3, 3, 17], [2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [2, 3, 3, 3, 3, 3, 3, 7, 13], [2, 3, 3, 3, 3, 3, 5, 5, 13], [2, 3, 3, 3, 3, 3, 5, 7, 11], [2, 3, 3, 3, 3, 3, 23], [2, 3, 3, 3, 3, 5, 5, 5, 11], [2, 3, 3, 3, 3, 5, 7, 7, 7], [2, 3, 3, 3, 3, 7, 19], [2, 3, 3, 3, 3, 13, 13], [2, 3, 3, 3, 5, 5, 5, 7, 7], [2, 3, 3, 3, 5, 5, 19], [2, 3, 3, 3, 5, 7, 17], [2, 3, 3, 3, 5, 11, 13], [2, 3, 3, 3, 7, 11, 11], [2, 3, 3, 3, 29], [2, 3, 3, 5, 5, 5, 5, 5, 7], [2, 3, 3, 5, 5, 5, 17], [2, 3, 3, 5, 5, 11, 11], [2, 3, 3, 5, 7, 7, 13], [2, 3, 3, 7, 7, 7, 11], [2, 3, 3, 13, 19], [2, 3, 5, 5, 5, 5, 5, 5, 5], [2, 3, 5, 5, 5, 7, 13], [2, 3, 5, 5, 7, 7, 11], [2, 3, 5, 7, 23], [2, 3, 5, 11, 19], [2, 3, 5, 13, 17], [2, 3, 7, 7, 7, 7, 7], [2, 3, 7, 11, 17], [2, 3, 11, 11, 13], [2, 5, 5, 5, 5, 5, 13], [2, 5, 5, 5, 5, 7, 11], [2, 5, 5, 5, 23], [2, 5, 5, 7, 7, 7, 7], [2, 5, 5, 11, 17], [2, 5, 7, 7, 19], [2, 5, 7, 13, 13], [2, 5, 11, 11, 11], [2, 7, 7, 7, 17], [2, 7, 7, 11, 13], [2, 19, 19], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 13], [3, 3, 3, 3, 3, 3, 3, 3, 5, 11], [3, 3, 3, 3, 3, 3, 3, 5, 7, 7], [3, 3, 3, 3, 3, 3, 3, 19], [3, 3, 3, 3, 3, 3, 5, 5, 5, 7], [3, 3, 3, 3, 3, 3, 5, 17], [3, 3, 3, 3, 3, 3, 11, 11], [3, 3, 3, 3, 3, 5, 5, 5, 5, 5], [3, 3, 3, 3, 3, 5, 7, 13], [3, 3, 3, 3, 3, 7, 7, 11], [3, 3, 3, 3, 5, 5, 5, 13], [3, 3, 3, 3, 5, 5, 7, 11], [3, 3, 3, 3, 5, 23], [3, 3, 3, 3, 7, 7, 7, 7], [3, 3, 3, 3, 11, 17], [3, 3, 3, 5, 5, 5, 5, 11], [3, 3, 3, 5, 5, 7, 7, 7], [3, 3, 3, 5, 7, 19], [3, 3, 3, 5, 13, 13], [3, 3, 3, 7, 7, 17], [3, 3, 3, 7, 11, 13], [3, 3, 5, 5, 5, 5, 7, 7], [3, 3, 5, 5, 5, 19], [3, 3, 5, 5, 7, 17], [3, 3, 5, 5, 11, 13], [3, 3, 5, 7, 11, 11], [3, 3, 5, 29], [3, 3, 7, 7, 7, 13], [3, 3, 11, 23], [3, 3, 17, 17], [3, 5, 5, 5, 5, 5, 5, 7], [3, 5, 5, 5, 5, 17], [3, 5, 5, 5, 11, 11], [3, 5, 5, 7, 7, 13], [3, 5, 7, 7, 7, 11], [3, 5, 13, 19], [3, 7, 7, 23], [3, 7, 11, 19], [3, 7, 13, 17], [3, 11, 13, 13], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 7, 13], [5, 5, 5, 7, 7, 11], [5, 5, 7, 23], [5, 5, 11, 19], [5, 5, 13, 17], [5, 7, 7, 7, 7, 7], [5, 7, 11, 17], [5, 11, 11, 13], [7, 7, 7, 19], [7, 7, 13, 13], [7, 11, 11, 11], [11, 29], [17, 23]])\n assert answers_match(candidate(candidates=[2, 4, 6, 8, 10, 12, 14], target=32), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 14], [2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 8], [2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 4, 12], [2, 2, 2, 2, 2, 2, 2, 2, 6, 10], [2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 6], [2, 2, 2, 2, 2, 2, 2, 4, 4, 10], [2, 2, 2, 2, 2, 2, 2, 4, 6, 8], [2, 2, 2, 2, 2, 2, 2, 4, 14], [2, 2, 2, 2, 2, 2, 2, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 6, 12], [2, 2, 2, 2, 2, 2, 2, 8, 10], [2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 4, 4, 4, 8], [2, 2, 2, 2, 2, 2, 4, 4, 6, 6], [2, 2, 2, 2, 2, 2, 4, 4, 12], [2, 2, 2, 2, 2, 2, 4, 6, 10], [2, 2, 2, 2, 2, 2, 4, 8, 8], [2, 2, 2, 2, 2, 2, 6, 6, 8], [2, 2, 2, 2, 2, 2, 6, 14], [2, 2, 2, 2, 2, 2, 8, 12], [2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 4, 4, 4, 4, 6], [2, 2, 2, 2, 2, 4, 4, 4, 10], [2, 2, 2, 2, 2, 4, 4, 6, 8], [2, 2, 2, 2, 2, 4, 4, 14], [2, 2, 2, 2, 2, 4, 6, 6, 6], [2, 2, 2, 2, 2, 4, 6, 12], [2, 2, 2, 2, 2, 4, 8, 10], [2, 2, 2, 2, 2, 6, 6, 10], [2, 2, 2, 2, 2, 6, 8, 8], [2, 2, 2, 2, 2, 8, 14], [2, 2, 2, 2, 2, 10, 12], [2, 2, 2, 2, 4, 4, 4, 4, 4, 4], [2, 2, 2, 2, 4, 4, 4, 4, 8], [2, 2, 2, 2, 4, 4, 4, 6, 6], [2, 2, 2, 2, 4, 4, 4, 12], [2, 2, 2, 2, 4, 4, 6, 10], [2, 2, 2, 2, 4, 4, 8, 8], [2, 2, 2, 2, 4, 6, 6, 8], [2, 2, 2, 2, 4, 6, 14], [2, 2, 2, 2, 4, 8, 12], [2, 2, 2, 2, 4, 10, 10], [2, 2, 2, 2, 6, 6, 6, 6], [2, 2, 2, 2, 6, 6, 12], [2, 2, 2, 2, 6, 8, 10], [2, 2, 2, 2, 8, 8, 8], [2, 2, 2, 2, 10, 14], [2, 2, 2, 2, 12, 12], [2, 2, 2, 4, 4, 4, 4, 4, 6], [2, 2, 2, 4, 4, 4, 4, 10], [2, 2, 2, 4, 4, 4, 6, 8], [2, 2, 2, 4, 4, 4, 14], [2, 2, 2, 4, 4, 6, 6, 6], [2, 2, 2, 4, 4, 6, 12], [2, 2, 2, 4, 4, 8, 10], [2, 2, 2, 4, 6, 6, 10], [2, 2, 2, 4, 6, 8, 8], [2, 2, 2, 4, 8, 14], [2, 2, 2, 4, 10, 12], [2, 2, 2, 6, 6, 6, 8], [2, 2, 2, 6, 6, 14], [2, 2, 2, 6, 8, 12], [2, 2, 2, 6, 10, 10], [2, 2, 2, 8, 8, 10], [2, 2, 2, 12, 14], [2, 2, 4, 4, 4, 4, 4, 4, 4], [2, 2, 4, 4, 4, 4, 4, 8], [2, 2, 4, 4, 4, 4, 6, 6], [2, 2, 4, 4, 4, 4, 12], [2, 2, 4, 4, 4, 6, 10], [2, 2, 4, 4, 4, 8, 8], [2, 2, 4, 4, 6, 6, 8], [2, 2, 4, 4, 6, 14], [2, 2, 4, 4, 8, 12], [2, 2, 4, 4, 10, 10], [2, 2, 4, 6, 6, 6, 6], [2, 2, 4, 6, 6, 12], [2, 2, 4, 6, 8, 10], [2, 2, 4, 8, 8, 8], [2, 2, 4, 10, 14], [2, 2, 4, 12, 12], [2, 2, 6, 6, 6, 10], [2, 2, 6, 6, 8, 8], [2, 2, 6, 8, 14], [2, 2, 6, 10, 12], [2, 2, 8, 8, 12], [2, 2, 8, 10, 10], [2, 2, 14, 14], [2, 4, 4, 4, 4, 4, 4, 6], [2, 4, 4, 4, 4, 4, 10], [2, 4, 4, 4, 4, 6, 8], [2, 4, 4, 4, 4, 14], [2, 4, 4, 4, 6, 6, 6], [2, 4, 4, 4, 6, 12], [2, 4, 4, 4, 8, 10], [2, 4, 4, 6, 6, 10], [2, 4, 4, 6, 8, 8], [2, 4, 4, 8, 14], [2, 4, 4, 10, 12], [2, 4, 6, 6, 6, 8], [2, 4, 6, 6, 14], [2, 4, 6, 8, 12], [2, 4, 6, 10, 10], [2, 4, 8, 8, 10], [2, 4, 12, 14], [2, 6, 6, 6, 6, 6], [2, 6, 6, 6, 12], [2, 6, 6, 8, 10], [2, 6, 8, 8, 8], [2, 6, 10, 14], [2, 6, 12, 12], [2, 8, 8, 14], [2, 8, 10, 12], [2, 10, 10, 10], [4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 8], [4, 4, 4, 4, 4, 6, 6], [4, 4, 4, 4, 4, 12], [4, 4, 4, 4, 6, 10], [4, 4, 4, 4, 8, 8], [4, 4, 4, 6, 6, 8], [4, 4, 4, 6, 14], [4, 4, 4, 8, 12], [4, 4, 4, 10, 10], [4, 4, 6, 6, 6, 6], [4, 4, 6, 6, 12], [4, 4, 6, 8, 10], [4, 4, 8, 8, 8], [4, 4, 10, 14], [4, 4, 12, 12], [4, 6, 6, 6, 10], [4, 6, 6, 8, 8], [4, 6, 8, 14], [4, 6, 10, 12], [4, 8, 8, 12], [4, 8, 10, 10], [4, 14, 14], [6, 6, 6, 6, 8], [6, 6, 6, 14], [6, 6, 8, 12], [6, 6, 10, 10], [6, 8, 8, 10], [6, 12, 14], [8, 8, 8, 8], [8, 10, 14], [8, 12, 12], [10, 10, 12]])\n assert answers_match(candidate(candidates=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29], target=30), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 3, 19], [2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 11, 11], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 5, 19], [2, 2, 2, 7, 17], [2, 2, 2, 11, 13], [2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 3, 3, 3, 17], [2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 3, 3, 7, 13], [2, 2, 3, 5, 5, 13], [2, 2, 3, 5, 7, 11], [2, 2, 3, 23], [2, 2, 5, 5, 5, 11], [2, 2, 5, 7, 7, 7], [2, 2, 7, 19], [2, 2, 13, 13], [2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 3, 3, 3, 3, 3, 13], [2, 3, 3, 3, 3, 5, 11], [2, 3, 3, 3, 5, 7, 7], [2, 3, 3, 3, 19], [2, 3, 3, 5, 5, 5, 7], [2, 3, 3, 5, 17], [2, 3, 3, 11, 11], [2, 3, 5, 5, 5, 5, 5], [2, 3, 5, 7, 13], [2, 3, 7, 7, 11], [2, 5, 5, 5, 13], [2, 5, 5, 7, 11], [2, 5, 23], [2, 7, 7, 7, 7], [2, 11, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 5, 19], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [7, 23], [11, 19], [13, 17]])\n assert answers_match(candidate(candidates=[5, 10, 15, 20], target=30), [[5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 10], [5, 5, 5, 15], [5, 5, 10, 10], [5, 5, 20], [5, 10, 15], [10, 10, 10], [10, 20], [15, 15]])\n assert answers_match(candidate(candidates=[2, 3, 5, 7, 11, 13, 17], target=30), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 11, 11], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 7, 17], [2, 2, 2, 11, 13], [2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 3, 3, 3, 17], [2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 3, 3, 7, 13], [2, 2, 3, 5, 5, 13], [2, 2, 3, 5, 7, 11], [2, 2, 5, 5, 5, 11], [2, 2, 5, 7, 7, 7], [2, 2, 13, 13], [2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 3, 3, 3, 3, 3, 13], [2, 3, 3, 3, 3, 5, 11], [2, 3, 3, 3, 5, 7, 7], [2, 3, 3, 5, 5, 5, 7], [2, 3, 3, 5, 17], [2, 3, 3, 11, 11], [2, 3, 5, 5, 5, 5, 5], [2, 3, 5, 7, 13], [2, 3, 7, 7, 11], [2, 5, 5, 5, 13], [2, 5, 5, 7, 11], [2, 7, 7, 7, 7], [2, 11, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [13, 17]])\n assert answers_match(candidate(candidates=[2, 6, 10, 14, 18, 22], target=40), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 22], [2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 6, 18], [2, 2, 2, 2, 2, 2, 2, 2, 10, 14], [2, 2, 2, 2, 2, 2, 2, 6, 6, 14], [2, 2, 2, 2, 2, 2, 2, 6, 10, 10], [2, 2, 2, 2, 2, 2, 6, 6, 6, 10], [2, 2, 2, 2, 2, 2, 6, 22], [2, 2, 2, 2, 2, 2, 10, 18], [2, 2, 2, 2, 2, 2, 14, 14], [2, 2, 2, 2, 2, 6, 6, 6, 6, 6], [2, 2, 2, 2, 2, 6, 6, 18], [2, 2, 2, 2, 2, 6, 10, 14], [2, 2, 2, 2, 2, 10, 10, 10], [2, 2, 2, 2, 6, 6, 6, 14], [2, 2, 2, 2, 6, 6, 10, 10], [2, 2, 2, 2, 10, 22], [2, 2, 2, 2, 14, 18], [2, 2, 2, 6, 6, 6, 6, 10], [2, 2, 2, 6, 6, 22], [2, 2, 2, 6, 10, 18], [2, 2, 2, 6, 14, 14], [2, 2, 2, 10, 10, 14], [2, 2, 6, 6, 6, 6, 6, 6], [2, 2, 6, 6, 6, 18], [2, 2, 6, 6, 10, 14], [2, 2, 6, 10, 10, 10], [2, 2, 14, 22], [2, 2, 18, 18], [2, 6, 6, 6, 6, 14], [2, 6, 6, 6, 10, 10], [2, 6, 10, 22], [2, 6, 14, 18], [2, 10, 10, 18], [2, 10, 14, 14], [6, 6, 6, 6, 6, 10], [6, 6, 6, 22], [6, 6, 10, 18], [6, 6, 14, 14], [6, 10, 10, 14], [10, 10, 10, 10], [18, 22]])\n assert answers_match(candidate(candidates=[2, 3, 5, 7, 11], target=29), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 5, 5, 5], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 3, 3, 11], [2, 2, 2, 2, 2, 2, 3, 7, 7], [2, 2, 2, 2, 2, 2, 5, 5, 7], [2, 2, 2, 2, 2, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 3, 5, 11], [2, 2, 2, 2, 2, 5, 7, 7], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3, 5, 7], [2, 2, 2, 2, 3, 3, 5, 5, 5], [2, 2, 2, 2, 3, 7, 11], [2, 2, 2, 2, 5, 5, 11], [2, 2, 2, 2, 7, 7, 7], [2, 2, 2, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 3, 3, 3, 3, 11], [2, 2, 2, 3, 3, 3, 7, 7], [2, 2, 2, 3, 3, 5, 5, 7], [2, 2, 2, 3, 5, 5, 5, 5], [2, 2, 2, 5, 7, 11], [2, 2, 3, 3, 3, 3, 3, 3, 7], [2, 2, 3, 3, 3, 3, 3, 5, 5], [2, 2, 3, 3, 3, 5, 11], [2, 2, 3, 3, 5, 7, 7], [2, 2, 3, 5, 5, 5, 7], [2, 2, 3, 11, 11], [2, 2, 5, 5, 5, 5, 5], [2, 2, 7, 7, 11], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3, 3, 5, 7], [2, 3, 3, 3, 3, 5, 5, 5], [2, 3, 3, 3, 7, 11], [2, 3, 3, 5, 5, 11], [2, 3, 3, 7, 7, 7], [2, 3, 5, 5, 7, 7], [2, 5, 5, 5, 5, 7], [2, 5, 11, 11], [3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 11], [3, 3, 3, 3, 3, 7, 7], [3, 3, 3, 3, 5, 5, 7], [3, 3, 3, 5, 5, 5, 5], [3, 3, 5, 7, 11], [3, 5, 5, 5, 11], [3, 5, 7, 7, 7], [5, 5, 5, 7, 7], [7, 11, 11]])\n assert answers_match(candidate(candidates=[3, 5, 7, 11, 13, 17, 19], target=30), [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 5, 19], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [11, 19], [13, 17]])\n assert answers_match(candidate(candidates=[3, 5, 7, 8, 10], target=25), [[3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 10], [3, 3, 3, 3, 5, 8], [3, 3, 3, 8, 8], [3, 3, 5, 7, 7], [3, 5, 5, 5, 7], [3, 5, 7, 10], [3, 7, 7, 8], [5, 5, 5, 5, 5], [5, 5, 5, 10], [5, 5, 7, 8], [5, 10, 10], [7, 8, 10]])\n assert answers_match(candidate(candidates=[3, 5, 7, 11, 13, 17], target=30), [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [13, 17]])\n assert answers_match(candidate(candidates=[13, 11, 7, 5, 3, 2], target=25), [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 11], [2, 2, 2, 2, 2, 2, 3, 3, 7], [2, 2, 2, 2, 2, 2, 3, 5, 5], [2, 2, 2, 2, 2, 2, 13], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 3, 5, 7], [2, 2, 2, 2, 2, 5, 5, 5], [2, 2, 2, 2, 3, 3, 3, 3, 5], [2, 2, 2, 2, 3, 3, 11], [2, 2, 2, 2, 3, 7, 7], [2, 2, 2, 2, 5, 5, 7], [2, 2, 2, 3, 3, 3, 3, 7], [2, 2, 2, 3, 3, 3, 5, 5], [2, 2, 2, 3, 3, 13], [2, 2, 2, 3, 5, 11], [2, 2, 2, 5, 7, 7], [2, 2, 3, 3, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 5, 7], [2, 2, 3, 3, 5, 5, 5], [2, 2, 3, 5, 13], [2, 2, 3, 7, 11], [2, 2, 5, 5, 11], [2, 2, 7, 7, 7], [2, 3, 3, 3, 3, 3, 3, 5], [2, 3, 3, 3, 3, 11], [2, 3, 3, 3, 7, 7], [2, 3, 3, 5, 5, 7], [2, 3, 5, 5, 5, 5], [2, 3, 7, 13], [2, 5, 5, 13], [2, 5, 7, 11], [3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 13], [3, 3, 3, 5, 11], [3, 3, 5, 7, 7], [3, 5, 5, 5, 7], [3, 11, 11], [5, 5, 5, 5, 5], [5, 7, 13], [7, 7, 11]])\n", "comparison": "unordered"}, "public_tests": ["[2,3,6,7]\n7", "[2,3,5]\n8", "[2]\n1"], "hints": [], "metadata": {"canonical_parameter_names": ["candidates", "target"], "leetcode_dataset_entry_point": "Solution().combinationSum", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:36:55+00:00", "tests_total": 93, "tests_dropped": 63, "flags": ["any_order"], "topic_tags": ["array", "backtracking"]}, "language": "cpp", "interface": {"raw_signature": "vector> combinationSum(vector& candidates, int target) {", "container": "Solution", "callable": "combinationSum", "parameters": [{"name": "candidates", "type": "vector&"}, {"name": "target", "type": "int"}], "return_type": "vector>", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} @@ -131,7 +131,7 @@ {"question_id": 229, "task_id": "majority-element-ii", "difficulty": "Medium", "problem_description": "Given an integer array of size n, find all elements that appear more than ⌊n / 3⌋ times.\n\nExample 1:\n\nInput: nums = [3,2,3]\nOutput: [3]\n\nExample 2:\n\nInput: nums = [1]\nOutput: [1]\n\nExample 3:\n\nInput: nums = [1,2]\nOutput: [1,2]\n\nConstraints:\n\n- 1 <= nums.length <= 5 * 10^4\n- -10^9 <= nums[i] <= 10^9\n\nFollow up: Could you solve the problem in linear time and in O(1) space?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [3, 2, 3]) == [3]\n assert candidate(nums = [1]) == [1]\n assert candidate(nums = [1, 2]) == [2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1]) == []\n assert candidate(nums = [3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [3]\n assert candidate(nums = [1, 1, 1, 3, 3, 2, 2, 2]) == [2, 1]\n assert candidate(nums = [2, 2, 1, 1, 1, 2, 2]) == [2, 1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == []\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 2, 3, 4, 5, 6, 7, 8, 9]) == [10]\n assert candidate(nums = [2, 2, 1, 3]) == [2]\n assert candidate(nums = [4, 1, 2, 3, 4, 2, 3, 4, 5, 6, 7, 8, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == [4]\n assert candidate(nums = [-1, -2, -3, -1, -1, -1, 0]) == [-1]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1]) == [1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [5, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == []\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == [2, 1]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == [1000000000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4]) == []\n assert candidate(nums = [10, 20, 10, 10, 30, 20, 10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]) == [20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == []\n assert candidate(nums = [10, 20, 10, 10, 30, 10, 40, 10, 50, 10, 60, 10, 70, 10, 80, 10, 90, 10, 10, 10, 10, 10]) == [10]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == []\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000]) == [1000000000, -1000000000]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == []\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == [6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5]) == []\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == []\n assert candidate(nums = [10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30]) == []\n assert candidate(nums = [10, 10, 20, 20, 30, 30, 40, 40, 50, 50, 60, 60, 70, 70, 80, 80, 90, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == []\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [9]\n assert candidate(nums = [-1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3]) == []\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == []\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == []\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]) == [42]\n assert candidate(nums = [100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200]) == [100, 200]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [10, 20, 10, 10, 30, 10, 40, 10, 10, 50, 60, 10, 10, 70, 10, 10, 80, 10, 10, 90, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == [10]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [100, 200, 300, 100, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200]) == [100, 200]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, -1000000000, -1000000000, -1000000000, -1000000000]) == [1000000000, -1000000000]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums = [9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3]) == [9, 3]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == []\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [-1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -1, -1, -1]) == [-1]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2]) == [2, 1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30]) == [10, 20]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]) == []\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == []\n assert candidate(nums = [5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == []\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30]) == []\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == []\n assert candidate(nums = [999999999, -999999999, 0, 999999999, -999999999, 0, 999999999, -999999999, 0, 999999999, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums = [-1, -1, -1, -1, -1, -2, -2, -3, -3, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4]) == [-4]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == []\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [2]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == []\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == []\n", "comparison": "exact"}, "public_tests": ["[3,2,3]", "[1]", "[1,2]"], "hints": ["Think about the possible number of elements that can appear more than ⌊ n/3 ⌋ times in the array.", "It can be at most two. Why?", "Consider using Boyer-Moore Voting Algorithm, which is efficient for finding elements that appear more than a certain threshold."], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().majorityElement", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:42:50+00:00", "tests_total": 77, "tests_dropped": 0, "flags": [], "topic_tags": ["array", "hash-table", "sorting", "counting", "boyer-moore-majority-vote-algorithm"]}, "language": "cpp", "interface": {"raw_signature": "vector majorityElement(vector& nums) {", "container": "Solution", "callable": "majorityElement", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 231, "task_id": "power-of-two", "difficulty": "Easy", "problem_description": "Given an integer n, return true if it is a power of two. Otherwise, return false.\n\nAn integer n is a power of two, if there exists an integer x such that n == 2^x.\n\nExample 1:\n\nInput: n = 1\nOutput: true\nExplanation: 2^0 = 1\n\nExample 2:\n\nInput: n = 16\nOutput: true\nExplanation: 2^4 = 16\n\nExample 3:\n\nInput: n = 3\nOutput: false\n\nConstraints:\n\n- -2^31 <= n <= 2^31 - 1\n\nFollow up: Could you solve it without loops/recursion?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == False\n assert candidate(n = 2097152) == True\n assert candidate(n = -16) == False\n assert candidate(n = 67108864) == True\n assert candidate(n = 4096) == True\n assert candidate(n = 2147483647) == False\n assert candidate(n = 536870912) == True\n assert candidate(n = 524288) == True\n assert candidate(n = 268435456) == True\n assert candidate(n = 16384) == True\n assert candidate(n = 16777216) == True\n assert candidate(n = -1) == False\n assert candidate(n = 4) == True\n assert candidate(n = 64) == True\n assert candidate(n = 16) == True\n assert candidate(n = 134217728) == True\n assert candidate(n = 4194304) == True\n assert candidate(n = 2) == True\n assert candidate(n = 33554432) == True\n assert candidate(n = 1024) == True\n assert candidate(n = 128) == True\n assert candidate(n = 0) == False\n assert candidate(n = 1073741824) == True\n assert candidate(n = 8) == True\n assert candidate(n = 1048576) == True\n assert candidate(n = 8192) == True\n assert candidate(n = 2048) == True\n assert candidate(n = 65536) == True\n assert candidate(n = 256) == True\n assert candidate(n = 32) == True\n assert candidate(n = 262144) == True\n assert candidate(n = 131072) == True\n assert candidate(n = 32768) == True\n assert candidate(n = 512) == True\n assert candidate(n = 1) == True\n assert candidate(n = 8388608) == True\n assert candidate(n = 262143) == False\n assert candidate(n = 2047) == False\n assert candidate(n = 5) == False\n assert candidate(n = 23) == False\n assert candidate(n = -2147483648) == False\n assert candidate(n = 8191) == False\n assert candidate(n = 27) == False\n assert candidate(n = 1000000000) == False\n assert candidate(n = 24) == False\n assert candidate(n = -4) == False\n assert candidate(n = 11) == False\n assert candidate(n = 1048575) == False\n assert candidate(n = 29) == False\n assert candidate(n = 131071) == False\n assert candidate(n = -128) == False\n assert candidate(n = 21) == False\n assert candidate(n = -2) == False\n assert candidate(n = 524287) == False\n assert candidate(n = 268435455) == False\n assert candidate(n = 28) == False\n assert candidate(n = 17) == False\n assert candidate(n = 1073741823) == False\n assert candidate(n = 16777215) == False\n assert candidate(n = 9) == False\n assert candidate(n = -8) == False\n assert candidate(n = 6) == False\n assert candidate(n = 10) == False\n assert candidate(n = 63) == False\n assert candidate(n = 67108863) == False\n assert candidate(n = 32767) == False\n assert candidate(n = 511) == False\n assert candidate(n = 4194303) == False\n assert candidate(n = 30) == False\n assert candidate(n = 255) == False\n assert candidate(n = 18) == False\n assert candidate(n = 1023) == False\n assert candidate(n = 127) == False\n assert candidate(n = 15) == False\n assert candidate(n = 14) == False\n assert candidate(n = 26) == False\n assert candidate(n = 536870911) == False\n assert candidate(n = 1000000) == False\n assert candidate(n = 33554431) == False\n assert candidate(n = 12) == False\n assert candidate(n = 16383) == False\n assert candidate(n = 134217727) == False\n assert candidate(n = 8388607) == False\n assert candidate(n = 2097151) == False\n assert candidate(n = 4095) == False\n assert candidate(n = 22) == False\n assert candidate(n = -32) == False\n assert candidate(n = -64) == False\n assert candidate(n = 19) == False\n assert candidate(n = 65535) == False\n assert candidate(n = 31) == False\n assert candidate(n = 7) == False\n assert candidate(n = 25) == False\n", "comparison": "exact"}, "public_tests": ["1", "16", "3"], "hints": [], "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().isPowerOfTwo", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:42:55+00:00", "tests_total": 103, "tests_dropped": 10, "flags": [], "topic_tags": ["math", "bit-manipulation", "recursion"]}, "language": "cpp", "interface": {"raw_signature": "bool isPowerOfTwo(int n) {", "container": "Solution", "callable": "isPowerOfTwo", "parameters": [{"name": "n", "type": "int"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 233, "task_id": "number-of-digit-one", "difficulty": "Hard", "problem_description": "Given an integer n, count the total number of digit 1 appearing in all non-negative integers less than or equal to n.\n\nExample 1:\n\nInput: n = 13\nOutput: 6\n\nExample 2:\n\nInput: n = 0\nOutput: 0\n\nConstraints:\n\n- 0 <= n <= 10^9\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 987654321) == 891632373\n assert candidate(n = 100000) == 50001\n assert candidate(n = 999999999) == 900000000\n assert candidate(n = 999) == 300\n assert candidate(n = 1000000) == 600001\n assert candidate(n = 501) == 201\n assert candidate(n = 9999) == 4000\n assert candidate(n = 100) == 21\n assert candidate(n = 1000000000) == 900000001\n assert candidate(n = 1000) == 301\n assert candidate(n = 55) == 16\n assert candidate(n = 50000000) == 45000000\n assert candidate(n = 13) == 6\n assert candidate(n = 99999) == 50000\n assert candidate(n = 210) == 142\n assert candidate(n = 1010) == 313\n assert candidate(n = 500000005) == 500000001\n assert candidate(n = 12345) == 8121\n assert candidate(n = 50123) == 30057\n assert candidate(n = 909090909) == 826446281\n assert candidate(n = 202020202) == 262218141\n assert candidate(n = 111) == 36\n assert candidate(n = 213456789) == 273589849\n assert candidate(n = 111000111) == 99600372\n assert candidate(n = 123000000) == 129800001\n assert candidate(n = 56789) == 33059\n assert candidate(n = 110) == 33\n assert candidate(n = 807060504) == 745234201\n assert candidate(n = 300) == 160\n assert candidate(n = 10001) == 4003\n assert candidate(n = 100100100) == 80150223\n assert candidate(n = 10999) == 5300\n assert candidate(n = 99) == 20\n assert candidate(n = 876543210) == 803978042\n assert candidate(n = 1001) == 303\n assert candidate(n = 808080808) == 745842261\n assert candidate(n = 5001) == 2501\n assert candidate(n = 101010101) == 81624329\n assert candidate(n = 200000000) == 260000000\n assert candidate(n = 303030303) == 342822161\n assert candidate(n = 800000000) == 740000000\n assert candidate(n = 101) == 23\n assert candidate(n = 10000000) == 7000001\n assert candidate(n = 432109876) == 453263855\n assert candidate(n = 2020) == 1612\n assert candidate(n = 10101) == 4125\n assert candidate(n = 600000000) == 580000000\n assert candidate(n = 1023) == 337\n assert candidate(n = 555555555) == 549382716\n assert candidate(n = 50001) == 30001\n assert candidate(n = 111111111) == 100000008\n assert candidate(n = 888888888) == 812345679\n assert candidate(n = 50005) == 30001\n assert candidate(n = 654321098) == 628668419\n assert candidate(n = 700000000) == 660000000\n assert candidate(n = 200) == 140\n assert candidate(n = 98765) == 49657\n assert candidate(n = 500000000) == 500000000\n assert candidate(n = 400000000) == 420000000\n assert candidate(n = 100100) == 50122\n assert candidate(n = 123456789) == 130589849\n assert candidate(n = 100001) == 50003\n assert candidate(n = 199) == 140\n assert candidate(n = 800000008) == 740000001\n assert candidate(n = 100010001) == 80014005\n assert candidate(n = 100000000) == 80000001\n", "comparison": "exact"}, "public_tests": ["13", "0"], "hints": ["Beware of overflow."], "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countDigitOne", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:42:57+00:00", "tests_total": 76, "tests_dropped": 9, "flags": [], "topic_tags": ["math", "dynamic-programming", "recursion"]}, "language": "cpp", "interface": {"raw_signature": "int countDigitOne(int n) {", "container": "Solution", "callable": "countDigitOne", "parameters": [{"name": "n", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} -{"question_id": 238, "task_id": "product-of-array-except-self", "difficulty": "Medium", "problem_description": "Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].\n\nThe product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.\n\nYou must write an algorithm that runs in O(n) time and without using the division operation.\n\nExample 1:\n\nInput: nums = [1,2,3,4]\nOutput: [24,12,8,6]\n\nExample 2:\n\nInput: nums = [-1,1,0,-3,3]\nOutput: [0,0,9,0,0]\n\nConstraints:\n\n- 2 <= nums.length <= 10^5\n- -30 <= nums[i] <= 30\n- The input is generated such that answer[i] is guaranteed to fit in a 32-bit integer.\n\nFollow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 3, 0, 2, 1]) == [0, 0, 30, 0, 0]\n assert candidate(nums = [1, 0, -1, 2, -2]) == [0, 4, 0, 0, 0]\n assert candidate(nums = [1, -1, 2, -2, 3, -3]) == [-36, 36, -18, 18, -12, 12]\n assert candidate(nums = [5, 3, 2, 4, 1]) == [24, 40, 60, 30, 120]\n assert candidate(nums = [1, 2, 3, 4]) == [24, 12, 8, 6]\n assert candidate(nums = [-1, 1, 0, -3, 3]) == [0, 0, 9, 0, 0]\n assert candidate(nums = [2, -3, 4, -5]) == [60, -40, 30, -24]\n assert candidate(nums = [0, 0, 0, 0]) == [0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5]) == [125, 125, 125, 125]\n assert candidate(nums = [1, 0, 2, 3]) == [0, 6, 0, 0]\n assert candidate(nums = [1, 0, 3, 4]) == [0, 12, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [3628800, 1814400, 1209600, 907200, 725760, 604800, 518400, 453600, 403200, 362880]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17]) == [255255, 170170, 102102, 72930, 46410, 39270, 30030]\n assert candidate(nums = [29, -29, 14, -14, 7, -7, 3.5, -3.5, 1.75, -1.75]) == [-10448701.8125, 10448701.8125, -21643739.46875, 21643739.46875, -43287478.9375, 43287478.9375, -86574957.875, 86574957.875, -173149915.75, 173149915.75]\n assert candidate(nums = [30, -20, 10, -5, 4, -2, 1]) == [-8000, 12000, -24000, 48000, -60000, 120000, -240000]\n assert candidate(nums = [2, -3, 5, 7, 0, -1, 4]) == [0, 0, 0, 0, 840, 0, 0]\n assert candidate(nums = [29, -29, 14, -14, 7, -7, 3, -3, 1, -1]) == [-2506644, 2506644, -5192334, 5192334, -10384668, 10384668, -24230892, 24230892, -72692676, 72692676]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [0, 0, 0, 1]) == [0, 0, 0, 0]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [2, 5, 1, 9, 3, 6, 8, 7]) == [45360, 18144, 90720, 10080, 30240, 15120, 11340, 12960]\n assert candidate(nums = [0, 0, 0, 0, 1]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [2, 3, 0, 5, 6, 0, 7]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == [536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 1073741824]\n assert candidate(nums = [-10, 9, 0, 5, -2, 3, -1, 8]) == [0, 0, -21600, 0, 0, 0, 0, 0]\n assert candidate(nums = [15, 10, 20, 5, 3, 8, 6, 12, 4, 7]) == [48384000, 72576000, 36288000, 145152000, 241920000, 90720000, 120960000, 60480000, 181440000, 103680000]\n assert candidate(nums = [-10, 10, -10, 10, -10]) == [10000, -10000, 10000, -10000, 10000]\n assert candidate(nums = [-1, -2, -3, -4, -5]) == [120, 60, 40, 30, 24]\n assert candidate(nums = [1, 2, 3, 4, 5, 0, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 604800, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 0, 0, 0, 3, 4, 5]) == [0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [2, 3, -5, 7, 11, -13, 17]) == [255255, 170170, -102102, 72930, 46410, -39270, 30030]\n assert candidate(nums = [2, -3, 4, -5, 6, -7]) == [-2520, 1680, -1260, 1008, -840, 720]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [3628800, 1814400, 1209600, 907200, 725760, 604800, 518400, 453600, 403200, 362880]\n assert candidate(nums = [-2, -4, -6, -8, -10, -12, -14, -16, -18, -20]) == [-1857945600, -928972800, -619315200, -464486400, -371589120, -309657600, -265420800, -232243200, -206438400, -185794560]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6]) == [-720, -360, -240, -180, -144, -120]\n assert candidate(nums = [0, 0, 0, 1, 2, 3]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-2, -3, -4, -5, -6]) == [360, 240, 180, 144, 120]\n assert candidate(nums = [1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1]\n assert candidate(nums = [0, 0, 0, 0, 0, 1]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683]\n assert candidate(nums = [1, 2, 0, 4, 5, 0, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [7, -2, 5, 0, -3, 1]) == [0, 0, 0, 210, 0, 0]\n assert candidate(nums = [1, 2, 0, 4, 5, 0, 7, 8, 9]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-3628800, -1814400, -1209600, -907200, -725760, -604800, -518400, -453600, -403200, -362880]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [2, 3, -1, 0, 5, 6, -7, 8, -9, 10]) == [0, 0, 0, -907200, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == [-14400, 14400, -7200, 7200, -4800, 4800, -3600, 3600, -2880, 2880]\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == [1857945600, 928972800, 619315200, 464486400, 371589120, 309657600, 265420800, 232243200, 206438400, 185794560]\n assert candidate(nums = [7, 1, 2, 3, 4, 5]) == [120, 840, 420, 280, 210, 168]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 0, 3, 4, 0, 5]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-3628800, -1814400, -1209600, -907200, -725760, -604800, -518400, -453600, -403200, -362880]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n", "comparison": "exact"}, "public_tests": ["[1,2,3,4]", "[-1,1,0,-3,3]"], "hints": ["Think how you can efficiently utilize prefix and suffix products to calculate the product of all elements except self for each index. Can you pre-compute the prefix and suffix products in linear time to avoid redundant calculations?", "Can you minimize additional space usage by reusing memory or modifying the input array to store intermediate results?"], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().productExceptSelf", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:43:04+00:00", "tests_total": 100, "tests_dropped": 38, "flags": [], "topic_tags": ["array", "prefix-sum"]}, "language": "cpp", "interface": {"raw_signature": "vector productExceptSelf(vector& nums) {", "container": "Solution", "callable": "productExceptSelf", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 238, "task_id": "product-of-array-except-self", "difficulty": "Medium", "problem_description": "Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].\n\nThe product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.\n\nYou must write an algorithm that runs in O(n) time and without using the division operation.\n\nExample 1:\n\nInput: nums = [1,2,3,4]\nOutput: [24,12,8,6]\n\nExample 2:\n\nInput: nums = [-1,1,0,-3,3]\nOutput: [0,0,9,0,0]\n\nConstraints:\n\n- 2 <= nums.length <= 10^5\n- -30 <= nums[i] <= 30\n- The input is generated such that answer[i] is guaranteed to fit in a 32-bit integer.\n\nFollow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 3, 0, 2, 1]) == [0, 0, 30, 0, 0]\n assert candidate(nums = [1, 0, -1, 2, -2]) == [0, 4, 0, 0, 0]\n assert candidate(nums = [1, -1, 2, -2, 3, -3]) == [-36, 36, -18, 18, -12, 12]\n assert candidate(nums = [5, 3, 2, 4, 1]) == [24, 40, 60, 30, 120]\n assert candidate(nums = [1, 2, 3, 4]) == [24, 12, 8, 6]\n assert candidate(nums = [-1, 1, 0, -3, 3]) == [0, 0, 9, 0, 0]\n assert candidate(nums = [2, -3, 4, -5]) == [60, -40, 30, -24]\n assert candidate(nums = [0, 0, 0, 0]) == [0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5]) == [125, 125, 125, 125]\n assert candidate(nums = [1, 0, 2, 3]) == [0, 6, 0, 0]\n assert candidate(nums = [1, 0, 3, 4]) == [0, 12, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [3628800, 1814400, 1209600, 907200, 725760, 604800, 518400, 453600, 403200, 362880]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17]) == [255255, 170170, 102102, 72930, 46410, 39270, 30030]\n assert candidate(nums = [30, -20, 10, -5, 4, -2, 1]) == [-8000, 12000, -24000, 48000, -60000, 120000, -240000]\n assert candidate(nums = [2, -3, 5, 7, 0, -1, 4]) == [0, 0, 0, 0, 840, 0, 0]\n assert candidate(nums = [29, -29, 14, -14, 7, -7, 3, -3, 1, -1]) == [-2506644, 2506644, -5192334, 5192334, -10384668, 10384668, -24230892, 24230892, -72692676, 72692676]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [0, 0, 0, 1]) == [0, 0, 0, 0]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [2, 5, 1, 9, 3, 6, 8, 7]) == [45360, 18144, 90720, 10080, 30240, 15120, 11340, 12960]\n assert candidate(nums = [0, 0, 0, 0, 1]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [2, 3, 0, 5, 6, 0, 7]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == [536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 1073741824]\n assert candidate(nums = [-10, 9, 0, 5, -2, 3, -1, 8]) == [0, 0, -21600, 0, 0, 0, 0, 0]\n assert candidate(nums = [15, 10, 20, 5, 3, 8, 6, 12, 4, 7]) == [48384000, 72576000, 36288000, 145152000, 241920000, 90720000, 120960000, 60480000, 181440000, 103680000]\n assert candidate(nums = [-10, 10, -10, 10, -10]) == [10000, -10000, 10000, -10000, 10000]\n assert candidate(nums = [-1, -2, -3, -4, -5]) == [120, 60, 40, 30, 24]\n assert candidate(nums = [1, 2, 3, 4, 5, 0, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 604800, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 0, 0, 0, 3, 4, 5]) == [0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [2, 3, -5, 7, 11, -13, 17]) == [255255, 170170, -102102, 72930, 46410, -39270, 30030]\n assert candidate(nums = [2, -3, 4, -5, 6, -7]) == [-2520, 1680, -1260, 1008, -840, 720]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [3628800, 1814400, 1209600, 907200, 725760, 604800, 518400, 453600, 403200, 362880]\n assert candidate(nums = [-2, -4, -6, -8, -10, -12, -14, -16, -18, -20]) == [-1857945600, -928972800, -619315200, -464486400, -371589120, -309657600, -265420800, -232243200, -206438400, -185794560]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6]) == [-720, -360, -240, -180, -144, -120]\n assert candidate(nums = [0, 0, 0, 1, 2, 3]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-2, -3, -4, -5, -6]) == [360, 240, 180, 144, 120]\n assert candidate(nums = [1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1]\n assert candidate(nums = [0, 0, 0, 0, 0, 1]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683]\n assert candidate(nums = [1, 2, 0, 4, 5, 0, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [7, -2, 5, 0, -3, 1]) == [0, 0, 0, 210, 0, 0]\n assert candidate(nums = [1, 2, 0, 4, 5, 0, 7, 8, 9]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-3628800, -1814400, -1209600, -907200, -725760, -604800, -518400, -453600, -403200, -362880]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [2, 3, -1, 0, 5, 6, -7, 8, -9, 10]) == [0, 0, 0, -907200, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == [-14400, 14400, -7200, 7200, -4800, 4800, -3600, 3600, -2880, 2880]\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == [1857945600, 928972800, 619315200, 464486400, 371589120, 309657600, 265420800, 232243200, 206438400, 185794560]\n assert candidate(nums = [7, 1, 2, 3, 4, 5]) == [120, 840, 420, 280, 210, 168]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 0, 3, 4, 0, 5]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-3628800, -1814400, -1209600, -907200, -725760, -604800, -518400, -453600, -403200, -362880]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n", "comparison": "exact"}, "public_tests": ["[1,2,3,4]", "[-1,1,0,-3,3]"], "hints": ["Think how you can efficiently utilize prefix and suffix products to calculate the product of all elements except self for each index. Can you pre-compute the prefix and suffix products in linear time to avoid redundant calculations?", "Can you minimize additional space usage by reusing memory or modifying the input array to store intermediate results?"], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().productExceptSelf", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:43:04+00:00", "tests_total": 100, "tests_dropped": 39, "flags": [], "topic_tags": ["array", "prefix-sum"]}, "language": "cpp", "interface": {"raw_signature": "vector productExceptSelf(vector& nums) {", "container": "Solution", "callable": "productExceptSelf", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 239, "task_id": "sliding-window-maximum", "difficulty": "Hard", "problem_description": "You are given an array of integers nums, there is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position.\n\nReturn the max sliding window.\n\nExample 1:\n\nInput: nums = [1,3,-1,-3,5,3,6,7], k = 3\nOutput: [3,3,5,5,6,7]\nExplanation:\nWindow position Max\n--------------- -----\n[1 3 -1] -3 5 3 6 7 3\n 1 [3 -1 -3] 5 3 6 7 3\n 1 3 [-1 -3 5] 3 6 7 5\n 1 3 -1 [-3 5 3] 6 7 5\n 1 3 -1 -3 [5 3 6] 7 6\n 1 3 -1 -3 5 [3 6 7] 7\n\nExample 2:\n\nInput: nums = [1], k = 1\nOutput: [1]\n\nConstraints:\n\n- 1 <= nums.length <= 10^5\n- -10^4 <= nums[i] <= 10^4\n- 1 <= k <= nums.length\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7],k = 3) == [3, 3, 5, 5, 6, 7]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5],k = 5) == [5, 5, 5, 5, 5]\n assert candidate(nums = [4, -2],k = 2) == [4]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 4) == [9, 8, 7, 6, 5, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 2) == [2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [1],k = 1) == [1]\n assert candidate(nums = [1, 3, 1, 2, 0, 5],k = 3) == [3, 3, 2, 5]\n assert candidate(nums = [7, 2, 4],k = 2) == [7, 4]\n assert candidate(nums = [9, 11],k = 2) == [11]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 4, 2, 3, 1, 5, 6, 7, 8, 9, 10],k = 4) == [4, 5, 6, 6, 6, 6, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 3) == [100, 90, 80, 70, 60, 50, 40, 30]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == [3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 5) == [100, 90, 80, 70, 60, 50]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 4) == [-1, -2, -3, -4, -5, -6, -7]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 15) == [1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == [5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 25) == [1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 2) == [10, 10, 10, 10, 10, 10, 10, 10, 10]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7, 1, 2, 4, 5, 6],k = 4) == [3, 5, 5, 6, 7, 7, 7, 7, 5, 6]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11],k = 6) == [5, 6, 6, 7, 8, 8, 9, 10, 10, 11]\n assert candidate(nums = [5, 3, 5, 2, 8, 1, 9, 6, 4, 7],k = 5) == [8, 8, 9, 9, 9, 9]\n assert candidate(nums = [5, 3, 4, 4, 1, 5, 3, 6, 9, 5, 12, 2, 8, 7],k = 5) == [5, 5, 5, 6, 9, 9, 12, 12, 12, 12]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 10) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 3) == [3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 7) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [5, 3, 4, 2, 1, 8, 7, 6, 9, 10, 11],k = 5) == [5, 8, 8, 8, 9, 10, 11]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 6) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 2) == [10, 9, 8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1],k = 2) == [2, 3, 4, 5, 5, 4, 3, 2]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 3) == [0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]\n assert candidate(nums = [2, 1, 3, 5, 4, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5],k = 5) == [5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 5]\n assert candidate(nums = [1, -1, 3, -3, 5, -5, 6, -6, 7, -7],k = 5) == [5, 5, 6, 6, 7, 7]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],k = 5) == [-6, -5, -4, -3, -2, -1]\n assert candidate(nums = [5, 3, 8, 1, 9, 2, 7, 4, 6, 0],k = 3) == [8, 8, 9, 9, 9, 7, 7, 6]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5],k = 10) == [10, 9, 8, 7, 6, 5]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3],k = 4) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [10, -5, 3, 8, 2, -9, 15, 11, 1],k = 4) == [10, 8, 8, 15, 15, 15]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4],k = 4) == [4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 3, 3, 4]\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 12],k = 4) == [11, 11, 10, 12]\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1],k = 5) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 9, 6, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [11, 11, 10, 10, 12, 12, 12, 12, 12, 11, 10, 9, 8, 7, 6, 5]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 3) == [5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 4) == [10, 9, 8, 7, 6, 5, 4]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90],k = 2) == [100, 99, 98, 97, 96, 95, 94, 93, 92, 91]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 5) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [9, 11, 8, 5, 7, 10, 6],k = 4) == [11, 11, 10, 10]\n assert candidate(nums = [10, 14, 13, 7, 10, 6, 5, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1],k = 4) == [14, 14, 13, 10, 10, 9, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20) == [20]\n assert candidate(nums = [1, 3, 2, 1, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 8, 7, 6, 5]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 2) == [3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [-7, -8, 7, 5, 7, 1, 6, 0, 1, 2, -7, -8, -2, -2, 0, 5, 0, 1, 2, -1, -4, -2, -1, -2, 4, 1, -5, 0, -7, -1, 10, 1, -6, 5, -8, 9, 10, 3, -4, -5, -9, -9, -3, -9, -8, -7, 7, -1, -7, -6, -6, 7, 0, 1, 4, 5, -5, -5, 2, -7, 9, 7, 9, 8, -9, -2, -5, -8, 2, -8, -6, -6, -6, 0, 1, 4, -8, -5, -6, -6, 6, -8, -8, -5, -6, -6, -7, -7, 7, -8, -6, -4, -6, -5, -8, -9, -6, -9, -7, -7, -8, -6, -7, -7, 7, -8, -5, -5, -5, 7, -7, 7, -7, -8, -6, -4, -6, -5, -8, -9, -6, -9, -7, -7, -8, -6, -7, -7, 7, -8, -5, -5, -5, 7, -7, 7, -7, -8, -6, -4, -6, -5],k = 25) == [7, 7, 7, 7, 7, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 6) == [3, 3, 3, 3, 3]\n assert candidate(nums = [8, 5, 10, 7, 9, 4, 15, 12, 90, 13],k = 3) == [10, 10, 10, 9, 15, 15, 90, 90]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 6) == [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1],k = 8) == [25, 23, 21, 19, 17, 15]\n assert candidate(nums = [10000, -10000, 5000, -5000, 2500, -2500, 1250, -1250, 625, -625, 312, -312, 156, -156, 78, -78, 39, -39, 19, -19, 9, -9, 4, -4, 2, -2, 1, -1],k = 5) == [10000, 5000, 5000, 2500, 2500, 1250, 1250, 625, 625, 312, 312, 156, 156, 78, 78, 39, 39, 19, 19, 9, 9, 4, 4, 2]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 3) == [1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 4) == [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 7) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3],k = 3) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [5, 3, 8, 7, 6, 5, 4, 3, 2, 1],k = 3) == [8, 8, 8, 7, 6, 5, 4, 3]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7, 8, 1, 2, 3, 4, 5],k = 4) == [3, 5, 5, 6, 7, 8, 8, 8, 8, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5],k = 3) == [3, 4, 5, 5, 5, 4, 3, 2, 3, 4, 5, 5, 5, 4, 3, 2, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3],k = 5) == [4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3]\n assert candidate(nums = [3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3],k = 4) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],k = 7) == [13, 15, 17, 19, 21, 23, 25]\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],k = 3) == [-10, -20, -30, -40, -50, -60, -70, -80]\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3],k = 2) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [3, 2, 2, 3, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],k = 6) == [5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(nums = [5, 3, 8, 2, 1, 4, 7, 6, 9],k = 4) == [8, 8, 8, 7, 7, 9]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 4) == [40, 50, 60, 70, 80, 90, 100]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 5) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1],k = 4) == [3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 5, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7) == [7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [5, 3, 4, 2, 1, 6, 7, 8, 9, 10],k = 4) == [5, 4, 6, 7, 8, 9, 10]\n assert candidate(nums = [10000, -10000, 10000, -10000, 10000, -10000, 10000, -10000, 10000],k = 3) == [10000, 10000, 10000, 10000, 10000, 10000, 10000]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5],k = 2) == [1, 2, 2, 3, 3, 4, 4, 5, 5]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 3) == [-1, -2, -3, -4, -5, -6, -7, -8]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5],k = 3) == [5, 4, 3, 2, 3, 4, 5]\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18],k = 3) == [10, 9, 5, 7, 101, 101]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 7) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 12) == [20, 19, 18, 17, 16, 15, 14, 13, 12]\n assert candidate(nums = [5, 3, 4, 2, 6, 1, 8, 9, 7],k = 4) == [5, 6, 6, 8, 9, 9]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [9, 11, 8, 9, 10, 1, 7, 3, 8, 9],k = 4) == [11, 11, 10, 10, 10, 8, 9]\n assert candidate(nums = [9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == [14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [1]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [10, 9, 8, 7, 6, 5]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 7) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1],k = 5) == [5, 5, 5, 5, 5, 4, 3, 4, 5, 5, 5, 5, 5]\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1],k = 3) == [5, 4, 3, 2, 3, 4, 5, 5, 5, 4, 3]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 3) == [9, 8, 7, 6, 5, 4, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 2) == [2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 10, 5, 6],k = 4) == [11, 11, 10, 10, 10, 10]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 5) == [100, 90, 80, 70, 60, 50]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 6) == [6, 7, 8, 9, 10]\n assert candidate(nums = [5, 2, 2, 4, 1, 6, 1, 3, 2, 5, 2, 2, 4, 6, 1, 6, 3, 3, 5, 2, 1, 1, 4, 6, 3, 2, 1, 1, 5, 6, 1, 3, 5, 6, 3, 5, 6, 3, 6, 5, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10) == [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 8) == [15, 14, 13, 12, 11, 10, 9, 8]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 10) == [0]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1]\n", "comparison": "exact"}, "public_tests": ["[1,3,-1,-3,5,3,6,7]\n3", "[1]\n1"], "hints": ["How about using a data structure such as deque (double-ended queue)?", "The queue size need not be the same as the window’s size.", "Remove redundant elements and the queue should store only elements that need to be considered."], "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().maxSlidingWindow", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:43:06+00:00", "tests_total": 104, "tests_dropped": 0, "flags": [], "topic_tags": ["array", "queue", "sliding-window", "heap-priority-queue", "monotonic-queue", "range-minimum-maximum-query"]}, "language": "cpp", "interface": {"raw_signature": "vector maxSlidingWindow(vector& nums, int k) {", "container": "Solution", "callable": "maxSlidingWindow", "parameters": [{"name": "nums", "type": "vector&"}, {"name": "k", "type": "int"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 240, "task_id": "search-a-2d-matrix-ii", "difficulty": "Medium", "problem_description": "Write an efficient algorithm that searches for a value target in an m x n integer matrix matrix. This matrix has the following properties:\n\n- Integers in each row are sorted in ascending from left to right.\n- Integers in each column are sorted in ascending from top to bottom.\n\nExample 1:\n\nInput: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5\nOutput: true\n\nExample 2:\n\nInput: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20\nOutput: false\n\nConstraints:\n\n- m == matrix.length\n- n == matrix[i].length\n- 1 <= n, m <= 300\n- -10^9 <= matrix[i][j] <= 10^9\n- All the integers in each row are sorted in ascending order.\n- All the integers in each column are sorted in ascending order.\n- -10^9 <= target <= 10^9\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [5, 6, 7, 8, 9], [15, 16, 17, 18, 19], [25, 26, 27, 28, 29], [35, 36, 37, 38, 39]],target = 0) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 20) == False\n assert candidate(matrix = [[-10, -5, -3, -1, -1], [0, 1, 1, 2, 2], [3, 3, 4, 4, 5], [6, 7, 8, 8, 9], [10, 10, 12, 13, 15]],target = 8) == True\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 3) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 5) == True\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19], [20, 21, 22, 23, 24]],target = 0) == False\n assert candidate(matrix = [[-10, -8, -6, -4, -3], [-9, -7, -5, -3, -1], [-4, -2, 0, 2, 4], [-3, 1, 3, 5, 7], [2, 4, 6, 8, 10]],target = 0) == True\n assert candidate(matrix = [[1, 3, 5, 7], [2, 4, 6, 8], [0, 11, 16, 20], [13, 14, 17, 18]],target = 14) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 15) == True\n assert candidate(matrix = [[-10, -8, -6, -4, -2], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],target = -5) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 13) == True\n assert candidate(matrix = [[-10, -8, -5, -3, -1], [0, 2, 3, 5, 7], [8, 9, 10, 12, 13], [15, 17, 18, 20, 21], [23, 25, 26, 27, 29]],target = 14) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [4, 6, 8, 10, 12, 14, 16, 18, 20, 22]],target = 100) == False\n assert candidate(matrix = [[1, 3, 5], [2, 6, 9], [4, 11, 16], [7, 12, 18], [8, 13, 19], [10, 14, 20], [15, 17, 21]],target = 17) == True\n assert candidate(matrix = [[1, 10, 20, 30, 40, 50, 60, 70, 80, 90], [11, 21, 31, 41, 51, 61, 71, 81, 91, 100], [22, 32, 42, 52, 62, 72, 82, 92, 102, 110], [33, 43, 53, 63, 73, 83, 93, 103, 113, 120], [44, 54, 64, 74, 84, 94, 104, 114, 124, 130]],target = 2) == False\n assert candidate(matrix = [[-100, -90, -80, -70, -60, -50, -40, -30, -20, -10], [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], [20, 30, 40, 50, 60, 70, 80, 90, 100, 110], [30, 40, 50, 60, 70, 80, 90, 100, 110, 120], [40, 50, 60, 70, 80, 90, 100, 110, 120, 130], [50, 60, 70, 80, 90, 100, 110, 120, 130, 140], [60, 70, 80, 90, 100, 110, 120, 130, 140, 150], [70, 80, 90, 100, 110, 120, 130, 140, 150, 160], [80, 90, 100, 110, 120, 130, 140, 150, 160, 170], [90, 100, 110, 120, 130, 140, 150, 160, 170, 180]],target = 125) == False\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [50, 51, 52, 53, 54, 55, 56, 57, 58, 59], [60, 61, 62, 63, 64, 65, 66, 67, 68, 69], [70, 71, 72, 73, 74, 75, 76, 77, 78, 79]],target = 37) == True\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],target = -15) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [4, 6, 8, 10, 12, 14, 16, 18, 20, 22], [5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [6, 8, 10, 12, 14, 16, 18, 20, 22, 24], [7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [8, 10, 12, 14, 16, 18, 20, 22, 24, 26], [9, 11, 13, 15, 17, 19, 21, 23, 25, 27], [10, 12, 14, 16, 18, 20, 22, 24, 26, 28]],target = 16) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],target = 55) == True\n assert candidate(matrix = [[-100, -90, -80, -70, -60, -50], [-90, -80, -70, -60, -50, -40], [-80, -70, -60, -50, -40, -30], [-70, -60, -50, -40, -30, -20], [-60, -50, -40, -30, -20, -10], [-50, -40, -30, -20, -10, 0]],target = -65) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15, 18], [2, 5, 8, 12, 19, 22], [3, 6, 9, 16, 22, 24], [10, 13, 14, 17, 24, 26], [18, 21, 23, 26, 30, 35], [20, 24, 27, 29, 33, 40]],target = 27) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 50) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 25) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 23, 25, 27, 29]],target = 25) == True\n assert candidate(matrix = [[-1000000000, -999999999, -999999998], [-999999997, -999999996, -999999995], [-999999994, -999999993, -999999992]],target = -999999995) == True\n assert candidate(matrix = [[-1000000000, -999999999, -999999998, -999999997], [-999999996, -999999995, -999999994, -999999993], [-999999992, -999999991, -999999990, -999999989], [-999999988, -999999987, -999999986, -999999985]],target = -999999993) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 23, 25, 27, 29]],target = 15) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 19], [2, 5, 8, 12, 19, 23], [3, 6, 9, 16, 22, 26], [10, 13, 14, 17, 24, 28], [18, 21, 23, 26, 30, 34], [29, 33, 35, 39, 43, 47]],target = 34) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60]],target = 33) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 20], [2, 5, 8, 12, 19, 25], [3, 6, 9, 16, 22, 30], [10, 13, 14, 17, 24, 35], [18, 21, 23, 26, 30, 40], [22, 27, 31, 37, 41, 45]],target = 37) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -89) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5], [-4, -3, -2, -1, 0, 1], [2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13], [14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25]],target = -5) == True\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, -1, 4, 9], [-8, -3, 1, 6, 11], [-7, -2, 2, 7, 12], [-6, -1, 3, 8, 13]],target = 13) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 19], [2, 5, 8, 12, 16, 20], [3, 6, 9, 13, 17, 21], [10, 14, 18, 22, 26, 24], [18, 22, 26, 30, 34, 32], [27, 31, 35, 39, 43, 41]],target = 35) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -93) == True\n assert candidate(matrix = [[5]],target = 5) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [10, 11, 13, 15, 17], [18, 19, 20, 21, 22], [25, 26, 27, 28, 29], [30, 31, 32, 33, 34]],target = 25) == True\n assert candidate(matrix = [[1000000000]],target = 1000000000) == True\n assert candidate(matrix = [[1, 10, 20, 30, 40, 50, 60, 70, 80, 90], [11, 21, 31, 41, 51, 61, 71, 81, 91, 100], [22, 32, 42, 52, 62, 72, 82, 92, 102, 110], [33, 43, 53, 63, 73, 83, 93, 103, 113, 120], [44, 54, 64, 74, 84, 94, 104, 114, 124, 130]],target = 114) == True\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],target = -13) == False\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],target = 10) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11], [2, 4, 6, 8, 10, 12], [13, 15, 17, 19, 21, 23], [24, 26, 28, 30, 32, 34], [35, 37, 39, 41, 43, 45], [46, 48, 50, 52, 54, 56]],target = 29) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 22, 23, 24, 25]],target = 0) == False\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, -1, 4, 9], [-8, -3, 1, 6, 11], [-7, -2, 2, 7, 12], [-6, -1, 3, 8, 13]],target = 14) == False\n assert candidate(matrix = [[-10, -8, -6, -4, -2, 0], [1, 3, 5, 7, 9, 11], [2, 4, 6, 8, 10, 12], [3, 5, 7, 9, 11, 13], [4, 6, 8, 10, 12, 14], [5, 7, 9, 11, 13, 15]],target = 7) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13], [2, 4, 6, 8, 10, 12, 14], [3, 5, 7, 9, 11, 13, 15], [4, 6, 8, 10, 12, 14, 16], [5, 7, 9, 11, 13, 15, 17], [6, 8, 10, 12, 14, 16, 18]],target = 17) == True\n assert candidate(matrix = [[5, 10, 15, 20, 25, 30, 35, 40, 45, 50], [6, 11, 16, 21, 26, 31, 36, 41, 46, 51], [7, 12, 17, 22, 27, 32, 37, 42, 47, 52], [8, 13, 18, 23, 28, 33, 38, 43, 48, 53], [9, 14, 19, 24, 29, 34, 39, 44, 49, 54]],target = 38) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 37) == True\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, -1, 4, 9], [-8, -3, 1, 6, 11], [-7, -2, 2, 7, 12], [-6, -1, 3, 8, 13]],target = -10) == True\n assert candidate(matrix = [[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9], [-8, -6, -4, -2, 0, 2, 4, 6, 8, 10], [-7, -5, -3, -1, 1, 3, 5, 7, 9, 11], [-6, -4, -2, 0, 2, 4, 6, 8, 10, 12], [-5, -3, -1, 1, 3, 5, 7, 9, 11, 13], [-4, -2, 0, 2, 4, 6, 8, 10, 12, 14], [-3, -1, 1, 3, 5, 7, 9, 11, 13, 15], [-2, 0, 2, 4, 6, 8, 10, 12, 14, 16], [-1, 1, 3, 5, 7, 9, 11, 13, 15, 17], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]],target = 15) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 20], [2, 5, 8, 12, 19, 25], [3, 6, 9, 16, 22, 30], [10, 13, 14, 17, 24, 35], [18, 21, 23, 26, 30, 40], [27, 32, 33, 36, 39, 45]],target = 23) == True\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]],target = 1) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [3, 5, 7, 9, 11], [4, 6, 8, 10, 12], [5, 7, 9, 11, 13]],target = 7) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = -3) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 22, 23, 24, 25]],target = 13) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 26) == False\n assert candidate(matrix = [[3, 6, 9, 12, 15], [6, 9, 12, 15, 18], [9, 12, 15, 18, 21], [12, 15, 18, 21, 24], [15, 18, 21, 24, 27]],target = 13) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [22, 24, 26, 28, 30, 32, 34, 36, 38, 40], [41, 43, 45, 47, 49, 51, 53, 55, 57, 59], [42, 44, 46, 48, 50, 52, 54, 56, 58, 60], [61, 63, 65, 67, 69, 71, 73, 75, 77, 79], [62, 64, 66, 68, 70, 72, 74, 76, 78, 80], [81, 83, 85, 87, 89, 91, 93, 95, 97, 99], [82, 84, 86, 88, 90, 92, 94, 96, 98, 100]],target = 64) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = -5) == True\n assert candidate(matrix = [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]],target = 5) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]],target = 5) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = 7) == True\n assert candidate(matrix = [[-10, -5, -1, 3, 7, 9], [0, 0, 1, 4, 6, 8], [1, 2, 2, 5, 8, 9], [2, 3, 4, 6, 9, 10], [5, 6, 7, 8, 10, 11], [6, 7, 8, 10, 11, 12]],target = 13) == False\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4], [-3, -2, -1, 0, 1, 2, 3], [4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23, 24]],target = -5) == True\n assert candidate(matrix = [[-1, 3, 5, 7, 9, 11, 13, 15], [2, 4, 6, 8, 10, 12, 14, 16], [17, 19, 21, 23, 25, 27, 29, 31], [33, 35, 37, 39, 41, 43, 45, 47], [49, 51, 53, 55, 57, 59, 61, 63]],target = 30) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13], [2, 4, 6, 8, 10, 12, 14], [15, 17, 19, 21, 23, 25, 27], [29, 31, 33, 35, 37, 39, 41], [43, 45, 47, 49, 51, 53, 55]],target = 30) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15, 19], [2, 5, 8, 12, 19, 23], [3, 6, 9, 16, 22, 25], [10, 13, 14, 17, 24, 26], [18, 21, 23, 26, 30, 35], [27, 32, 33, 34, 36, 37]],target = 14) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31], [4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32]],target = 17) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40]],target = 25) == True\n assert candidate(matrix = [[-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1]],target = -1) == True\n assert candidate(matrix = [[5]],target = 10) == False\n assert candidate(matrix = [[-1000000000, -900000000, -800000000], [-700000000, -600000000, -500000000], [-400000000, -300000000, -200000000], [-100000000, 0, 100000000], [200000000, 300000000, 400000000], [500000000, 600000000, 700000000], [800000000, 900000000, 1000000000]],target = -500000000) == True\n assert candidate(matrix = [[-10, -5, 0, 5, 10, 15], [1, 6, 11, 16, 21, 26], [2, 7, 12, 17, 22, 27], [3, 8, 13, 18, 23, 28], [4, 9, 14, 19, 24, 29], [5, 10, 15, 20, 25, 30]],target = 3) == True\n assert candidate(matrix = [[1]],target = 1) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -90) == True\n assert candidate(matrix = [[-1000000000, -500000000, -100000000, -50000000, -10000000], [-5000000, -2500000, -1000000, -500000, -100000], [-50000, -25000, -10000, -5000, -1000], [-500, -250, -100, -50, -10], [-5, -2, -1, -1, 0]],target = -2500) == False\n assert candidate(matrix = [[1, 10, 19, 28, 37, 46], [2, 11, 20, 29, 38, 47], [3, 12, 21, 30, 39, 48], [4, 13, 22, 31, 40, 49], [5, 14, 23, 32, 41, 50], [6, 15, 24, 33, 42, 51]],target = 100) == False\n assert candidate(matrix = [[-9, -8, -7, -6, -5, -4, -3, -2, -1, 0], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]],target = 7) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 22, 23, 24, 25]],target = 25) == True\n assert candidate(matrix = [[1, 10, 20, 30], [2, 11, 21, 31], [3, 12, 22, 32], [4, 13, 23, 33], [5, 14, 24, 34]],target = 15) == False\n assert candidate(matrix = [[1, 5, 9, 13, 17, 21, 25, 29, 33, 37], [2, 6, 10, 14, 18, 22, 26, 30, 34, 38], [3, 7, 11, 15, 19, 23, 27, 31, 35, 39], [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]],target = 38) == True\n assert candidate(matrix = [[1]],target = 0) == False\n assert candidate(matrix = [[1, 10, 20, 30, 40], [2, 12, 22, 32, 42], [3, 13, 23, 33, 43], [4, 14, 24, 34, 44], [5, 15, 25, 35, 45]],target = 28) == False\n assert candidate(matrix = [[-1, 0, 1], [0, 1, 2], [1, 2, 3]],target = 0) == True\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]],target = 2) == False\n assert candidate(matrix = [[10, 20, 30, 40, 50], [60, 70, 80, 90, 100], [110, 120, 130, 140, 150], [160, 170, 180, 190, 200], [210, 220, 230, 240, 250]],target = 155) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 31) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],target = 55) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 1) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 30) == True\n assert candidate(matrix = [[100, 101, 102, 103, 104, 105], [106, 107, 108, 109, 110, 111], [112, 113, 114, 115, 116, 117], [118, 119, 120, 121, 122, 123], [124, 125, 126, 127, 128, 129], [130, 131, 132, 133, 134, 135]],target = 122) == True\n", "comparison": "exact"}, "public_tests": ["[[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]]\n5", "[[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]]\n20"], "hints": [], "metadata": {"canonical_parameter_names": ["matrix", "target"], "leetcode_dataset_entry_point": "Solution().searchMatrix", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:43:08+00:00", "tests_total": 95, "tests_dropped": 3, "flags": ["has_images"], "topic_tags": ["array", "binary-search", "divide-and-conquer", "matrix"]}, "language": "cpp", "interface": {"raw_signature": "bool searchMatrix(vector>& matrix, int target) {", "container": "Solution", "callable": "searchMatrix", "parameters": [{"name": "matrix", "type": "vector>&"}, {"name": "target", "type": "int"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 241, "task_id": "different-ways-to-add-parentheses", "difficulty": "Medium", "problem_description": "Given a string expression of numbers and operators, return all possible results from computing all the different possible ways to group numbers and operators. You may return the answer in any order.\n\nThe test cases are generated such that the output values fit in a 32-bit integer and the number of different results does not exceed 10^4.\n\nExample 1:\n\nInput: expression = \"2-1-1\"\nOutput: [0,2]\nExplanation:\n((2-1)-1) = 0\n(2-(1-1)) = 2\n\nExample 2:\n\nInput: expression = \"2*3-4*5\"\nOutput: [-34,-14,-10,-10,10]\nExplanation:\n(2*(3-(4*5))) = -34\n((2*3)-(4*5)) = -14\n((2*(3-4))*5) = -10\n(2*((3-4)*5)) = -10\n(((2*3)-4)*5) = 10\n\nConstraints:\n\n- 1 <= expression.length <= 20\n- expression consists of digits and the operator '+', '-', and '*'.\n- All the integer values in the input expression are in the range [0, 99].\n- The integer values in the input expression do not have a leading '-' or '+' denoting the sign.\n", "canonical_tests": {"language": "python", "source": "def answers_match(result, expected):\n \"\"\"The answer may list its items in any order (only the top-level order is free).\"\"\"\n if isinstance(result, list) and isinstance(expected, list):\n return sorted(result, key=repr) == sorted(expected, key=repr)\n return result == expected\n\n\ndef check(candidate):\n assert answers_match(candidate(expression='4*5-2*3'), [-4, 36, 14, 36, 54])\n assert answers_match(candidate(expression='9-3*2+1'), [0, 2, 18, 4, 13])\n assert answers_match(candidate(expression='1+1+1+1'), [4, 4, 4, 4, 4])\n assert answers_match(candidate(expression='9*8+7*6-5*4+3*2-1'), [-1755, -2385, -1755, -2385, -3645, -999, -1125, -1755, -999, -2637, -3897, -1125, -3897, -2385, 513, 639, 513, 639, 891, -621, -495, 513, 639, -1755, -999, 513, -621, 513, -2763, -4023, -1251, -4023, -2511, 639, 891, -495, 639, -3645, -2133, 891, -1377, 891, 135, 45, 135, 45, -135, 243, 225, 135, 243, 9, -171, 225, -171, 45, 513, 639, 513, 639, 891, 2403, 3069, 2403, 3069, 4401, -783, -765, 351, 369, 297, 315, 351, 369, 1431, 1449, -1755, -999, 513, -621, 513, 135, 243, 513, 2403, -783, 351, 297, 351, 1431, -2709, -3969, -1197, -3969, -2457, 693, 945, -441, 693, -3591, -2079, 945, -1323, 945, -9, -189, 207, -189, 27, 693, 945, 3393, 4725, -765, 369, 315, 369, 1449, -3591, -2079, 945, -1323, 945, 189, 405, 945, 4725, -1647, 621, 513, 621, 2781, -3915, -5265, -3915, -5265, -7965, -2295, -2565, -3915, -2295, -5805, -8505, -2565, -8505, -5265, 945, 1215, 945, 1215, 1755, -1485, -1215, 945, 1215, -3915, -2295, 945, -1485, 945, -6075, -8775, -2835, -8775, -5535, 1215, 1755, -1215, 1215, -7965, -4725, 1755, -3105, 1755, 135, 45, 135, 45, -135, 243, 225, 135, 243, 9, -171, 225, -171, 45, 495, 405, 495, 405, 225, 603, 585, 495, 603, 369, 189, 585, 189, 405, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 5355, 6885, 5355, 6885, 9945, -783, -765, 351, 369, 297, 315, 351, 369, 1431, 1449, -1863, -1845, 567, 585, 297, 315, 657, 675, 567, 585, 1647, 1665, 567, 585, 1647, 1665, 3087, 3105, -1755, -999, 513, -621, 513, 135, 243, 513, 2403, -783, 351, 297, 351, 1431, -3915, -2295, 945, -1485, 945, 135, 243, 495, 603, 945, 2835, 945, 2835, 5355, -783, 351, 297, 351, 1431, -1863, 567, 297, 657, 567, 1647, 567, 1647, 3087, -2709, -3969, -1197, -3969, -2457, 693, 945, -441, 693, -3591, -2079, 945, -1323, 945, -9, -189, 207, -189, 27, 693, 945, 3393, 4725, -765, 369, 315, 369, 1449, -3591, -2079, 945, -1323, 945, 189, 405, 945, 4725, -1647, 621, 513, 621, 2781, -5949, -8649, -2709, -8649, -5409, 1341, 1881, -1089, 1341, -7839, -4599, 1881, -2979, 1881, -9, -189, 207, -189, 27, 351, 171, 567, 171, 387, 1341, 1881, 4041, 5661, 1341, 1881, 4041, 5661, 7641, 10701, -765, 369, 315, 369, 1449, -1845, 585, 315, 675, 585, 1665, 585, 1665, 3105, -3519, -2007, 1017, -1251, 1017, 261, 477, 1017, 4797, -1575, 693, 585, 693, 2853, -7839, -4599, 1881, -2979, 1881, 261, 477, 981, 1197, 1881, 5661, 1881, 5661, 10701, -1575, 693, 585, 693, 2853, -3735, 1125, 585, 1305, 1125, 3285, 1125, 3285, 6165, -131, -201, -131, -201, -341, -47, -61, -131, -47, -229, -369, -61, -369, -201, 121, 135, 121, 135, 163, -5, 9, 121, 135, -131, -47, 121, -5, 121, -243, -383, -75, -383, -215, 135, 163, 9, 135, -341, -173, 163, -89, 163, 79, 69, 79, 69, 49, 91, 89, 79, 91, 65, 45, 89, 45, 69, 121, 135, 121, 135, 163, 331, 405, 331, 405, 553, -23, -21, 103, 105, 97, 99, 103, 105, 223, 225, -131, -47, 121, -5, 121, 79, 91, 121, 331, -23, 103, 97, 103, 223, -237, -377, -69, -377, -209, 141, 169, 15, 141, -335, -167, 169, -83, 169, 63, 43, 87, 43, 67, 141, 169, 441, 589, -21, 105, 99, 105, 225, -335, -167, 169, -83, 169, 85, 109, 169, 589, -119, 133, 121, 133, 373, -3915, -5265, -3915, -5265, -7965, -2295, -2565, -3915, -2295, -5805, -8505, -2565, -8505, -5265, 945, 1215, 945, 1215, 1755, -1485, -1215, 945, 1215, -3915, -2295, 945, -1485, 945, -6075, -8775, -2835, -8775, -5535, 1215, 1755, -1215, 1215, -7965, -4725, 1755, -3105, 1755, -2291, -3081, -2291, -3081, -4661, -1343, -1501, -2291, -1343, -3397, -4977, -1501, -4977, -3081, 553, 711, 553, 711, 1027, -869, -711, 553, 711, -2291, -1343, 553, -869, 553, -3555, -5135, -1659, -5135, -3239, 711, 1027, -711, 711, -4661, -2765, 1027, -1817, 1027, 415, 405, 415, 405, 385, 427, 425, 415, 427, 401, 381, 425, 381, 405, 775, 765, 775, 765, 745, 787, 785, 775, 787, 761, 741, 785, 741, 765, 79, 69, 79, 69, 49, 91, 89, 79, 91, 65, 45, 89, 45, 69, 775, 765, 775, 765, 745, 787, 785, 775, 787, 761, 741, 785, 741, 765, 439, 429, 439, 429, 409, 451, 449, 439, 451, 425, 405, 449, 405, 429, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 5355, 6885, 5355, 6885, 9945, 553, 711, 553, 711, 1027, 763, 981, 763, 981, 1417, 945, 1215, 945, 1215, 1755, 553, 711, 553, 711, 1027, 3115, 4005, 3115, 4005, 5785, 5635, 7245, 5635, 7245, 10465, 763, 981, 763, 981, 1417, 5635, 7245, 5635, 7245, 10465, 3283, 4221, 3283, 4221, 6097, -807, -805, 327, 329, 273, 275, 327, 329, 1407, 1409, -1887, -1885, 543, 545, 273, 275, 633, 635, 543, 545, 1623, 1625, 543, 545, 1623, 1625, 3063, 3065, -23, -21, 103, 105, 97, 99, 103, 105, 223, 225, -1887, -1885, 543, 545, -1103, -1101, 319, 321, 433, 435, 793, 795, 97, 99, 793, 795, 457, 459, 543, 545, 1623, 1625, 543, 545, 1623, 1625, 3063, 3065, 319, 321, 439, 441, 543, 545, 319, 321, 1783, 1785, 3223, 3225, 439, 441, 3223, 3225, 1879, 1881, -1755, -999, 513, -621, 513, 135, 243, 513, 2403, -783, 351, 297, 351, 1431, -3915, -2295, 945, -1485, 945, 135, 243, 495, 603, 945, 2835, 945, 2835, 5355, -783, 351, 297, 351, 1431, -1863, 567, 297, 657, 567, 1647, 567, 1647, 3087, -131, -47, 121, -5, 121, 79, 91, 121, 331, -23, 103, 97, 103, 223, -3915, -2295, 945, -1485, 945, -2291, -1343, 553, -869, 553, 415, 427, 775, 787, 79, 91, 775, 787, 439, 451, 945, 2835, 945, 2835, 5355, 553, 763, 945, 553, 3115, 5635, 763, 5635, 3283, -807, 327, 273, 327, 1407, -1887, 543, 273, 633, 543, 1623, 543, 1623, 3063, -23, 103, 97, 103, 223, -1887, 543, -1103, 319, 433, 793, 97, 793, 457, 543, 1623, 543, 1623, 3063, 319, 439, 543, 319, 1783, 3223, 439, 3223, 1879, -2701, -3961, -1189, -3961, -2449, 701, 953, -433, 701, -3583, -2071, 953, -1315, 953, -1, -181, 215, -181, 35, 701, 953, 3401, 4733, -757, 377, 323, 377, 1457, -3583, -2071, 953, -1315, 953, 197, 413, 953, 4733, -1639, 629, 521, 629, 2789, -5941, -8641, -2701, -8641, -5401, 1349, 1889, -1081, 1349, -7831, -4591, 1889, -2971, 1889, -1, -181, 215, -181, 35, 359, 179, 575, 179, 395, 1349, 1889, 4049, 5669, 1349, 1889, 4049, 5669, 7649, 10709, -757, 377, 323, 377, 1457, -1837, 593, 323, 683, 593, 1673, 593, 1673, 3113, -3511, -1999, 1025, -1243, 1025, 269, 485, 1025, 4805, -1567, 701, 593, 701, 2861, -7831, -4591, 1889, -2971, 1889, 269, 485, 989, 1205, 1889, 5669, 1889, 5669, 10709, -1567, 701, 593, 701, 2861, -3727, 1133, 593, 1313, 1133, 3293, 1133, 3293, 6173, -237, -377, -69, -377, -209, 141, 169, 15, 141, -335, -167, 169, -83, 169, 63, 43, 87, 43, 67, 141, 169, 441, 589, -21, 105, 99, 105, 225, -335, -167, 169, -83, 169, 85, 109, 169, 589, -119, 133, 121, 133, 373, -5941, -8641, -2701, -8641, -5401, 1349, 1889, -1081, 1349, -7831, -4591, 1889, -2971, 1889, -3477, -5057, -1581, -5057, -3161, 789, 1105, -633, 789, -4583, -2687, 1105, -1739, 1105, 399, 379, 423, 379, 403, 759, 739, 783, 739, 763, 63, 43, 87, 43, 67, 759, 739, 783, 739, 763, 423, 403, 447, 403, 427, 1349, 1889, 4049, 5669, 1349, 1889, 4049, 5669, 7649, 10709, 789, 1105, 1089, 1525, 1349, 1889, 789, 1105, 4449, 6229, 8049, 11269, 1089, 1525, 8049, 11269, 4689, 6565, -805, 329, 275, 329, 1409, -1885, 545, 275, 635, 545, 1625, 545, 1625, 3065, -21, 105, 99, 105, 225, -1885, 545, -1101, 321, 435, 795, 99, 795, 459, 545, 1625, 545, 1625, 3065, 321, 441, 545, 321, 1785, 3225, 441, 3225, 1881, -3511, -1999, 1025, -1243, 1025, 269, 485, 1025, 4805, -1567, 701, 593, 701, 2861, -7831, -4591, 1889, -2971, 1889, 269, 485, 989, 1205, 1889, 5669, 1889, 5669, 10709, -1567, 701, 593, 701, 2861, -3727, 1133, 593, 1313, 1133, 3293, 1133, 3293, 6173, -263, -95, 241, -11, 241, 157, 181, 241, 661, -47, 205, 193, 205, 445, -7831, -4591, 1889, -2971, 1889, -4583, -2687, 1105, -1739, 1105, 829, 853, 1549, 1573, 157, 181, 1549, 1573, 877, 901, 1889, 5669, 1889, 5669, 10709, 1105, 1525, 1889, 1105, 6229, 11269, 1525, 11269, 6565, -1615, 653, 545, 653, 2813, -3775, 1085, 545, 1265, 1085, 3245, 1085, 3245, 6125, -47, 205, 193, 205, 445, -3775, 1085, -2207, 637, 865, 1585, 193, 1585, 913, 1085, 3245, 1085, 3245, 6125, 637, 877, 1085, 637, 3565, 6445, 877, 6445, 3757])\n assert answers_match(candidate(expression='10+5-3*2'), [9, 14, 9, 24, 24])\n assert answers_match(candidate(expression='3+5*2'), [13, 16])\n assert answers_match(candidate(expression='2*3-4*5'), [-34, -10, -14, -10, 10])\n assert answers_match(candidate(expression='2*3+4*5'), [46, 70, 26, 70, 50])\n assert answers_match(candidate(expression='10+5-2*3'), [9, 19, 9, 39, 39])\n assert answers_match(candidate(expression='1+2*3'), [7, 9])\n assert answers_match(candidate(expression='4+2*3-5'), [0, 5, -12, 5, 13])\n assert answers_match(candidate(expression='1+2'), [3])\n assert answers_match(candidate(expression='2-1-1'), [2, 0])\n assert answers_match(candidate(expression='3-2*2+1'), [-3, -2, 3, 0, 3])\n assert answers_match(candidate(expression='1*2-3*4+5'), [-25, -15, -9, -5, 1, -25, -15, -9, -9, -5, 1, -5, 1, 1])\n assert answers_match(candidate(expression='8+2-1*3'), [7, 11, 7, 27, 27])\n assert answers_match(candidate(expression='100+200-50*2'), [200, 400, 200, 500, 500])\n assert answers_match(candidate(expression='3*4+2*5'), [42, 90, 22, 90, 70])\n assert answers_match(candidate(expression='1+2-3'), [0, 0])\n assert answers_match(candidate(expression='1+2*3-4'), [-1, 3, -3, 3, 5])\n assert answers_match(candidate(expression='3+2*2'), [7, 10])\n assert answers_match(candidate(expression='10+5-3*2+4'), [-3, 5, 22, 13, 18, -3, 5, 72, 72, 13, 18, 13, 28, 28])\n assert answers_match(candidate(expression='1*1*1*1'), [1, 1, 1, 1, 1])\n assert answers_match(candidate(expression='1*2-3+4*5'), [-21, -33, 19, -25, 15, -21, -33, 19, 19, -25, 15, -25, 15, 15])\n assert answers_match(candidate(expression='9*8-7+6-5*4'), [135, -27, 135, -216, -216, -117, 45, -225, -117, 0, 0, 72, -360, 72, 79, 61, 79, 40, 40, -5, 13, 51, 69, -65, 43, 39, -5, 51, 0, 0, 72, -360, 72, 256, 256, 40, 264, -200, 232, 216, 40, 264])\n assert answers_match(candidate(expression='1*2+3*4+5'), [29, 19, 45, 19, 25, 29, 19, 45, 45, 19, 25, 19, 25, 25])\n assert answers_match(candidate(expression='3+5*2-8'), [-27, 5, -48, 5, 8])\n assert answers_match(candidate(expression='1+2+3'), [6, 6])\n assert answers_match(candidate(expression='7*8-2+3'), [21, 63, 51, 45, 57])\n assert answers_match(candidate(expression='2+3*4-5+6'), [-19, 17, 3, 5, 15, -35, 25, 3, 9, 5, 15, 1, 15, 21])\n assert answers_match(candidate(expression='9+8-7*6+5-4*3+2-1'), [52, 52, 31, 73, 31, -53, -53, 17, -53, 87, 45, -53, 17, -53, 52, 52, 31, 73, 31, -179, -179, -179, -179, 17, -53, 17, -137, -137, 87, 45, -53, 17, -53, 87, 45, -221, -221, 17, -53, 17, -137, -137, -14, -14, -17, -11, -17, -29, -29, -19, -29, -9, -15, -29, -19, -29, -44, -44, -47, -41, -47, -14, -14, -17, -11, -17, -179, -179, -179, -179, -155, -155, -275, -275, -155, -155, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, 81, 39, -59, 11, -59, 81, 39, -227, -227, 11, -59, 11, -143, -143, -9, -15, -29, -19, -29, -39, -45, -9, -15, -227, -227, -197, -347, -197, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, 4, 4, 7, 1, 7, 19, 19, 9, 19, -1, 5, 19, 9, 19, 4, 4, 7, 1, 7, 37, 37, 37, 37, 9, 19, 9, 31, 31, -1, 5, 19, 9, 19, -1, 5, 43, 43, 9, 19, 9, 31, 31, -36, -36, -33, -39, -33, -21, -21, -31, -21, -41, -35, -21, -31, -21, 4, 4, 7, 1, 7, 19, 19, 9, 19, -1, 5, 19, 9, 19, -76, -76, -73, -79, -73, -46, -46, -43, -49, -43, 4, 4, 7, 1, 7, -36, -36, -33, -39, -33, 4, 4, 7, 1, 7, -155, -155, -155, -155, -131, -131, -251, -251, -131, -131, 37, 37, 37, 37, -123, -123, 37, 37, -283, -283, -163, -163, 37, 37, -123, -123, 37, 37, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 79, 37, -61, 9, -61, 79, 37, -229, -229, 9, -61, 9, -145, -145, -11, -17, -31, -21, -31, -41, -47, -11, -17, -229, -229, -199, -349, -199, 21, -49, 21, -133, -133, -21, -31, -51, -21, -133, -133, -115, -205, -115, -1, 5, 19, 9, 19, -1, 5, 43, 43, 9, 19, 9, 31, 31, -41, -35, -21, -31, -21, -1, 5, 19, 9, 19, -81, -75, -51, -45, -1, 5, -41, -35, -1, 5, -197, -197, -167, -317, -167, 43, 43, -157, 43, -357, -207, 43, -157, 43, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 52, 52, 31, 73, 31, -53, -53, 17, -53, 87, 45, -53, 17, -53, 52, 52, 31, 73, 31, -179, -179, -179, -179, 17, -53, 17, -137, -137, 87, 45, -53, 17, -53, 87, 45, -221, -221, 17, -53, 17, -137, -137, -14, -14, -17, -11, -17, -29, -29, -19, -29, -9, -15, -29, -19, -29, -44, -44, -47, -41, -47, -14, -14, -17, -11, -17, -179, -179, -179, -179, -155, -155, -275, -275, -155, -155, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, 81, 39, -59, 11, -59, 81, 39, -227, -227, 11, -59, 11, -143, -143, -9, -15, -29, -19, -29, -39, -45, -9, -15, -227, -227, -197, -347, -197, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, -50, -50, -20, -80, -20, 100, 100, 0, 100, -100, -40, 100, 0, 100, -50, -50, -20, -80, -20, 280, 280, 280, 280, 0, 100, 0, 220, 220, -100, -40, 100, 0, 100, -100, -40, 340, 340, 0, 100, 0, 220, 220, -50, -50, -20, -80, -20, 100, 100, 0, 100, -100, -40, 100, 0, 100, -50, -50, -20, -80, -20, 280, 280, 280, 280, 0, 100, 0, 220, 220, -100, -40, 100, 0, 100, -100, -40, 340, 340, 0, 100, 0, 220, 220, -36, -36, -33, -39, -33, -21, -21, -31, -21, -41, -35, -21, -31, -21, 4, 4, 7, 1, 7, 19, 19, 9, 19, -1, 5, 19, 9, 19, -36, -36, -33, -39, -33, -21, -21, -31, -21, -41, -35, -21, -31, -21, 49, 49, 52, 46, 52, 64, 64, 54, 64, 44, 50, 64, 54, 64, 49, 49, 52, 46, 52, 64, 64, 54, 64, 44, 50, 64, 54, 64, -76, -76, -73, -79, -73, -46, -46, -43, -49, -43, 4, 4, 7, 1, 7, -36, -36, -33, -39, -33, 4, 4, 7, 1, 7, -76, -76, -73, -79, -73, -46, -46, -43, -49, -43, 94, 94, 97, 91, 97, 94, 94, 97, 91, 97, -36, -36, -33, -39, -33, 4, 4, 7, 1, 7, -36, -36, -33, -39, -33, 49, 49, 52, 46, 52, 49, 49, 52, 46, 52, -128, -128, -128, -128, -104, -104, -224, -224, -104, -104, 64, 64, 64, 64, -96, -96, 64, 64, -256, -256, -136, -136, 64, 64, -96, -96, 64, 64, -128, -128, -128, -128, -104, -104, -224, -224, -104, -104, 280, 280, 280, 280, 280, 280, 280, 280, -96, -96, 64, 64, -96, -96, 244, 244, 244, 244, -256, -256, -136, -136, 64, 64, -96, -96, 64, 64, -256, -256, -136, -136, 424, 424, 424, 424, -96, -96, 64, 64, -96, -96, 244, 244, 244, 244, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, -9, 91, -9, 211, 211, -9, 91, -9, 211, 211, -31, -21, 9, 19, -31, -21, 54, 64, 54, 64, -71, -41, 9, -31, 9, -71, -41, 99, 99, -31, 9, -31, 54, 54, -95, -95, -77, -167, -77, 49, 49, -71, 49, -191, -101, 49, -71, 49, -95, -95, -77, -167, -77, 211, 211, 211, 211, -71, 49, -71, 184, 184, -191, -101, 49, -71, 49, -191, -101, 319, 319, -71, 49, -71, 184, 184, 79, 37, -61, 9, -61, 79, 37, -229, -229, 9, -61, 9, -145, -145, -11, -17, -31, -21, -31, -41, -47, -11, -17, -229, -229, -199, -349, -199, 21, -49, 21, -133, -133, -21, -31, -51, -21, -133, -133, -115, -205, -115, -1, 5, 19, 9, 19, -1, 5, 43, 43, 9, 19, 9, 31, 31, -41, -35, -21, -31, -21, -1, 5, 19, 9, 19, -81, -75, -51, -45, -1, 5, -41, -35, -1, 5, -197, -197, -167, -317, -167, 43, 43, -157, 43, -357, -207, 43, -157, 43, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 79, 37, -61, 9, -61, 79, 37, -229, -229, 9, -61, 9, -145, -145, -11, -17, -31, -21, -31, -41, -47, -11, -17, -229, -229, -199, -349, -199, 21, -49, 21, -133, -133, -21, -31, -51, -21, -133, -133, -115, -205, -115, -91, -31, 109, 9, 109, -91, -31, 349, 349, 9, 109, 9, 229, 229, -91, -31, 109, 9, 109, -91, -31, 349, 349, 9, 109, 9, 229, 229, -41, -35, -21, -31, -21, -1, 5, 19, 9, 19, -41, -35, -21, -31, -21, 44, 50, 64, 54, 64, 44, 50, 64, 54, 64, -81, -75, -51, -45, -1, 5, -41, -35, -1, 5, -81, -75, -51, -45, 89, 95, 89, 95, -41, -35, -1, 5, -41, -35, 44, 50, 44, 50, -161, -161, -131, -281, -131, 79, 79, -121, 79, -321, -171, 79, -121, 79, -161, -161, -131, -281, -131, 349, 349, 349, 349, -121, 79, -121, 304, 304, -321, -171, 79, -121, 79, -321, -171, 529, 529, -121, 79, -121, 304, 304, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, -9, 91, -9, 211, 211, -9, 91, -9, 211, 211, -31, -21, 9, 19, -31, -21, 54, 64, 54, 64, -71, -41, 9, -31, 9, -71, -41, 99, 99, -31, 9, -31, 54, 54, -95, -95, -77, -167, -77, 49, 49, -71, 49, -191, -101, 49, -71, 49, -95, -95, -77, -167, -77, 211, 211, 211, 211, -71, 49, -71, 184, 184, -191, -101, 49, -71, 49, -191, -101, 319, 319, -71, 49, -71, 184, 184])\n assert answers_match(candidate(expression='5*3+8-2*4+9*2'), [-165, -205, -75, -205, -115, 675, 795, 105, 225, -165, -75, 795, 105, 345, -165, -205, -75, -205, -115, 990, 1170, 990, 1170, 105, 225, 105, 270, 270, -150, -60, 810, 120, 360, -150, -60, 1170, 1170, 120, 360, 120, 450, 450, -21, -29, -3, -29, -11, 147, 171, 33, 57, -21, -3, 171, 33, 81, 11, 3, 29, 3, 21, -21, -29, -3, -29, -11, 990, 1170, 990, 1170, 462, 546, 1166, 1378, 462, 546, 33, 153, 33, 198, 198, 33, 57, 65, 33, 198, 198, 102, 230, 102, -150, -60, 810, 120, 360, -150, -60, 1170, 1170, 120, 360, 120, 450, 450, -6, 12, 186, 48, 96, 58, 76, -6, 12, 1170, 1170, 546, 1378, 546, 48, 288, 48, 378, 378, 48, 96, 112, 48, 378, 378, 186, 442, 186])\n assert answers_match(candidate(expression='9-8+7-6+5-4'), [1, 1, -1, 9, -1, 1, 1, -1, -1, 9, -1, 9, -1, -1, 1, 1, 3, -7, 3, -13, -13, 1, 1, 1, 1, 3, -11, 3, 1, -9, 1, -9, -9, -7, 3, -21, -7, 1, 1, 3, -11, 3])\n assert answers_match(candidate(expression='5+4+3+2+1+0'), [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15])\n assert answers_match(candidate(expression='5*6-7*8+9*10-11*12'), [38180, 3530, 1220, 3530, -33430, 72620, 7170, 1220, -1300, 450, -36510, 7170, -36510, -66750, 5240, 290, -40, 290, -4990, 72620, 7170, 39680, 3930, -2740, -5260, -40, -5260, -2560, 450, -36510, 7170, -36510, -66750, -2790, -8070, 7170, 3930, -40470, -70710, -8070, -70710, -38310, 5450, 500, 170, 500, -4780, 10370, 1020, 170, -190, 60, -5220, 1020, -5220, -9540, -5740, -790, -460, -790, 4490, -5530, -580, -250, -580, 4700, 68930, 6780, 35990, 3540, 10370, 1020, 25010, 2460, -610, -60, -4060, -6580, -1360, -6580, -3880, -1150, -1510, -460, -250, -6310, -3610, -1510, -2710, -610, 780, -36180, 7500, -36180, -66420, -2460, -7740, 7500, 4260, -40140, -70380, -7740, -70380, -37980, 60, -5220, 1020, -5220, -9540, -3540, 1740, -1020, 4260, 6780, 3540, 1020, 2460, -60, -41460, -71700, -9060, -71700, -39300, -6540, -10860, 1740, 4260, -68460, -36060, -10860, -25260, -60, 7660, 730, 268, 730, -6662, 14548, 1458, 268, -236, 114, -7278, 1458, -7278, -13326, 1072, 82, 16, 82, -974, 14548, 1458, 7960, 810, -524, -1028, 16, -1028, -488, 114, -7278, 1458, -7278, -13326, -534, -1590, 1458, 810, -8070, -14118, -1590, -14118, -7638, 5450, 500, 170, 500, -4780, 10370, 1020, 170, -190, 60, -5220, 1020, -5220, -9540, -25070, -2300, -782, -2300, 21988, -47702, -4692, -782, 874, -276, 24012, -4692, 24012, 43884, -1348, -358, -292, -358, 698, -1138, -148, -82, -148, 908, -1124, -134, -68, -134, 922, -1138, -148, -82, -148, 908, -914, 76, 142, 76, 1132, 68930, 6780, 35990, 3540, 10370, 1020, 25010, 2460, -610, -60, 10858, 1068, 4270, 420, 10370, 1020, -47702, -4692, 29402, 2892, 3782, 372, 2074, 204, 3782, 372, -23546, -2316, -3532, -6052, -832, -6052, -3352, -622, -982, 68, 278, -5782, -3082, -982, -2182, -82, -788, -1292, -248, -1292, -752, -622, -982, 2122, 3778, -292, -82, -68, -82, 142, -5782, -3082, -982, -2182, -82, -1022, -482, -982, 3778, -2542, -442, -302, -442, 1798, 780, -36180, 7500, -36180, -66420, -2460, -7740, 7500, 4260, -40140, -70380, -7740, -70380, -37980, 60, -5220, 1020, -5220, -9540, -3540, 1740, -1020, 4260, 6780, 3540, 1020, 2460, -60, -41460, -71700, -9060, -71700, -39300, -6540, -10860, 1740, 4260, -68460, -36060, -10860, -25260, -60, 444, -6948, 1788, -6948, -12996, -204, -1260, 1788, 1140, -7740, -13788, -1260, -13788, -7308, 60, -5220, 1020, -5220, -9540, -276, 24012, -4692, 24012, 43884, -3108, -2052, -588, 468, -420, 636, -588, 468, 2100, 3156, 6780, 3540, 1020, 2460, -60, 1068, 420, 1020, -4692, 2892, 372, 204, 372, -2316, -40932, -71172, -8532, -71172, -38772, -6012, -10332, 2268, 4788, -67932, -35532, -10332, -24732, 468, -8004, -14052, -1524, -14052, -7572, -6012, -10332, 26916, 46788, -2052, 468, 636, 468, 3156, -67932, -35532, -10332, -24732, 468, -10812, -4332, -10332, 46788, -29052, -3852, -2172, -3852, 23028])\n assert answers_match(candidate(expression='10+5*2-3*2+1'), [-25, -15, -5, -5, 5, 11, 13, -5, 31, -9, 1, 15, 1, 25, -105, -75, -45, -45, -15, 11, 13, 21, 23, 15, 51, -45, 51, 81, -9, 1, 15, 1, 25, -59, -29, 15, 25, 11, 35, -29, 35, 55])\n assert answers_match(candidate(expression='99-9*9+8*8-7*7+6*6'), [21114, 38754, 5562, 38754, 23202, -3078, -5598, 378, -3078, 35874, 20322, -5598, 15138, -5598, 2151, 4356, 207, 4356, 2412, -3078, -5598, -22041, -39996, 2646, -810, -441, -810, -3897, 35874, 20322, -5598, 15138, -5598, 1476, -468, -5598, -39996, 17406, -3330, -1116, -3330, -21852, 44928, 82413, 11880, 82413, 49365, -6480, -11835, 864, -6480, 76293, 43245, -11835, 32229, -11835, 2151, 4356, 207, 4356, 2412, 1584, 3789, -360, 3789, 1845, -6480, -11835, -25443, -46233, -6480, -11835, -25443, -46233, -49824, -90459, 2646, -810, -441, -810, -3897, 6048, -1296, -441, -1008, -1296, -4383, -1296, -4383, -8352, 35469, 19917, -6003, 14733, -6003, 1071, -873, -6003, -40401, 17001, -3735, -1521, -3735, -22257, 76293, 43245, -11835, 32229, -11835, 1071, -873, -2331, -4275, -11835, -46233, -11835, -46233, -90459, 17001, -3735, -1521, -3735, -22257, 37413, -6651, -1521, -4923, -6651, -25173, -6651, -25173, -48987, 2362, 4322, 634, 4322, 2594, -326, -606, 58, -326, 4002, 2274, -606, 1698, -606, 255, 500, 39, 500, 284, -326, -606, -2433, -4428, 310, -74, -33, -74, -417, 4002, 2274, -606, 1698, -606, 180, -36, -606, -4428, 1950, -354, -108, -354, -2412, 44928, 82413, 11880, 82413, 49365, -6480, -11835, 864, -6480, 76293, 43245, -11835, 32229, -11835, 26176, 47981, 6952, 47981, 28757, -3728, -6843, 544, -3728, 44421, 25197, -6843, 18789, -6843, -257, -12, -473, -12, -228, -824, -579, -1040, -579, -795, 255, 500, 39, 500, 284, -824, -579, -1040, -579, -795, -312, -67, -528, -67, -283, -6480, -11835, -25443, -46233, -6480, -11835, -25443, -46233, -49824, -90459, -3728, -6843, -5835, -10665, -6480, -11835, -3728, -6843, -27851, -50601, -52232, -94827, -5835, -10665, -52232, -94827, -30216, -54891, 2934, -522, -153, -522, -3609, 6336, -1008, -153, -720, -1008, -4095, -1008, -4095, -8064, 310, -74, -33, -74, -417, 6336, -1008, 3712, -560, -545, -1112, -33, -1112, -600, -1008, -4095, -1008, -4095, -8064, -560, -903, -1008, -560, -4487, -8456, -903, -8456, -4872, 35469, 19917, -6003, 14733, -6003, 1071, -873, -6003, -40401, 17001, -3735, -1521, -3735, -22257, 76293, 43245, -11835, 32229, -11835, 1071, -873, -2331, -4275, -11835, -46233, -11835, -46233, -90459, 17001, -3735, -1521, -3735, -22257, 37413, -6651, -1521, -4923, -6651, -25173, -6651, -25173, -48987, 3597, 1869, -1011, 1293, -1011, -225, -441, -1011, -4833, 1545, -759, -513, -759, -2817, 76293, 43245, -11835, 32229, -11835, 44421, 25197, -6843, 18789, -6843, -3297, -3513, -6699, -6915, -225, -441, -6699, -6915, -3627, -3843, -11835, -46233, -11835, -46233, -90459, -6843, -10665, -11835, -6843, -50601, -94827, -10665, -94827, -54891, 17289, -3447, -1233, -3447, -21969, 37701, -6363, -1233, -4635, -6363, -24885, -6363, -24885, -48699, 1545, -759, -513, -759, -2817, 37701, -6363, 21957, -3675, -3585, -6987, -513, -6987, -3915, -6363, -24885, -6363, -24885, -48699, -3675, -5733, -6363, -3675, -27237, -51051, -5733, -51051, -29547, -210150, -386550, -54630, -386550, -231030, 31770, 56970, -2790, 31770, -357750, -202230, 56970, -150390, 56970, -20520, -42570, -1080, -42570, -23130, 31770, 56970, 221400, 400950, -25470, 9090, 5400, 9090, 39960, -357750, -202230, 56970, -150390, 56970, -13770, 5670, 56970, 400950, -173070, 34290, 12150, 34290, 219510, -448290, -823140, -117810, -823140, -492660, 65790, 119340, -7650, 65790, -761940, -431460, 119340, -321300, 119340, -20520, -42570, -1080, -42570, -23130, -14850, -36900, 4590, -36900, -17460, 65790, 119340, 255420, 463320, 65790, 119340, 255420, 463320, 499230, 905580, -25470, 9090, 5400, 9090, 39960, -59490, 13950, 5400, 11070, 13950, 44820, 13950, 44820, 84510, -353700, -198180, 61020, -146340, 61020, -9720, 9720, 61020, 405000, -169020, 38340, 16200, 38340, 223560, -761940, -431460, 119340, -321300, 119340, -9720, 9720, 24300, 43740, 119340, 463320, 119340, 463320, 905580, -169020, 38340, 16200, 38340, 223560, -373140, 67500, 16200, 50220, 67500, 252720, 67500, 252720, 490860, -2326, -4286, -598, -4286, -2558, 362, 642, -22, 362, -3966, -2238, 642, -1662, 642, -219, -464, -3, -464, -248, 362, 642, 2469, 4464, -274, 110, 69, 110, 453, -3966, -2238, 642, -1662, 642, -144, 72, 642, 4464, -1914, 390, 144, 390, 2448, -1534, -3494, 194, -3494, -1766, 1154, 1434, 770, 1154, -3174, -1446, 1434, -870, 1434, 573, 328, 789, 328, 544, 1154, 1434, 3261, 5256, 518, 902, 861, 902, 1245, -3174, -1446, 1434, -870, 1434, 648, 864, 1434, 5256, -1122, 1182, 936, 1182, 3240, 15822, 29052, 4158, 29052, 17388, -2322, -4212, 270, -2322, 26892, 15228, -4212, 11340, -4212, -2930, -5380, -770, -5380, -3220, 430, 780, -50, 430, -4980, -2820, 780, -2100, 780, -448290, -823140, -117810, -823140, -492660, 65790, 119340, -7650, 65790, -761940, -431460, 119340, -321300, 119340, -7618, -13988, -2002, -13988, -8372, 1118, 2028, -130, 1118, -12948, -7332, 2028, -5460, 2028, -239674, -440084, -62986, -440084, -263396, 35174, 63804, -4090, 35174, -407364, -230676, 63804, -171780, 63804, -859, -1104, -643, -1104, -888, -1426, -1671, -1210, -1671, -1455, -347, -592, -131, -592, -376, -1426, -1671, -1210, -1671, -1455, -914, -1159, -698, -1159, -943, 6269, 6024, 6485, 6024, 6240, 11939, 11694, 12155, 11694, 11910, -219, -464, -3, -464, -248, 573, 328, 789, 328, 544, -733, -978, -517, -978, -762, -221, -466, -5, -466, -250, 11939, 11694, 12155, 11694, 11910, -93, -338, 123, -338, -122, 6243, 5998, 6459, 5998, 6214, -2322, -4212, -21285, -38610, -2322, -4212, -21285, -38610, -45666, -82836, 430, 780, -1677, -3042, -2322, -4212, 430, 780, -23693, -42978, -48074, -87204, -1677, -3042, -48074, -87204, -26058, -47268, 65790, 119340, 255420, 463320, 65790, 119340, 255420, 463320, 499230, 905580, 1118, 2028, 3225, 5850, 35174, 63804, 37281, 67626, -2322, -4212, 430, 780, 65790, 119340, 1118, 2028, 35174, 63804, -24295, -44070, -48676, -88296, -2279, -4134, -48676, -88296, -26660, -48360, 282209, 511914, 526019, 954174, 3225, 5850, 37281, 67626, -18877, -34242, 3139, 5694, 526019, 954174, 8643, 15678, 281091, 509886, 3006, -450, -81, -450, -3537, 6408, -936, -81, -648, -936, -4023, -936, -4023, -7992, 382, -2, 39, -2, -345, 6408, -936, 3784, -488, -473, -1040, 39, -1040, -528, -936, -4023, -936, -4023, -7992, -488, -831, -936, -488, -4415, -8384, -831, -8384, -4800, -28674, 5886, 2196, 5886, 36756, -62694, 10746, 2196, 7866, 10746, 41616, 10746, 41616, 81306, -274, 110, 69, 110, 453, 518, 902, 861, 902, 1245, 2250, -342, -374, 106, -62694, 10746, -1030, 218, -33502, 5762, -571, -1138, -59, -1138, -626, 6557, 12227, 69, 861, -445, 67, 12227, 195, 6531, -342, -3429, -342, -3429, -7398, 106, -237, -342, 106, -3821, -7790, -237, -7790, -4206, 10746, 41616, 10746, 41616, 81306, 218, 561, 5762, 6105, -342, 106, 10746, 218, 5762, -3919, -7888, -335, -7888, -4304, 45977, 85667, 561, 6105, -3037, 547, 85667, 1443, 45795, 35964, 20412, -5508, 15228, -5508, 1566, -378, -5508, -39906, 17496, -3240, -1026, -3240, -21762, 76788, 43740, -11340, 32724, -11340, 1566, -378, -1836, -3780, -11340, -45738, -11340, -45738, -89964, 17496, -3240, -1026, -3240, -21762, 37908, -6156, -1026, -4428, -6156, -24678, -6156, -24678, -48492, 4092, 2364, -516, 1788, -516, 270, 54, -516, -4338, 2040, -264, -18, -264, -2322, 76788, 43740, -11340, 32724, -11340, 44916, 25692, -6348, 19284, -6348, -2802, -3018, -6204, -6420, 270, 54, -6204, -6420, -3132, -3348, -11340, -45738, -11340, -45738, -89964, -6348, -10170, -11340, -6348, -50106, -94332, -10170, -94332, -54396, 17784, -2952, -738, -2952, -21474, 38196, -5868, -738, -4140, -5868, -24390, -5868, -24390, -48204, 2040, -264, -18, -264, -2322, 38196, -5868, 22452, -3180, -3090, -6492, -18, -6492, -3420, -5868, -24390, -5868, -24390, -48204, -3180, -5238, -5868, -3180, -26742, -50556, -5238, -50556, -29052, -353700, -198180, 61020, -146340, 61020, -9720, 9720, 61020, 405000, -169020, 38340, 16200, 38340, 223560, -761940, -431460, 119340, -321300, 119340, -9720, 9720, 24300, 43740, 119340, 463320, 119340, 463320, 905580, -169020, 38340, 16200, 38340, 223560, -373140, 67500, 16200, 50220, 67500, 252720, 67500, 252720, 490860, -3876, -2148, 732, -1572, 732, -54, 162, 732, 4554, -1824, 480, 234, 480, 2538, 876, 2604, 5484, 3180, 5484, 4698, 4914, 5484, 9306, 2928, 5232, 4986, 5232, 7290, 26892, 15228, -4212, 11340, -4212, -4980, -2820, 780, -2100, 780, -761940, -431460, 119340, -321300, 119340, -12948, -7332, 2028, -5460, 2028, -407364, -230676, 63804, -171780, 63804, -3894, -3678, -7296, -7080, -822, -606, -7296, -7080, -4224, -4008, 38874, 39090, 72894, 73110, -54, 162, 4698, 4914, -3138, -2922, -66, 150, 72894, 73110, 702, 918, 38718, 38934, -4212, -38610, -4212, -38610, -82836, 780, -3042, -4212, 780, -42978, -87204, -3042, -87204, -47268, 119340, 463320, 119340, 463320, 905580, 2028, 5850, 63804, 67626, -4212, 780, 119340, 2028, 63804, -44070, -88296, -4134, -88296, -48360, 511914, 954174, 5850, 67626, -34242, 5694, 954174, 15678, 509886, 17856, -2880, -666, -2880, -21402, 38268, -5796, -666, -4068, -5796, -24318, -5796, -24318, -48132, 2112, -192, 54, -192, -2250, 38268, -5796, 22524, -3108, -3018, -6420, 54, -6420, -3348, -5796, -24318, -5796, -24318, -48132, -3108, -5166, -5796, -3108, -26670, -50484, -5166, -50484, -28980, -172224, 35136, 12996, 35136, 220356, -376344, 64296, 12996, 47016, 64296, 249516, 64296, 249516, 487656, -1824, 480, 234, 480, 2538, 2928, 5232, 4986, 5232, 7290, 13320, -2232, -2424, 456, -376344, 64296, -6360, 1128, -201192, 34392, -3606, -7008, -534, -7008, -3936, 39162, 73182, 234, 4986, -2850, 222, 73182, 990, 39006, -2232, -20754, -2232, -20754, -44568, 456, -1602, -2232, 456, -23106, -46920, -1602, -46920, -25416, 64296, 249516, 64296, 249516, 487656, 1128, 3186, 34392, 36450, -2232, 456, 64296, 1128, 34392, -23694, -47508, -2190, -47508, -26004, 275682, 513822, 3186, 36450, -18402, 3102, 513822, 8478, 274590])\n assert answers_match(candidate(expression='3*5-2*3+4'), [-27, -15, 63, 9, 39, 1, 5, 63, 91, 1, 31, 13, 31, 43])\n assert answers_match(candidate(expression='10+5*2-3*4'), [-40, -10, 8, -10, 38, -150, -60, 8, 18, 20, 68, -60, 68, 108])\n assert answers_match(candidate(expression='1+2+3+4+5+6'), [21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21])\n assert answers_match(candidate(expression='8*9-7+6*5-4'), [-32, -192, -32, -192, -416, 64, 224, -32, 64, -256, -480, 224, -192, 288, 59, 39, 59, 39, 11, 22, 42, 71, 91, -32, 64, 59, 22, 71, -228, -452, 252, -164, 316, 31, 3, 42, 91, -164, 316, 291, 106, 351])\n assert answers_match(candidate(expression='8*3+2*4-1+9'), [-72, 216, 8, 144, 152, -240, 480, 8, 80, 144, 152, 192, 152, 224, 12, 48, 22, 39, 40, -240, 480, -156, 312, 78, 150, 22, 150, 94, 81, 89, 129, 89, 161, 39, 40, 129, 87, 96, 168, 40, 168, 112])\n assert answers_match(candidate(expression='3*2+2-1*2+1'), [3, 3, 15, 9, 15, 3, 3, 27, 27, 9, 15, 9, 21, 21, 5, 5, 9, 7, 9, 9, 9, 5, 5, 27, 27, 21, 33, 21, 7, 13, 7, 19, 19, 7, 9, 11, 7, 19, 19, 15, 23, 15])\n assert answers_match(candidate(expression='9*2+10-3*4+5-1+8'), [108, -324, 108, -324, -324, 36, -108, -54, 36, -180, -180, -108, -198, -108, 18, 1026, 18, 1026, 1026, -36, 108, 234, 378, -216, -126, 504, -36, 234, -36, -36, 36, -54, 36, 594, 594, 108, 378, -72, 18, 648, 108, 378, 108, -324, 108, -324, -324, 36, -108, -54, 36, -180, -180, -108, -198, -108, 0, 1296, 0, 1296, 1296, 0, 1296, 0, 1296, 1296, -36, 108, 234, 378, -36, 108, 288, 432, 288, 432, -216, -126, 504, -36, 234, -216, -126, 648, 648, -36, 234, -36, 288, 288, -36, -36, 36, -54, 36, 594, 594, 108, 378, -72, 18, 648, 108, 378, -36, -36, 36, -54, 36, 720, 720, 720, 720, 108, 378, 108, 432, 432, -72, 18, 648, 108, 378, -72, 18, 792, 792, 108, 378, 108, 432, 432, 28, -20, 28, -20, -20, 20, 4, 10, 20, -4, -4, 4, -6, 4, 18, 130, 18, 130, 130, 12, 28, 42, 58, -8, 2, 72, 12, 42, 12, 12, 20, 10, 20, 82, 82, 28, 58, 8, 18, 88, 28, 58, 108, 60, 108, 60, 60, 100, 84, 90, 100, 76, 76, 84, 74, 84, 28, -20, 28, -20, -20, 20, 4, 10, 20, -4, -4, 4, -6, 4, 0, 1296, 0, 1296, 1296, 0, 1296, 0, 1296, 1296, 0, 400, 0, 400, 400, 0, 1680, 0, 1680, 1680, 0, 400, 0, 400, 400, -4, 12, 266, 282, -4, 12, 320, 336, 320, 336, 12, 28, 42, 58, 92, 108, 12, 28, 320, 336, 320, 336, 96, 112, 416, 432, 96, 112, -144, -54, 576, 36, 306, -144, -54, 720, 720, 36, 306, 36, 360, 360, -8, 2, 72, 12, 42, 72, 82, -8, 2, 720, 720, 216, 936, 216, -4, 266, -4, 320, 320, 12, 42, 92, 12, 320, 320, 96, 416, 96, -100, -100, -28, -118, -28, 530, 530, 44, 314, -136, -46, 584, 44, 314, -100, -100, -28, -118, -28, 656, 656, 656, 656, 44, 314, 44, 368, 368, -136, -46, 584, 44, 314, -136, -46, 728, 728, 44, 314, 44, 368, 368, 12, 12, 20, 10, 20, 82, 82, 28, 58, 8, 18, 88, 28, 58, 92, 92, 100, 90, 100, 12, 12, 20, 10, 20, 656, 656, 656, 656, 208, 208, 848, 848, 208, 208, 12, 282, 12, 336, 336, 28, 58, 108, 28, 336, 336, 112, 432, 112, -128, -38, 592, 52, 322, -128, -38, 736, 736, 52, 322, 52, 376, 376, 8, 18, 88, 28, 58, 88, 98, 8, 18, 736, 736, 232, 952, 232, 12, 282, 12, 336, 336, 28, 58, 108, 28, 336, 336, 112, 432, 112])\n assert answers_match(candidate(expression='3+2*2+1-5*3+4'), [-61, -29, -49, -13, -9, -61, -29, -25, -25, -13, -9, -13, -1, -1, -27, -11, -21, -3, -1, -26, -10, -27, -11, -25, -25, 3, 10, 3, -17, -13, -17, -5, -5, -3, -1, -2, -3, -5, -5, 7, 10, 7, -160, -80, -130, -40, -30, -160, -80, -70, -70, -40, -30, -40, -10, -10, -27, -11, -21, -3, -1, -24, -8, -18, 0, 2, -26, -10, -27, -11, -20, -4, -27, -11, -24, -8, -7, -7, 21, 28, 21, -70, -70, 21, 42, 28, 21, 70, 21, 42, -17, -13, -17, -5, -5, -3, -1, -2, -3, -5, -5, 7, 10, 7, -56, -46, -56, -26, -26, -3, -1, 0, 2, -2, -3, 4, -3, 0, 1, 1, 13, 16, 13, -26, -26, 13, 22, 16, 13, 34, 13, 22])\n assert answers_match(candidate(expression='3*3-2*2+1*1-0*0+1'), [-9, -3, -9, -15, -9, -9, -3, -9, -9, -15, -9, -15, -9, -9, -9, 9, -9, -27, -9, -9, -3, -9, -3, -9, -9, -9, -9, -9, -15, -9, -15, -9, -9, -15, 3, -15, -15, 3, 3, 3, 3, 3, -6, -3, -6, -9, -6, -6, -3, -6, -6, -9, -6, -9, -6, -6, -9, 9, -9, -27, -9, -6, 9, -6, -21, -6, -9, -6, -9, -6, -6, -3, -9, -6, -6, -3, -9, -9, -9, -9, -9, -6, -6, -9, -6, -9, -9, -6, -9, -6, -12, -6, -12, -6, -6, -12, 6, -12, -12, 6, 6, 6, 6, 6, -9, -6, -9, -6, -6, -12, 6, -9, 6, -12, -12, -9, -12, -9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 9, 12, 9, 9, 6, 9, 9, 12, 9, 12, 9, 9, 9, 0, 9, 18, 9, 9, 6, 9, 6, 9, 9, 9, 9, 9, 12, 9, 12, 9, 9, 12, 3, 12, 12, 3, 3, 3, 3, 3, 0, -3, 0, 3, 0, 0, -3, 0, 0, 3, 0, 3, 0, 0, 9, 6, 9, 12, 9, 9, 6, 9, 9, 12, 9, 12, 9, 9, -9, 0, -9, -18, -9, -6, 0, -6, -12, -6, 9, 0, 9, 18, 9, 0, 0, 0, 0, 0, 9, 0, 9, 18, 9, -9, -12, -9, -12, -6, -9, -9, -12, -6, -9, 9, 6, 9, 6, 0, -3, 9, 6, -9, -12, -6, -9, 9, 6, 0, -3, 9, 6, -9, -9, -9, -9, -9, -6, -6, -9, -6, -9, -9, -6, -9, -6, 9, 9, 9, 9, 9, 0, 0, 9, 9, -9, -6, 9, 0, 9, -9, -9, -6, -9, -6, 9, 9, 0, 9, -9, -6, 9, 0, 9, -6, 0, -6, 0, 0, -6, 12, -6, -6, 12, 12, 12, 12, 12, -3, 0, -3, 0, 0, -6, 12, -3, 12, -6, -6, -3, -6, -3, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 9, 12, 9, 9, 12, 3, 12, 12, 3, 3, 3, 3, 3, 3, 0, 3, 0, 0, 12, 9, 12, 9, 9, -6, 3, -3, 3, 12, 3, 3, 3, 12, 3, -6, -6, -3, -6, -3, 12, 12, 3, 12, -6, -3, 12, 3, 12, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 1, 3, 3, 5, 3, 3, 1, 3, 1, 3, 3, 3, 9, 3, -3, 3, 3, 5, 3, 5, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 1, 7, 1, 1, 7, 7, 7, 7, 7, 4, 5, 4, 3, 4, 4, 5, 4, 4, 3, 4, 3, 4, 4, 3, 9, 3, -3, 3, 4, 9, 4, -1, 4, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 3, 3, 3, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 2, 4, 2, 4, 4, 2, 8, 2, 2, 8, 8, 8, 8, 8, 3, 4, 3, 4, 4, 2, 8, 3, 8, 2, 2, 3, 2, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 6, 9, 12, 9, 9, 6, 9, 9, 12, 9, 12, 9, 9, 9, 0, 9, 18, 9, 9, 6, 9, 6, 9, 9, 9, 9, 9, 12, 9, 12, 9, 9, 12, 3, 12, 12, 3, 3, 3, 3, 3, 21, 14, 21, 28, 21, 21, 14, 21, 21, 28, 21, 28, 21, 21, 21, 0, 21, 42, 21, 21, 14, 21, 14, 21, 21, 21, 21, 21, 28, 21, 28, 21, 21, 28, 7, 28, 28, 7, 7, 7, 7, 7, -2, -3, -2, -1, -2, -2, -3, -2, -2, -1, -2, -1, -2, -2, 7, 6, 7, 8, 7, 7, 6, 7, 7, 8, 7, 8, 7, 7, 6, 5, 6, 7, 6, 6, 5, 6, 6, 7, 6, 7, 6, 6, 7, 6, 7, 8, 7, 7, 6, 7, 7, 8, 7, 8, 7, 7, 15, 14, 15, 16, 15, 15, 14, 15, 15, 16, 15, 16, 15, 15, -9, 0, -9, -18, -9, -6, 0, -6, -12, -6, 9, 0, 9, 18, 9, 0, 0, 0, 0, 0, 9, 0, 9, 18, 9, 3, 0, 3, 6, 3, 4, 0, 4, 8, 4, 9, 0, 9, 18, 9, 21, 0, 21, 42, 21, -2, 0, -2, -4, -2, 7, 0, 7, 14, 7, 6, 0, 6, 12, 6, 7, 0, 7, 14, 7, 15, 0, 15, 30, 15, -9, -10, -9, -10, -6, -7, -9, -10, -6, -7, 9, 8, 9, 8, 0, -1, 9, 8, -9, -10, -6, -7, 9, 8, 0, -1, 9, 8, 3, 2, 3, 2, 4, 3, 3, 2, 4, 3, 9, 8, 9, 8, 21, 20, 21, 20, -2, -3, 7, 6, 6, 5, 7, 6, 15, 14, -9, -10, -6, -7, 9, 8, 0, -1, 9, 8, 3, 2, 4, 3, 9, 8, 21, 20, -2, -3, 7, 6, 6, 5, 7, 6, 15, 14, -9, -9, -9, -9, -9, -6, -6, -9, -6, -9, -9, -6, -9, -6, 9, 9, 9, 9, 9, 0, 0, 9, 9, -9, -6, 9, 0, 9, -9, -9, -6, -9, -6, 9, 9, 0, 9, -9, -6, 9, 0, 9, 3, 3, 3, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 9, 9, 9, 9, 9, 21, 21, 21, 21, 21, -2, -2, 7, 7, 6, 6, 7, 7, 15, 15, -9, -6, 9, 0, 9, 3, 4, 9, 21, -2, 7, 6, 7, 15, -9, -9, -6, -9, -6, 9, 9, 0, 9, -9, -6, 9, 0, 9, 3, 3, 4, 3, 4, 9, 9, 21, 21, -2, 7, 6, 7, 15, -9, -6, 9, 0, 9, 3, 4, 9, 21, -2, 7, 6, 7, 15, -8, -2, -8, -2, -2, -8, 10, -8, -8, 10, 10, 10, 10, 10, -5, -2, -5, -2, -2, -8, 10, -5, 10, -8, -8, -5, -8, -5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 10, 7, 7, 10, 1, 10, 10, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 10, 7, 10, 7, 7, -8, 1, -5, 1, 10, 1, 1, 1, 10, 1, -8, -8, -5, -8, -5, 10, 10, 1, 10, -8, -5, 10, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 6, 4, 6, 6, 4, 10, 4, 4, 10, 10, 10, 10, 10, 5, 6, 5, 6, 6, 4, 10, 5, 10, 4, 4, 5, 4, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 10, 7, 7, 10, 1, 10, 10, 1, 1, 1, 1, 1, 22, 15, 22, 15, 15, 22, 1, 22, 22, 1, 1, 1, 1, 1, -1, -2, -1, -2, -2, 8, 7, 8, 7, 7, 7, 6, 7, 6, 6, 8, 7, 8, 7, 7, 16, 15, 16, 15, 15, -8, 1, -5, 1, 10, 1, 1, 1, 10, 1, 4, 1, 5, 1, 10, 1, 22, 1, -1, 1, 8, 1, 7, 1, 8, 1, 16, 1, -8, -8, -5, -8, -5, 10, 10, 1, 10, -8, -5, 10, 1, 10, 4, 4, 5, 4, 5, 10, 10, 22, 22, -1, 8, 7, 8, 16, -8, -5, 10, 1, 10, 4, 5, 10, 22, -1, 8, 7, 8, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n assert answers_match(candidate(expression='10*2-5*3+1'), [-180, -140, -120, -120, -80, 0, 4, -120, 60, -129, -89, 6, -89, 46])\n assert answers_match(candidate(expression='3*3*3-2*2*2+1*1*1'), [-81, -81, -81, -81, -81, -63, -63, -81, -63, -81, -81, -63, -81, -63, -81, -81, -81, -81, -81, -54, -54, -54, -54, -81, -63, -81, -54, -54, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, -36, -36, -36, -36, 45, 45, -9, -9, 45, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -9, -9, -9, -9, -3, -3, -9, -3, -9, -9, -3, -9, -3, -9, -9, -9, -9, -9, 0, 0, 0, 0, -9, -3, -9, 0, 0, -9, -9, -3, -9, -3, -9, -9, 0, 0, -9, -3, -9, 0, 0, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, 126, 126, 126, 126, 126, 105, 105, 126, 105, 126, 126, 105, 126, 105, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, 45, 45, 45, 45, 45, 54, 54, 54, 54, 54, 126, 126, 126, 126, 126, -42, -42, -42, -42, 39, 39, -15, -15, 39, 39, 6, 6, 6, 6, 39, 39, 87, 87, -15, -15, 39, 39, 33, 33, 39, 39, 87, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -9, -3, -9, -3, -9, -9, 0, 0, -9, -3, -9, 0, 0, 54, 54, 45, 54, 45, 126, 126, 105, 126, 105, -27, -27, 54, 54, 45, 45, 54, 54, 126, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -81, -81, -81, -81, -63, -63, -81, -63, -81, -81, -63, -81, -63, -81, -81, -81, -81, -81, -54, -54, -54, -54, -81, -63, -81, -54, -54, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, -36, -36, -36, -36, 45, 45, -9, -9, 45, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 15, 15, 15, 15, 17, 17, 15, 17, 15, 15, 17, 15, 17, 15, 15, 15, 15, 15, 18, 18, 18, 18, 15, 17, 15, 18, 18, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 15, 15, 15, 15, 15, 17, 17, 15, 17, 15, 15, 17, 15, 17, 15, 15, 15, 15, 15, 18, 18, 18, 18, 15, 17, 15, 18, 18, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, 126, 126, 126, 126, 126, 105, 105, 126, 105, 126, 126, 105, 126, 105, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, 150, 150, 150, 150, 150, 125, 125, 150, 125, 150, 150, 125, 150, 125, 150, 150, 150, 150, 150, 125, 125, 150, 125, 150, 150, 125, 150, 125, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, 45, 45, 45, 45, 45, 54, 54, 54, 54, 54, 126, 126, 126, 126, 126, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 54, 54, 54, 54, 54, 126, 126, 126, 126, 126, 54, 54, 54, 54, 54, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, -44, -44, -44, -44, 37, 37, -17, -17, 37, 37, 4, 4, 4, 4, 37, 37, 85, 85, -17, -17, 37, 37, 31, 31, 37, 37, 85, 85, -44, -44, -44, -44, 37, 37, -17, -17, 37, 37, 20, 20, 20, 20, 20, 20, 20, 20, 37, 37, 85, 85, 37, 37, 101, 101, 101, 101, -17, -17, 37, 37, 31, 31, 37, 37, 85, 85, -17, -17, 37, 37, 47, 47, 47, 47, 37, 37, 85, 85, 37, 37, 101, 101, 101, 101, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 17, 15, 18, 18, 15, 17, 15, 18, 18, 54, 45, 126, 105, 54, 45, 150, 125, 150, 125, -27, 54, 45, 54, 126, -27, 54, 69, 69, 54, 126, 54, 150, 150, -44, -44, 37, -17, 37, 4, 4, 37, 85, -17, 37, 31, 37, 85, -44, -44, 37, -17, 37, 20, 20, 20, 20, 37, 85, 37, 101, 101, -17, 37, 31, 37, 85, -17, 37, 47, 47, 37, 85, 37, 101, 101, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -9, -3, -9, -3, -9, -9, 0, 0, -9, -3, -9, 0, 0, 54, 54, 45, 54, 45, 126, 126, 105, 126, 105, -27, -27, 54, 54, 45, 45, 54, 54, 126, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 54, 54, 45, 54, 45, 126, 126, 105, 126, 105, 54, 54, 45, 54, 45, 150, 150, 125, 150, 125, 150, 150, 125, 150, 125, -27, -27, 54, 54, 45, 45, 54, 54, 126, 126, -27, -27, 54, 54, 69, 69, 69, 69, 54, 54, 126, 126, 54, 54, 150, 150, 150, 150, -44, -44, 37, -17, 37, 4, 4, 37, 85, -17, 37, 31, 37, 85, -44, -44, 37, -17, 37, 20, 20, 20, 20, 37, 85, 37, 101, 101, -17, 37, 31, 37, 85, -17, 37, 47, 47, 37, 85, 37, 101, 101, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 17, 15, 18, 18, 15, 17, 15, 18, 18, 54, 45, 126, 105, 54, 45, 150, 125, 150, 125, -27, 54, 45, 54, 126, -27, 54, 69, 69, 54, 126, 54, 150, 150, -44, -44, 37, -17, 37, 4, 4, 37, 85, -17, 37, 31, 37, 85, -44, -44, 37, -17, 37, 20, 20, 20, 20, 37, 85, 37, 101, 101, -17, 37, 31, 37, 85, -17, 37, 47, 47, 37, 85, 37, 101, 101])\n assert answers_match(candidate(expression='4+4+4+4+4+4+4+4+4+4'), [40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40])\n assert answers_match(candidate(expression='10-9-8-7-6-5-4-3-2-1'), [5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, 1, -1, 3, 1, 5, 5, 7, -3, -1, 3, 9, 1, 3, -5, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, 5, 7, 3, 5, 1, 15, 17, 13, 15, 11, 9, 7, 1, -1, 11, 9, 9, 7, 19, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 11, 15, 9, 11, 5, 7, 3, 17, 13, 9, 1, 11, 9, 19, 7, 13, 5, 7, -1, 15, 9, 7, 17, 13, 5, 15, 13, 23, -1, -3, 1, -1, 3, -5, -3, -1, -7, -3, 1, -5, -3, -9, 3, 5, 1, 3, -1, -1, -3, 7, 5, 1, -5, 3, 1, 9, -1, 3, -3, -1, -7, 5, 1, -1, 7, 3, -3, 5, 3, 11, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, -7, -5, -9, -7, -11, -3, -5, -7, -1, -5, -9, -3, -5, 1, 1, -1, 3, 1, 5, 11, 9, 13, 11, 15, -1, -3, 1, -1, 3, 1, -1, 3, 1, 5, -11, -13, -9, -11, -7, 5, 7, -3, -1, 7, 9, 5, 7, 15, 17, -5, -3, 3, 5, 5, 7, -7, -5, -3, -1, 7, 9, -5, -3, -3, -1, -15, -13, 3, 9, 1, 3, -5, 11, 5, 3, 13, 9, 1, 11, 9, 19, -1, -7, 1, -1, 7, 3, 9, -9, -3, 1, 11, -1, 1, -11, 3, -5, 5, 3, 13, -7, 1, 3, -9, -5, 5, -7, -5, -17, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 9, 13, 7, 9, 3, 5, 1, 15, 11, 7, -1, 9, 7, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, 5, 1, 7, 5, 11, -7, -11, -5, -7, -1, -1, 3, 9, 13, -3, 1, -1, 3, -13, -9, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -3, -9, -1, -3, 5, 1, 7, -11, -5, -1, 9, -3, -1, -13, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 13, 11, 15, 13, 17, 9, 11, 13, 7, 11, 15, 9, 11, 5, 17, 19, 15, 17, 13, 13, 11, 21, 19, 15, 9, 17, 15, 23, 13, 17, 11, 13, 7, 19, 15, 13, 21, 17, 11, 19, 17, 25, 7, 9, 5, 7, 3, 11, 9, 7, 13, 9, 5, 11, 9, 15, 13, 11, 15, 13, 17, 3, 1, 5, 3, 7, 9, 11, 17, 19, 7, 9, 9, 11, -1, 1, 13, 7, 15, 13, 21, 5, 11, 13, 3, 7, 15, 5, 7, -3, 11, 15, 9, 11, 5, 17, 13, 11, 19, 15, 9, 17, 15, 23, 7, 3, 9, 7, 13, 11, 15, 1, 5, 9, 17, 7, 9, -1, 11, 5, 13, 11, 19, 3, 9, 11, 1, 5, 13, 3, 5, -5, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, 1, -1, 3, 1, 5, 5, 7, -3, -1, 3, 9, 1, 3, -5, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 19, 21, 17, 19, 15, 23, 21, 19, 25, 21, 17, 23, 21, 27, 15, 13, 17, 15, 19, 19, 21, 11, 13, 17, 23, 15, 17, 9, 19, 15, 21, 19, 25, 13, 17, 19, 11, 15, 21, 13, 15, 7, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, -1, -3, 1, -1, 3, -5, -3, -1, -7, -3, 1, -5, -3, -9, 13, 11, 15, 13, 17, 9, 11, 13, 7, 11, 15, 9, 11, 5, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, 25, 23, 27, 25, 29, 21, 23, 25, 19, 23, 27, 21, 23, 17, 5, 7, 3, 5, 1, 15, 17, 13, 15, 11, 3, 5, 1, 3, -1, 5, 7, 3, 5, 1, -7, -5, -9, -7, -11, 17, 19, 15, 17, 13, 7, 9, 5, 7, 3, 5, 7, 3, 5, 1, 19, 21, 17, 19, 15, 15, 17, 13, 15, 11, 3, 5, 1, 3, -1, 17, 19, 15, 17, 13, 15, 17, 13, 15, 11, 29, 31, 27, 29, 25, 9, 7, 1, -1, 11, 9, 9, 7, 19, 17, -1, -3, 7, 5, 9, 7, -3, -5, 1, -1, 11, 9, -1, -3, 1, -1, -11, -13, 13, 11, 21, 19, 11, 9, 13, 11, 3, 1, 9, 7, 1, -1, 23, 21, 15, 13, 11, 9, -1, -3, 13, 11, 11, 9, 25, 23, 9, 7, 19, 17, 7, 5, 9, 7, -3, -5, 21, 19, 11, 9, 9, 7, 23, 21, 19, 17, 7, 5, 21, 19, 19, 17, 33, 31, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, 1, -5, 3, 1, 9, 5, 11, -7, -1, 3, 13, 1, 3, -9, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 15, 9, 17, 15, 23, 7, 13, 15, 5, 9, 17, 7, 9, -1, 5, 11, 3, 5, -3, 19, 25, 17, 19, 11, 13, 7, 1, -5, 15, 9, 13, 7, 27, 21, 5, 15, 3, 5, -7, 17, 7, 5, 19, 15, 3, 17, 15, 29, 11, 3, 13, 11, 21, 1, 9, 11, -1, 3, 13, 1, 3, -9, 15, 23, 13, 15, 5, 11, 3, 25, 17, 13, 1, 15, 13, 27, 11, 21, 9, 11, -1, 23, 13, 11, 25, 21, 9, 23, 21, 35, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 11, 15, 9, 11, 5, 7, 3, 17, 13, 9, 1, 11, 9, 19, 7, 13, 5, 7, -1, 15, 9, 7, 17, 13, 5, 15, 13, 23, -1, 3, -3, -1, -7, 5, 1, -1, 7, 3, -3, 5, 3, 11, 7, 3, 9, 7, 13, -5, -9, -3, -5, 1, 1, 5, 11, 15, -1, 3, 1, 5, -11, -7, 7, -1, 9, 7, 17, -3, 5, 7, -5, -1, 9, -3, -1, -13, 3, 9, 1, 3, -5, 11, 5, 3, 13, 9, 1, 11, 9, 19, -1, -7, 1, -1, 7, 3, 9, -9, -3, 1, 11, -1, 1, -11, 3, -5, 5, 3, 13, -7, 1, 3, -9, -5, 5, -7, -5, -17, 13, 17, 11, 13, 7, 19, 15, 13, 21, 17, 11, 19, 17, 25, 9, 5, 11, 9, 15, 13, 17, 3, 7, 11, 19, 9, 11, 1, 13, 7, 15, 13, 21, 5, 11, 13, 3, 7, 15, 5, 7, -3, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 21, 17, 23, 21, 27, 15, 19, 21, 13, 17, 23, 15, 17, 9, 11, 15, 9, 11, 5, -1, 3, -3, -1, -7, 13, 17, 11, 13, 7, 11, 15, 9, 11, 5, 25, 29, 23, 25, 19, 7, 3, 17, 13, 5, 1, 7, 3, -5, -9, 19, 15, 9, 5, 7, 3, 21, 17, 17, 13, 5, 1, 19, 15, 17, 13, 31, 27, 9, 1, 11, 9, 19, -1, 7, 9, -3, 1, 11, -1, 1, -11, 13, 21, 11, 13, 3, 9, 1, 23, 15, 11, -1, 13, 11, 25, 9, 19, 7, 9, -3, 21, 11, 9, 23, 19, 7, 21, 19, 33, 7, 13, 5, 7, -1, 15, 9, 7, 17, 13, 5, 15, 13, 23, 3, -3, 5, 3, 11, 7, 13, -5, 1, 5, 15, 3, 5, -7, 7, -1, 9, 7, 17, -3, 5, 7, -5, -1, 9, -3, -1, -13, 17, 11, 19, 17, 25, 9, 15, 17, 7, 11, 19, 9, 11, 1, 7, 13, 5, 7, -1, 21, 27, 19, 21, 13, 15, 9, 3, -3, 17, 11, 15, 9, 29, 23, 7, 17, 5, 7, -5, 19, 9, 7, 21, 17, 5, 19, 17, 31, 13, 5, 15, 13, 23, 3, 11, 13, 1, 5, 15, 3, 5, -7, 17, 25, 15, 17, 7, 13, 5, 27, 19, 15, 3, 17, 15, 29, 13, 23, 11, 13, 1, 25, 15, 13, 27, 23, 11, 25, 23, 37, -3, -5, -1, -3, 1, -7, -5, -3, -9, -5, -1, -7, -5, -11, 1, 3, -1, 1, -3, -3, -5, 5, 3, -1, -7, 1, -1, 7, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, -9, -7, -11, -9, -13, -5, -7, -9, -3, -7, -11, -5, -7, -1, -3, -5, -1, -3, 1, -13, -15, -11, -13, -9, -7, -5, 1, 3, -9, -7, -7, -5, -17, -15, -3, -9, -1, -3, 5, -11, -5, -3, -13, -9, -1, -11, -9, -19, -5, -1, -7, -5, -11, 1, -3, -5, 3, -1, -7, 1, -1, 7, -9, -13, -7, -9, -3, -5, -1, -15, -11, -7, 1, -9, -7, -17, -5, -11, -3, -5, 3, -13, -7, -5, -15, -11, -3, -13, -11, -21, 3, 5, 1, 3, -1, 7, 5, 3, 9, 5, 1, 7, 5, 11, -1, -3, 1, -1, 3, 3, 5, -5, -3, 1, 7, -1, 1, -7, 3, -1, 5, 3, 9, -3, 1, 3, -5, -1, 5, -3, -1, -9, -3, -5, -1, -3, 1, -7, -5, -3, -9, -5, -1, -7, -5, -11, 9, 7, 11, 9, 13, 5, 7, 9, 3, 7, 11, 5, 7, 1, 1, 3, -1, 1, -3, -9, -7, -11, -9, -13, 3, 5, 1, 3, -1, 1, 3, -1, 1, -3, 13, 15, 11, 13, 9, -3, -5, 5, 3, -5, -7, -3, -5, -13, -15, 7, 5, -1, -3, -3, -5, 9, 7, 5, 3, -5, -7, 7, 5, 5, 3, 17, 15, -1, -7, 1, -1, 7, -9, -3, -1, -11, -7, 1, -9, -7, -17, 3, 9, 1, 3, -5, -1, -7, 11, 5, 1, -9, 3, 1, 13, -1, 7, -3, -1, -11, 9, 1, -1, 11, 7, -3, 9, 7, 19, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, -7, -11, -5, -7, -1, -3, 1, -13, -9, -5, 3, -7, -5, -15, -3, -9, -1, -3, 5, -11, -5, -3, -13, -9, -1, -11, -9, -19, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, -3, 1, -5, -3, -9, 9, 13, 7, 9, 3, 3, -1, -7, -11, 5, 1, 3, -1, 15, 11, -3, 5, -5, -3, -13, 7, -1, -3, 9, 5, -5, 7, 5, 17, 1, -5, 3, 1, 9, -7, -1, 1, -9, -5, 3, -7, -5, -15, 5, 11, 3, 5, -3, 1, -5, 13, 7, 3, -7, 5, 3, 15, 1, 9, -1, 1, -9, 11, 3, 1, 13, 9, -1, 11, 9, 21, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, 1, -1, 3, 1, 5, 5, 7, -3, -1, 3, 9, 1, 3, -5, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, 5, 7, 3, 5, 1, 15, 17, 13, 15, 11, 9, 7, 1, -1, 11, 9, 9, 7, 19, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 11, 15, 9, 11, 5, 7, 3, 17, 13, 9, 1, 11, 9, 19, 7, 13, 5, 7, -1, 15, 9, 7, 17, 13, 5, 15, 13, 23, -11, -9, -13, -11, -15, -7, -9, -11, -5, -9, -13, -7, -9, -3, -15, -17, -13, -15, -11, -11, -9, -19, -17, -13, -7, -15, -13, -21, -11, -15, -9, -11, -5, -17, -13, -11, -19, -15, -9, -17, -15, -23, -5, -7, -3, -5, -1, -9, -7, -5, -11, -7, -3, -9, -7, -13, -11, -9, -13, -11, -15, -1, 1, -3, -1, -5, -7, -9, -15, -17, -5, -7, -7, -9, 3, 1, -11, -5, -13, -11, -19, -3, -9, -11, -1, -5, -13, -3, -5, 5, -9, -13, -7, -9, -3, -15, -11, -9, -17, -13, -7, -15, -13, -21, -5, -1, -7, -5, -11, -9, -13, 1, -3, -7, -15, -5, -7, 3, -9, -3, -11, -9, -17, -1, -7, -9, 1, -3, -11, -1, -3, 7, -1, -3, 1, -1, 3, -5, -3, -1, -7, -3, 1, -5, -3, -9, 3, 5, 1, 3, -1, -1, -3, 7, 5, 1, -5, 3, 1, 9, -1, 3, -3, -1, -7, 5, 1, -1, 7, 3, -3, 5, 3, 11, 13, 11, 15, 13, 17, 9, 11, 13, 7, 11, 15, 9, 11, 5, 17, 19, 15, 17, 13, 13, 11, 21, 19, 15, 9, 17, 15, 23, 13, 17, 11, 13, 7, 19, 15, 13, 21, 17, 11, 19, 17, 25, -3, -5, -1, -3, 1, -7, -5, -3, -9, -5, -1, -7, -5, -11, 1, 3, -1, 1, -3, -3, -5, 5, 3, -1, -7, 1, -1, 7, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, -1, -3, 1, -1, 3, -5, -3, -1, -7, -3, 1, -5, -3, -9, 3, 5, 1, 3, -1, -1, -3, 7, 5, 1, -5, 3, 1, 9, -1, 3, -3, -1, -7, 5, 1, -1, 7, 3, -3, 5, 3, 11, -17, -19, -15, -17, -13, -21, -19, -17, -23, -19, -15, -21, -19, -25, -13, -11, -15, -13, -17, -17, -19, -9, -11, -15, -21, -13, -15, -7, -17, -13, -19, -17, -23, -11, -15, -17, -9, -13, -19, -11, -13, -5, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, -7, -5, -9, -7, -11, -3, -5, -7, -1, -5, -9, -3, -5, 1, 7, 9, 5, 7, 3, 11, 9, 7, 13, 9, 5, 11, 9, 15, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, 19, 21, 17, 19, 15, 23, 21, 19, 25, 21, 17, 23, 21, 27, -9, -7, -11, -9, -13, -5, -7, -9, -3, -7, -11, -5, -7, -1, 3, 5, 1, 3, -1, 7, 5, 3, 9, 5, 1, 7, 5, 11, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, -11, -9, -13, -11, -15, -7, -9, -11, -5, -9, -13, -7, -9, -3, -7, -5, -9, -7, -11, -3, -5, -7, -1, -5, -9, -3, -5, 1, 7, 9, 5, 7, 3, 11, 9, 7, 13, 9, 5, 11, 9, 15, -9, -7, -11, -9, -13, -5, -7, -9, -3, -7, -11, -5, -7, -1, -7, -5, -9, -7, -11, -3, -5, -7, -1, -5, -9, -3, -5, 1, -23, -21, -25, -23, -27, -19, -21, -23, -17, -21, -25, -19, -21, -15, 1, -1, 3, 1, 5, 11, 9, 13, 11, 15, -1, -3, 1, -1, 3, 1, -1, 3, 1, 5, -11, -13, -9, -11, -7, 13, 11, 15, 13, 17, 3, 1, 5, 3, 7, 1, -1, 3, 1, 5, 15, 13, 17, 15, 19, 11, 9, 13, 11, 15, -1, -3, 1, -1, 3, 13, 11, 15, 13, 17, 11, 9, 13, 11, 15, 25, 23, 27, 25, 29, -3, -5, -1, -3, 1, -13, -15, -11, -13, -9, -1, -3, 1, -1, 3, -3, -5, -1, -3, 1, 9, 7, 11, 9, 13, 1, -1, 3, 1, 5, 11, 9, 13, 11, 15, -15, -17, -13, -15, -11, -5, -7, -3, -5, -1, -1, -3, 1, -1, 3, 13, 11, 15, 13, 17, -3, -5, -1, -3, 1, -1, -3, 1, -1, 3, -17, -19, -15, -17, -13, 1, -1, 3, 1, 5, -11, -13, -9, -11, -7, 3, 1, 5, 3, 7, 1, -1, 3, 1, 5, 15, 13, 17, 15, 19, -13, -15, -11, -13, -9, -1, -3, 1, -1, 3, 1, -1, 3, 1, 5, -15, -17, -13, -15, -11, -11, -13, -9, -11, -7, 3, 1, 5, 3, 7, -13, -15, -11, -13, -9, -11, -13, -9, -11, -7, -27, -29, -25, -27, -23, 5, 7, -3, -1, 7, 9, 5, 7, 15, 17, -5, -3, 3, 5, 5, 7, -7, -5, -3, -1, 7, 9, -5, -3, -3, -1, -15, -13, 9, 11, 17, 19, 7, 9, 9, 11, -1, 1, 5, 7, -3, -1, 19, 21, 11, 13, 7, 9, -5, -3, 9, 11, 7, 9, 21, 23, 5, 7, 15, 17, 3, 5, 5, 7, -7, -5, 17, 19, 7, 9, 5, 7, 19, 21, 15, 17, 3, 5, 17, 19, 15, 17, 29, 31, -7, -5, 1, 3, -9, -7, -7, -5, -17, -15, 3, 5, -5, -3, -7, -5, 5, 7, 1, 3, -9, -7, 3, 5, 1, 3, 13, 15, 5, 7, -3, -1, 7, 9, 5, 7, 15, 17, -11, -9, -19, -17, -9, -7, -11, -9, -1, 1, -5, -3, 3, 5, 9, 11, 17, 19, -7, -5, 1, 3, -5, -3, 3, 5, -21, -19, -13, -11, 5, 7, -7, -5, 7, 9, 5, 7, 19, 21, -9, -7, 3, 5, 5, 7, -11, -9, -7, -5, 7, 9, -9, -7, -7, -5, -23, -21, -3, -1, 7, 9, -5, -3, -3, -1, -15, -13, 9, 11, -1, 1, -3, -1, 11, 13, 7, 9, -5, -3, 9, 11, 7, 9, 21, 23, -7, -5, -17, -15, -5, -3, -7, -5, 5, 7, -3, -1, 7, 9, -19, -17, -9, -7, -5, -3, 9, 11, -7, -5, -5, -3, -21, -19, -3, -1, -15, -13, -1, 1, -3, -1, 11, 13, -17, -15, -5, -3, -3, -1, -19, -17, -15, -13, -1, 1, -17, -15, -15, -13, -31, -29, 3, 9, 1, 3, -5, 11, 5, 3, 13, 9, 1, 11, 9, 19, -1, -7, 1, -1, 7, 3, 9, -9, -3, 1, 11, -1, 1, -11, 3, -5, 5, 3, 13, -7, 1, 3, -9, -5, 5, -7, -5, -17, 13, 7, 15, 13, 21, 5, 11, 13, 3, 7, 15, 5, 7, -3, 3, 9, 1, 3, -5, 17, 23, 15, 17, 9, 11, 5, -1, -7, 13, 7, 11, 5, 25, 19, 3, 13, 1, 3, -9, 15, 5, 3, 17, 13, 1, 15, 13, 27, 9, 1, 11, 9, 19, -1, 7, 9, -3, 1, 11, -1, 1, -11, 13, 21, 11, 13, 3, 9, 1, 23, 15, 11, -1, 13, 11, 25, 9, 19, 7, 9, -3, 21, 11, 9, 23, 19, 7, 21, 19, 33, -3, -9, -1, -3, 5, -11, -5, -3, -13, -9, -1, -11, -9, -19, 1, 7, -1, 1, -7, -3, -9, 9, 3, -1, -11, 1, -1, 11, -3, 5, -5, -3, -13, 7, -1, -3, 9, 5, -5, 7, 5, 17, 3, 9, 1, 3, -5, 11, 5, 3, 13, 9, 1, 11, 9, 19, -13, -7, -15, -13, -21, -5, -11, -13, -3, -7, -15, -5, -7, 3, -1, -7, 1, -1, 7, 13, 7, 15, 13, 21, -3, -9, -1, -3, 5, -1, -7, 1, -1, 7, -17, -23, -15, -17, -9, 3, 9, -9, -3, 5, 11, 3, 9, 17, 23, -11, -5, 1, 7, 3, 9, -13, -7, -9, -3, 5, 11, -11, -5, -9, -3, -25, -19, 1, 11, -1, 1, -11, 13, 3, 1, 15, 11, -1, 13, 11, 25, -3, -13, -1, -3, 9, 1, 11, -15, -5, -1, 13, -3, -1, -17, 1, -11, 3, 1, 15, -13, -1, 1, -15, -11, 3, -13, -11, -27, 3, -5, 5, 3, 13, -7, 1, 3, -9, -5, 5, -7, -5, -17, 7, 15, 5, 7, -3, 3, -5, 17, 9, 5, -7, 7, 5, 19, 3, 13, 1, 3, -9, 15, 5, 3, 17, 13, 1, 15, 13, 27, -9, -1, -11, -9, -19, 1, -7, -9, 3, -1, -11, 1, -1, 11, 3, -5, 5, 3, 13, -13, -21, -11, -13, -3, -7, 1, 7, 15, -9, -1, -7, 1, -23, -15, 3, -9, 5, 3, 17, -11, 1, 3, -13, -9, 5, -11, -9, -25, -5, 5, -7, -5, -17, 7, -3, -5, 9, 5, -7, 7, 5, 19, -9, -19, -7, -9, 3, -5, 5, -21, -11, -7, 7, -9, -7, -23, -5, -17, -3, -5, 9, -19, -7, -5, -21, -17, -3, -19, -17, -33, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 9, 13, 7, 9, 3, 5, 1, 15, 11, 7, -1, 9, 7, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, 5, 1, 7, 5, 11, -7, -11, -5, -7, -1, -1, 3, 9, 13, -3, 1, -1, 3, -13, -9, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -3, -9, -1, -3, 5, 1, 7, -11, -5, -1, 9, -3, -1, -13, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 11, 15, 9, 11, 5, 17, 13, 11, 19, 15, 9, 17, 15, 23, 7, 3, 9, 7, 13, 11, 15, 1, 5, 9, 17, 7, 9, -1, 11, 5, 13, 11, 19, 3, 9, 11, 1, 5, 13, 3, 5, -5, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 19, 15, 21, 19, 25, 13, 17, 19, 11, 15, 21, 13, 15, 7, 9, 13, 7, 9, 3, -3, 1, -5, -3, -9, 11, 15, 9, 11, 5, 9, 13, 7, 9, 3, 23, 27, 21, 23, 17, 5, 1, 15, 11, 3, -1, 5, 1, -7, -11, 17, 13, 7, 3, 5, 1, 19, 15, 15, 11, 3, -1, 17, 13, 15, 11, 29, 25, 7, -1, 9, 7, 17, -3, 5, 7, -5, -1, 9, -3, -1, -13, 11, 19, 9, 11, 1, 7, -1, 21, 13, 9, -3, 11, 9, 23, 7, 17, 5, 7, -5, 19, 9, 7, 21, 17, 5, 19, 17, 31, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, 1, -5, 3, 1, 9, 5, 11, -7, -1, 3, 13, 1, 3, -9, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 15, 9, 17, 15, 23, 7, 13, 15, 5, 9, 17, 7, 9, -1, 5, 11, 3, 5, -3, 19, 25, 17, 19, 11, 13, 7, 1, -5, 15, 9, 13, 7, 27, 21, 5, 15, 3, 5, -7, 17, 7, 5, 19, 15, 3, 17, 15, 29, 11, 3, 13, 11, 21, 1, 9, 11, -1, 3, 13, 1, 3, -9, 15, 23, 13, 15, 5, 11, 3, 25, 17, 13, 1, 15, 13, 27, 11, 21, 9, 11, -1, 23, 13, 11, 25, 21, 9, 23, 21, 35, -5, -1, -7, -5, -11, 1, -3, -5, 3, -1, -7, 1, -1, 7, -9, -13, -7, -9, -3, -5, -1, -15, -11, -7, 1, -9, -7, -17, -5, -11, -3, -5, 3, -13, -7, -5, -15, -11, -3, -13, -11, -21, 3, -1, 5, 3, 9, -3, 1, 3, -5, -1, 5, -3, -1, -9, -5, -1, -7, -5, -11, 7, 11, 5, 7, 1, 1, -3, -9, -13, 3, -1, 1, -3, 13, 9, -5, 3, -7, -5, -15, 5, -3, -5, 7, 3, -7, 5, 3, 15, -1, -7, 1, -1, 7, -9, -3, -1, -11, -7, 1, -9, -7, -17, 3, 9, 1, 3, -5, -1, -7, 11, 5, 1, -9, 3, 1, 13, -1, 7, -3, -1, -11, 9, 1, -1, 11, 7, -3, 9, 7, 19, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 9, 13, 7, 9, 3, 5, 1, 15, 11, 7, -1, 9, 7, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, -11, -15, -9, -11, -5, -17, -13, -11, -19, -15, -9, -17, -15, -23, -7, -3, -9, -7, -13, -11, -15, -1, -5, -9, -17, -7, -9, 1, -11, -5, -13, -11, -19, -3, -9, -11, -1, -5, -13, -3, -5, 5, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, 11, 15, 9, 11, 5, 17, 13, 11, 19, 15, 9, 17, 15, 23, -5, -1, -7, -5, -11, 1, -3, -5, 3, -1, -7, 1, -1, 7, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, -19, -15, -21, -19, -25, -13, -17, -19, -11, -15, -21, -13, -15, -7, 5, 1, 7, 5, 11, -7, -11, -5, -7, -1, 7, 3, 9, 7, 13, 5, 1, 7, 5, 11, 19, 15, 21, 19, 25, -9, -13, -7, -9, -3, 3, -1, 5, 3, 9, 5, 1, 7, 5, 11, -11, -15, -9, -11, -5, -7, -11, -5, -7, -1, 7, 3, 9, 7, 13, -9, -13, -7, -9, -3, -7, -11, -5, -7, -1, -23, -27, -21, -23, -17, -1, 3, 9, 13, -3, 1, -1, 3, -13, -9, 11, 15, 1, 5, -1, 3, 13, 17, 9, 13, -3, 1, 11, 15, 9, 13, 23, 27, -5, -1, -15, -11, -3, 1, -5, -1, 7, 11, -1, 3, 9, 13, -17, -13, -7, -3, -3, 1, 11, 15, -5, -1, -3, 1, -19, -15, -1, 3, -13, -9, 1, 5, -1, 3, 13, 17, -15, -11, -3, 1, -1, 3, -17, -13, -13, -9, 1, 5, -15, -11, -13, -9, -29, -25, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 9, 17, 7, 9, -1, 5, -3, 19, 11, 7, -5, 9, 7, 21, 5, 15, 3, 5, -7, 17, 7, 5, 19, 15, 3, 17, 15, 29, -7, 1, -9, -7, -17, 3, -5, -7, 5, 1, -9, 3, 1, 13, 5, -3, 7, 5, 15, -11, -19, -9, -11, -1, -5, 3, 9, 17, -7, 1, -5, 3, -21, -13, 5, -7, 7, 5, 19, -9, 3, 5, -11, -7, 7, -9, -7, -23, -3, 7, -5, -3, -15, 9, -1, -3, 11, 7, -5, 9, 7, 21, -7, -17, -5, -7, 5, -3, 7, -19, -9, -5, 9, -7, -5, -21, -3, -15, -1, -3, 11, -17, -5, -3, -19, -15, -1, -17, -15, -31, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -3, -9, -1, -3, 5, 1, 7, -11, -5, -1, 9, -3, -1, -13, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 11, 5, 13, 11, 19, 3, 9, 11, 1, 5, 13, 3, 5, -5, 1, 7, -1, 1, -7, 15, 21, 13, 15, 7, 9, 3, -3, -9, 11, 5, 9, 3, 23, 17, 1, 11, -1, 1, -11, 13, 3, 1, 15, 11, -1, 13, 11, 25, 7, -1, 9, 7, 17, -3, 5, 7, -5, -1, 9, -3, -1, -13, 11, 19, 9, 11, 1, 7, -1, 21, 13, 9, -3, 11, 9, 23, 7, 17, 5, 7, -5, 19, 9, 7, 21, 17, 5, 19, 17, 31, -5, -11, -3, -5, 3, -13, -7, -5, -15, -11, -3, -13, -11, -21, -1, 5, -3, -1, -9, -5, -11, 7, 1, -3, -13, -1, -3, 9, -5, 3, -7, -5, -15, 5, -3, -5, 7, 3, -7, 5, 3, 15, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -15, -9, -17, -15, -23, -7, -13, -15, -5, -9, -17, -7, -9, 1, -3, -9, -1, -3, 5, 11, 5, 13, 11, 19, -5, -11, -3, -5, 3, -3, -9, -1, -3, 5, -19, -25, -17, -19, -11, 1, 7, -11, -5, 3, 9, 1, 7, 15, 21, -13, -7, -1, 5, 1, 7, -15, -9, -11, -5, 3, 9, -13, -7, -11, -5, -27, -21, -1, 9, -3, -1, -13, 11, 1, -1, 13, 9, -3, 11, 9, 23, -5, -15, -3, -5, 7, -1, 9, -17, -7, -3, 11, -5, -3, -19, -1, -13, 1, -1, 13, -15, -3, -1, -17, -13, 1, -15, -13, -29, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 5, 13, 3, 5, -5, 1, -7, 15, 7, 3, -9, 5, 3, 17, 1, 11, -1, 1, -11, 13, 3, 1, 15, 11, -1, 13, 11, 25, -11, -3, -13, -11, -21, -1, -9, -11, 1, -3, -13, -1, -3, 9, 1, -7, 3, 1, 11, -15, -23, -13, -15, -5, -9, -1, 5, 13, -11, -3, -9, -1, -25, -17, 1, -11, 3, 1, 15, -13, -1, 1, -15, -11, 3, -13, -11, -27, -7, 3, -9, -7, -19, 5, -5, -7, 7, 3, -9, 5, 3, 17, -11, -21, -9, -11, 1, -7, 3, -23, -13, -9, 5, -11, -9, -25, -7, -19, -5, -7, 7, -21, -9, -7, -23, -19, -5, -21, -19, -35])\n assert answers_match(candidate(expression='9-8+7-6*5+4-3*2+1'), [-6, 6, 42, 18, 42, -6, 6, 102, 102, 18, 42, 18, 72, 72, 19, 21, 27, 23, 27, 39, 41, 19, 21, 102, 102, 87, 147, 87, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, 1, -1, -7, -3, -7, 1, -1, -17, -17, -3, -7, -3, -12, -12, 29, 27, 21, 25, 21, 1, -1, -7, -3, -7, 57, 55, 37, 35, 1, -1, 29, 27, 1, -1, 88, 88, 73, 133, 73, -17, -17, 67, -17, 151, 91, -17, 67, -17, 11, 35, 11, 65, 65, 21, 25, 41, 21, 65, 65, 55, 95, 55, -3, -7, -3, -12, -12, 25, 21, -3, -7, 53, 33, -3, 25, -3, 58, 58, 48, 88, 48, -12, -12, 44, -12, 100, 60, -12, 44, -12, -6, 6, 42, 18, 42, -6, 6, 102, 102, 18, 42, 18, 72, 72, 19, 21, 27, 23, 27, 39, 41, 19, 21, 102, 102, 87, 147, 87, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, 9, -9, -63, -27, -63, 9, -9, -153, -153, -27, -63, -27, -108, -108, 9, -9, -63, -27, -63, 9, -9, -153, -153, -27, -63, -27, -108, -108, 29, 27, 21, 25, 21, 1, -1, -7, -3, -7, 29, 27, 21, 25, 21, -31, -33, -39, -35, -39, -31, -33, -39, -35, -39, 57, 55, 37, 35, 1, -1, 29, 27, 1, -1, 57, 55, 37, 35, -63, -65, -63, -65, 29, 27, 1, -1, 29, 27, -31, -33, -31, -33, 72, 72, 57, 117, 57, -33, -33, 51, -33, 135, 75, -33, 51, -33, 72, 72, 57, 117, 57, -153, -153, -153, -153, 51, -33, 51, -129, -129, 135, 75, -33, 51, -33, 135, 75, -225, -225, 51, -33, 51, -129, -129, 11, 35, 11, 65, 65, 21, 25, 41, 21, 65, 65, 55, 95, 55, -3, -7, -3, -12, -12, 25, 21, -3, -7, 53, 33, -3, 25, -3, 58, 58, 48, 88, 48, -12, -12, 44, -12, 100, 60, -12, 44, -12, 11, 35, 11, 65, 65, 21, 25, 41, 21, 65, 65, 55, 95, 55, -19, -55, -19, -100, -100, -19, -55, -19, -100, -100, 25, 21, -3, -7, 25, 21, -35, -39, -35, -39, 53, 33, -3, 25, -3, 53, 33, -67, -67, 25, -3, 25, -35, -35, 50, 50, 40, 80, 40, -20, -20, 36, -20, 92, 52, -20, 36, -20, 50, 50, 40, 80, 40, -100, -100, -100, -100, 36, -20, 36, -84, -84, 92, 52, -20, 36, -20, 92, 52, -148, -148, 36, -20, 36, -84, -84, 8, -4, -40, -16, -40, 8, -4, -100, -100, -16, -40, -16, -70, -70, -17, -19, -25, -21, -25, -37, -39, -17, -19, -100, -100, -85, -145, -85, -11, -35, -11, -65, -65, -21, -25, -41, -21, -65, -65, -55, -95, -55, 1, 3, 9, 5, 9, 1, 3, 19, 19, 5, 9, 5, 14, 14, -27, -25, -19, -23, -19, 1, 3, 9, 5, 9, -55, -53, -35, -33, 1, 3, -27, -25, 1, 3, -86, -86, -71, -131, -71, 19, 19, -65, 19, -149, -89, 19, -65, 19, -9, -33, -9, -63, -63, -19, -23, -39, -19, -63, -63, -53, -93, -53, 5, 9, 5, 14, 14, -23, -19, 5, 9, -51, -31, 5, -23, 5, -56, -56, -46, -86, -46, 14, 14, -42, 14, -98, -58, 14, -42, 14, -6, -18, -54, -30, -54, -6, -18, -114, -114, -30, -54, -30, -84, -84, -31, -33, -39, -35, -39, -51, -53, -31, -33, -114, -114, -99, -159, -99, -25, -49, -25, -79, -79, -35, -39, -55, -35, -79, -79, -69, -109, -69, 8, -4, -40, -16, -40, 8, -4, -100, -100, -16, -40, -16, -70, -70, -17, -19, -25, -21, -25, -37, -39, -17, -19, -100, -100, -85, -145, -85, -11, -35, -11, -65, -65, -21, -25, -41, -21, -65, -65, -55, -95, -55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 16, 8, 16, 0, 4, 36, 36, 8, 16, 8, 26, 26, 0, -24, -96, -48, -96, 0, -24, -216, -216, -48, -96, -48, -156, -156, 0, 4, 16, 8, 16, 0, 4, 36, 36, 8, 16, 8, 26, 26, 19, 21, 27, 23, 27, -9, -7, -1, -5, -1, 19, 21, 27, 23, 27, -41, -39, -33, -37, -33, -41, -39, -33, -37, -33, -27, -25, -19, -23, -19, 1, 3, 9, 5, 9, -41, -39, -33, -37, -33, -27, -25, -19, -23, -19, -5, -3, 3, -1, 3, -5, -3, 3, -1, 3, 5, 7, 13, 9, 13, -65, -63, -57, -61, -57, 5, 7, 13, 9, 13, 39, 41, 19, 21, -17, -15, 11, 13, -17, -15, 39, 41, 19, 21, -81, -79, -81, -79, 11, 13, -17, -15, 11, 13, -49, -47, -49, -47, -55, -53, -35, -33, 1, 3, -27, -25, 1, 3, -69, -67, -49, -47, -55, -53, -35, -33, -9, -7, -9, -7, 9, 11, -117, -115, 9, 11, 19, 21, -9, -7, 19, 21, -41, -39, -41, -39, -27, -25, 1, 3, -41, -39, -27, -25, -5, -3, -5, -3, 5, 7, -65, -63, 5, 7, 90, 90, 75, 135, 75, -15, -15, 69, -15, 153, 93, -15, 69, -15, 90, 90, 75, 135, 75, -135, -135, -135, -135, 69, -15, 69, -111, -111, 153, 93, -15, 69, -15, 153, 93, -207, -207, 69, -15, 69, -111, -111, -84, -84, -69, -129, -69, 21, 21, -63, 21, -147, -87, 21, -63, 21, -126, -126, -111, -171, -111, -84, -84, -69, -129, -69, 0, 0, 0, 0, 36, 36, -216, -216, 36, 36, 75, -9, 75, -105, -105, -63, 21, -105, -63, 3, 3, 33, -177, 33, 135, 75, -33, 51, -33, 135, 75, -225, -225, 51, -33, 51, -129, -129, -147, -87, 21, -63, 21, -189, -129, -147, -87, -9, -9, 45, -333, 45, 75, -9, 75, -105, -105, -63, 21, -105, -63, 3, 3, 33, -177, 33, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, -1, -5, -1, -10, -10, 27, 23, -1, -5, 55, 35, -1, 27, -1, 60, 60, 50, 90, 50, -10, -10, 46, -10, 102, 62, -10, 46, -10, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, -17, -53, -17, -98, -98, -17, -53, -17, -98, -98, 27, 23, -1, -5, 27, 23, -33, -37, -33, -37, 55, 35, -1, 27, -1, 55, 35, -65, -65, 27, -1, 27, -33, -33, 52, 52, 42, 82, 42, -18, -18, 38, -18, 94, 54, -18, 38, -18, 52, 52, 42, 82, 42, -98, -98, -98, -98, 38, -18, 38, -82, -82, 94, 54, -18, 38, -18, 94, 54, -146, -146, 38, -18, 38, -82, -82, -9, -33, -9, -63, -63, -19, -23, -39, -19, -63, -63, -53, -93, -53, 5, 9, 5, 14, 14, -23, -19, 5, 9, -51, -31, 5, -23, 5, -56, -56, -46, -86, -46, 14, 14, -42, 14, -98, -58, 14, -42, 14, -23, -47, -23, -77, -77, -33, -37, -53, -33, -77, -77, -67, -107, -67, -9, -33, -9, -63, -63, -19, -23, -39, -19, -63, -63, -53, -93, -53, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 15, 7, 25, 25, -35, -83, -35, -143, -143, 7, 15, 7, 25, 25, 23, 27, -5, -1, 23, 27, -37, -33, -37, -33, -23, -19, 5, 9, -37, -33, -23, -19, -1, 3, -1, 3, 9, 13, -61, -57, 9, 13, 43, 23, -13, 15, -13, 43, 23, -77, -77, 15, -13, 15, -45, -45, -51, -31, 5, -23, 5, -65, -45, -51, -31, -5, -5, 13, -113, 13, 23, -5, 23, -37, -37, -23, 5, -37, -23, -1, -1, 9, -61, 9, 61, 61, 51, 91, 51, -9, -9, 47, -9, 103, 63, -9, 47, -9, 61, 61, 51, 91, 51, -89, -89, -89, -89, 47, -9, 47, -73, -73, 103, 63, -9, 47, -9, 103, 63, -137, -137, 47, -9, 47, -73, -73, -55, -55, -45, -85, -45, 15, 15, -41, 15, -97, -57, 15, -41, 15, -83, -83, -73, -113, -73, -55, -55, -45, -85, -45, 1, 1, 1, 1, 25, 25, -143, -143, 25, 25, 51, -5, 51, -69, -69, -41, 15, -69, -41, 3, 3, 23, -117, 23, 91, 51, -21, 35, -21, 91, 51, -149, -149, 35, -21, 35, -85, -85, -97, -57, 15, -41, 15, -125, -85, -97, -57, -5, -5, 31, -221, 31, 51, -5, 51, -69, -69, -41, 15, -69, -41, 3, 3, 23, -117, 23])\n assert answers_match(candidate(expression='1*2*3*4*5*6*7*8-9'), [-5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311])\n assert answers_match(candidate(expression='100-50+25*5-12*2'), [525, 400, -51, 400, -176, 1525, 1150, -51, -251, 350, -226, 1150, -226, -626, -425, -300, 151, -300, 276, -475, -350, -1425, -1050, -99, -299, 151, 101, 351, 450, -126, 1250, -126, -526, -250, 326, -350, -1050, -174, -574, 326, 226, 726])\n assert answers_match(candidate(expression='4*4-3*3+2*2-1*1'), [-44, -44, -56, -44, -56, -44, -44, -56, -92, -44, -56, -44, -56, -92, -28, -28, -32, -28, -32, -44, -44, -28, -28, -64, -100, -32, -100, -68, -44, -56, -44, -56, -92, -28, -32, -44, -28, -64, -100, -32, -100, -68, 20, 20, 24, 20, 24, 20, 20, 24, 36, 20, 24, 20, 24, 36, -12, -12, -8, -12, -8, 20, 20, 24, 20, 24, -44, -44, -28, -28, 20, 20, -12, -12, 20, 20, -72, -108, -40, -108, -76, 24, 36, -8, 24, -92, -60, 36, -28, 36, -44, -56, -44, -56, -92, -28, -32, -44, -28, -64, -100, -32, -100, -68, 20, 24, 20, 24, 36, -12, -8, 20, 24, -44, -28, 20, -12, 20, -72, -108, -40, -108, -76, 24, 36, -8, 24, -92, -60, 36, -28, 36, 1, 1, -2, 1, -2, 1, 1, -2, -11, 1, -2, 1, -2, -11, 5, 5, 4, 5, 4, 1, 1, 5, 5, -4, -13, 4, -13, -5, 1, -2, 1, -2, -11, 5, 4, 1, 5, -4, -13, 4, -13, -5, 20, 20, 24, 20, 24, 20, 20, 24, 36, 20, 24, 20, 24, 36, 65, 65, 78, 65, 78, 65, 65, 78, 117, 65, 78, 65, 78, 117, -18, -18, -17, -18, -17, 14, 14, 15, 14, 15, 9, 9, 10, 9, 10, 14, 14, 15, 14, 15, 41, 41, 42, 41, 42, -44, -44, -28, -28, 20, 20, -12, -12, 20, 20, 1, 1, 5, 5, 20, 20, 65, 65, -18, -18, 14, 14, 9, 9, 14, 14, 41, 41, -69, -105, -37, -105, -73, 27, 39, -5, 27, -89, -57, 39, -25, 39, -6, -15, 2, -15, -7, 27, 39, 90, 129, -17, 15, 10, 15, 42, -89, -57, 39, -25, 39, 1, 9, 39, 129, -37, 27, 17, 27, 81, -44, -56, -44, -56, -92, -28, -32, -44, -28, -64, -100, -32, -100, -68, 20, 24, 20, 24, 36, -12, -8, 20, 24, -44, -28, 20, -12, 20, -72, -108, -40, -108, -76, 24, 36, -8, 24, -92, -60, 36, -28, 36, 1, -2, 1, -2, -11, 5, 4, 1, 5, -4, -13, 4, -13, -5, 20, 24, 20, 24, 36, 65, 78, 65, 78, 117, -18, -17, 14, 15, 9, 10, 14, 15, 41, 42, -44, -28, 20, -12, 20, 1, 5, 20, 65, -18, 14, 9, 14, 41, -69, -105, -37, -105, -73, 27, 39, -5, 27, -89, -57, 39, -25, 39, -6, -15, 2, -15, -7, 27, 39, 90, 129, -17, 15, 10, 15, 42, -89, -57, 39, -25, 39, 1, 9, 39, 129, -37, 27, 17, 27, 81])\n assert answers_match(candidate(expression='3*2-1+4*5-6*7+8*9'), [5631, 9663, 1311, 9663, 5343, 951, 1623, -417, -777, 9183, 4863, 1623, 3135, -105, 1365, 2373, 285, 2373, 1293, 951, 1623, -3315, -5667, 231, -129, -147, -129, -507, 9183, 4863, 1623, 3135, -105, 1893, 813, 1623, -5667, 3783, 543, 381, 543, -2859, 7041, 12081, 1641, 12081, 6681, 1191, 2031, -519, -969, 11481, 6081, 2031, 3921, -129, 1365, 2373, 285, 2373, 1293, 1353, 2361, 273, 2361, 1281, 717, 1221, -3549, -6069, 1191, 2031, -3549, -6069, -4497, -7689, 231, -129, -147, -129, -507, 345, -105, -147, -159, -147, -525, -105, -525, -609, 9159, 4839, 1599, 3111, -129, 1869, 789, 1599, -5691, 3759, 519, 357, 519, -2883, 11481, 6081, 2031, 3921, -129, 1869, 789, 1761, 681, 1221, -6069, 2031, -6069, -7689, 3759, 519, 357, 519, -2883, 4785, 735, 357, 249, 357, -3045, 735, -3045, -3801, -5625, -9657, -1305, -9657, -5337, -945, -1617, 423, 783, -9177, -4857, -1617, -3129, 111, -1359, -2367, -279, -2367, -1287, -945, -1617, 3321, 5673, -225, 135, 153, 135, 513, -9177, -4857, -1617, -3129, 111, -1887, -807, -1617, 5673, -3777, -537, -375, -537, 2865, 4221, 7245, 981, 7245, 4005, 711, 1215, -315, -585, 6885, 3645, 1215, 2349, -81, -7035, -12075, -1635, -12075, -6675, -1185, -2025, 525, 975, -11475, -6075, -2025, -3915, 135, -1479, -2487, -399, -2487, -1407, -1491, -2499, -411, -2499, -1419, -1359, -2367, -279, -2367, -1287, -1467, -2475, -387, -2475, -1395, -1347, -2355, -267, -2355, -1275, 1185, 2025, -3081, -5265, 1659, 2835, -3081, -5265, -4029, -6885, -711, -1215, 3555, 6075, 711, 1215, -1185, -2025, -5925, -10125, -6873, -11745, 3555, 6075, -4977, -8505, 4503, 7695, 663, 303, 285, 303, -75, 777, 327, 285, 273, 285, -93, 327, -93, -177, -225, 135, 153, 135, 513, 549, 279, -339, 111, 33, 21, 153, 45, 165, 321, -57, 363, -57, -141, 153, 531, 279, 111, -309, -393, 531, -225, 615, 9207, 4887, 1647, 3159, -81, 1917, 837, 1647, -5643, 3807, 567, 405, 567, -2835, 11529, 6129, 2079, 3969, -81, 1917, 837, 1809, 729, 1269, -6021, 2079, -6021, -7641, 3807, 567, 405, 567, -2835, 4833, 783, 405, 297, 405, -2997, 783, -2997, -3753, -9153, -4833, -1593, -3105, 135, -1863, -783, -1593, 5697, -3753, -513, -351, -513, 2889, 6885, 3645, 1215, 2349, -81, -11475, -6075, -2025, -3915, 135, -2943, -1863, -3051, -1971, -1863, -783, -2835, -1755, -1755, -675, 2025, -5265, 2835, -5265, -6885, -1215, 6075, 1215, -2025, -10125, -11745, 6075, -8505, 7695, 4239, 999, 837, 999, -2403, 5265, 1215, 837, 729, 837, -2565, 1215, -2565, -3321, -3753, -513, -351, -513, 2889, 3213, 783, -4779, -729, -1431, -1539, -351, -1323, -243, 1161, -2241, 1539, -2241, -2997, -351, 3051, 783, -729, -4509, -5265, 3051, -3753, 3807, 1881, 3225, 441, 3225, 1785, 321, 545, -135, -255, 3065, 1625, 545, 1049, -31, 459, 795, 99, 795, 435, 321, 545, -1101, -1885, 81, -39, -45, -39, -165, 3065, 1625, 545, 1049, -31, 635, 275, 545, -1885, 1265, 185, 131, 185, -949, 2351, 4031, 551, 4031, 2231, 401, 681, -169, -319, 3831, 2031, 681, 1311, -39, 459, 795, 99, 795, 435, 455, 791, 95, 791, 431, 243, 411, -1179, -2019, 401, 681, -1179, -2019, -1495, -2559, 81, -39, -45, -39, -165, 119, -31, -45, -49, -45, -171, -31, -171, -199, 3057, 1617, 537, 1041, -39, 627, 267, 537, -1893, 1257, 177, 123, 177, -957, 3831, 2031, 681, 1311, -39, 627, 267, 591, 231, 411, -2019, 681, -2019, -2559, 1257, 177, 123, 177, -957, 1599, 249, 123, 87, 123, -1011, 249, -1011, -1263, -1873, -3217, -433, -3217, -1777, -313, -537, 143, 263, -3057, -1617, -537, -1041, 39, -451, -787, -91, -787, -427, -313, -537, 1109, 1893, -73, 47, 53, 47, 173, -3057, -1617, -537, -1041, 39, -627, -267, -537, 1893, -1257, -177, -123, -177, 957, -1871, -3215, -431, -3215, -1775, -311, -535, 145, 265, -3055, -1615, -535, -1039, 41, -449, -785, -89, -785, -425, -311, -535, 1111, 1895, -71, 49, 55, 49, 175, -3055, -1615, -535, -1039, 41, -625, -265, -535, 1895, -1255, -175, -121, -175, 959, 4221, 7245, 981, 7245, 4005, 711, 1215, -315, -585, 6885, 3645, 1215, 2349, -81, -7035, -12075, -1635, -12075, -6675, -1185, -2025, 525, 975, -11475, -6075, -2025, -3915, 135, -469, -805, -109, -805, -445, -79, -135, 35, 65, -765, -405, -135, -261, 9, -3283, -5635, -763, -5635, -3115, -553, -945, 245, 455, -5355, -2835, -945, -1827, 63, -4221, -7245, -981, -7245, -4005, -711, -1215, 315, 585, -6885, -3645, -1215, -2349, 81, -531, -867, -171, -867, -507, -543, -879, -183, -879, -519, -411, -747, -51, -747, -387, -519, -855, -159, -855, -495, -399, -735, -39, -735, -375, -489, -825, -129, -825, -465, -493, -829, -133, -829, -469, -451, -787, -91, -787, -427, -449, -785, -89, -785, -425, -519, -855, -159, -855, -495, -399, -735, -39, -735, -375, -469, -805, -109, -805, -445, -439, -775, -79, -775, -415, -429, -765, -69, -765, -405, 1185, 2025, -3081, -5265, 1659, 2835, -3081, -5265, -4029, -6885, -711, -1215, 3555, 6075, 711, 1215, -1185, -2025, -5925, -10125, -6873, -11745, 3555, 6075, -4977, -8505, 4503, 7695, 711, 1215, -711, -1215, 869, 1485, -711, -1215, -1027, -1755, -79, -135, 1343, 2295, 79, 135, 1501, 2565, 711, 1215, -1185, -2025, -79, -135, -553, -945, -711, -1215, -4977, -8505, -5925, -10125, 4503, 7695, -4029, -6885, 5451, 9315, -1659, -2835, -1975, -3375, 1343, 2295, 1501, 2565, -4029, -6885, 5451, 9315, -79, -135, 2291, 3915, 3081, 5265, 519, 159, 141, 159, -219, 633, 183, 141, 129, 141, -237, 183, -237, -321, -369, -9, 9, -9, 369, 405, 135, -483, -33, -111, -123, 9, -99, 21, 177, -201, 219, -201, -285, 9, 387, 135, -33, -453, -537, 387, -369, 471, 225, 105, 99, 105, -21, 263, 113, 99, 95, 99, -27, 113, -27, -55, -73, 47, 53, 47, 173, -71, 49, 55, 49, 175, 405, 135, -483, -33, 35, 65, -187, 23, -261, 9, -27, -39, 93, -15, 105, 15, 11, 53, 55, -15, 105, 35, 65, 75, 177, -201, 219, -201, -285, 9, 387, 135, -33, -453, -537, 387, -369, 471, 135, 9, 149, 9, -19, 65, 191, 79, 205, 135, -33, 65, 23, 9, -369, -453, 471, -285, 555, -75, -103, 191, 205, -285, 555, 65, 275, 345, 9207, 4887, 1647, 3159, -81, 1917, 837, 1647, -5643, 3807, 567, 405, 567, -2835, 11529, 6129, 2079, 3969, -81, 1917, 837, 1809, 729, 1269, -6021, 2079, -6021, -7641, 3807, 567, 405, 567, -2835, 4833, 783, 405, 297, 405, -2997, 783, -2997, -3753, -9153, -4833, -1593, -3105, 135, -1863, -783, -1593, 5697, -3753, -513, -351, -513, 2889, 6885, 3645, 1215, 2349, -81, -11475, -6075, -2025, -3915, 135, -2943, -1863, -3051, -1971, -1863, -783, -2835, -1755, -1755, -675, 2025, -5265, 2835, -5265, -6885, -1215, 6075, 1215, -2025, -10125, -11745, 6075, -8505, 7695, 4239, 999, 837, 999, -2403, 5265, 1215, 837, 729, 837, -2565, 1215, -2565, -3321, -3753, -513, -351, -513, 2889, 3213, 783, -4779, -729, -1431, -1539, -351, -1323, -243, 1161, -2241, 1539, -2241, -2997, -351, 3051, 783, -729, -4509, -5265, 3051, -3753, 3807, 3105, 1665, 585, 1089, 9, 675, 315, 585, -1845, 1305, 225, 171, 225, -909, 3879, 2079, 729, 1359, 9, 675, 315, 639, 279, 459, -1971, 729, -1971, -2511, 1305, 225, 171, 225, -909, 1647, 297, 171, 135, 171, -963, 297, -963, -1215, -3033, -1593, -513, -1017, 63, -603, -243, -513, 1917, -1233, -153, -99, -153, 981, -3015, -1575, -495, -999, 81, -585, -225, -495, 1935, -1215, -135, -81, -135, 999, 6885, 3645, 1215, 2349, -81, -11475, -6075, -2025, -3915, 135, -765, -405, -135, -261, 9, -5355, -2835, -945, -1827, 63, -6885, -3645, -1215, -2349, 81, -1323, -963, -1431, -1071, -243, 117, -1215, -855, -135, 225, -945, -585, -981, -621, -603, -243, -585, -225, -1215, -855, -135, 225, -765, -405, -495, -135, -405, -45, 2025, -5265, 2835, -5265, -6885, -1215, 6075, 1215, -2025, -10125, -11745, 6075, -8505, 7695, 1215, -1215, 1485, -1215, -1755, -135, 2295, 135, 2565, 1215, -2025, -135, -945, -1215, -8505, -10125, 7695, -6885, 9315, -2835, -3375, 2295, 2565, -6885, 9315, -135, 3915, 5265, 4095, 855, 693, 855, -2547, 5121, 1071, 693, 585, 693, -2709, 1071, -2709, -3465, -3897, -657, -495, -657, 2745, 3069, 639, -4923, -873, -1575, -1683, -495, -1467, -387, 1017, -2385, 1395, -2385, -3141, -495, 2907, 639, -873, -4653, -5409, 2907, -3897, 3663, 1449, 369, 315, 369, -765, 1791, 441, 315, 279, 315, -819, 441, -819, -1071, -1233, -153, -99, -153, 981, -1215, -135, -81, -135, 999, 3069, 639, -4923, -873, -261, 9, -2259, -369, -2925, -495, -819, -927, 261, -711, 369, -441, -477, -99, -81, -711, 369, -261, 9, 99, 1017, -2385, 1395, -2385, -3141, -495, 2907, 639, -873, -4653, -5409, 2907, -3897, 3663, 639, -495, 765, -495, -747, 9, 1143, 135, 1269, 639, -873, 9, -369, -495, -3897, -4653, 3663, -3141, 4419, -1251, -1503, 1143, 1269, -3141, 4419, 9, 1899, 2529])\n assert answers_match(candidate(expression='3*3*3*3-2*2*2'), [-135, -135, 108, -54, 108, 9, 9, 108, 252, -54, 108, 90, 108, 252, -135, -135, 108, -54, 108, 57, 57, 57, 57, 108, 252, 108, 300, 300, -54, 108, 90, 108, 252, -54, 108, 138, 138, 108, 252, 108, 300, 300, -135, -135, 108, -54, 108, 9, 9, 108, 252, -54, 108, 90, 108, 252, -135, -135, 108, -54, 108, -135, -135, 108, -54, 108, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 108, 252, 108, 300, 300, 108, 252, 108, 108, 316, 316, 316, 316, 316, -54, 108, 90, 108, 252, -54, 108, 138, 138, 108, 252, 108, 300, 300, -54, 108, 90, 108, 252, -54, 108, -54, 108, 154, 154, 154, 154, 154, 108, 252, 108, 300, 300, 108, 252, 108, 108, 316, 316, 316, 316, 316])\n assert answers_match(candidate(expression='1+2+3+4+5+6+7+8'), [36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36])\n assert answers_match(candidate(expression='50+25-10*2+5'), [5, 50, 155, 60, 85, 5, 50, 455, 455, 60, 85, 60, 135, 135])\n assert answers_match(candidate(expression='5*5-4*4+3*3-2*2+1*1'), [125, 125, 65, 125, 65, -235, -235, -55, -235, 125, 65, -235, -55, -235, -115, -115, -135, -115, -135, -235, -235, -475, -475, -15, -195, -175, -195, -355, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 445, 305, 445, 305, -395, -395, 25, -395, 445, 305, -395, 25, -395, -115, -115, -135, -115, -135, -275, -275, -295, -275, -295, -395, -395, -635, -635, -395, -395, -635, -635, -1115, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -10, -25, -10, -25, -100, -100, -55, -100, -10, -25, -100, -55, -100, -70, -70, -75, -70, -75, -100, -100, -160, -160, -45, -90, -85, -90, -130, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 445, 305, 445, 305, -395, -395, 25, -395, 445, 305, -395, 25, -395, 310, 310, 215, 310, 215, -260, -260, 25, -260, 310, 215, -260, 25, -260, -205, -205, -210, -205, -210, -365, -365, -370, -365, -370, -70, -70, -75, -70, -75, -365, -365, -370, -365, -370, -230, -230, -235, -230, -235, -395, -395, -635, -635, -395, -395, -635, -635, -1115, -1115, -260, -260, -320, -320, -395, -395, -260, -260, -725, -725, -1205, -1205, -320, -320, -1205, -1205, -800, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 305, -395, 25, -395, 310, 215, -260, 25, -260, -205, -210, -365, -370, -70, -75, -365, -370, -230, -235, -395, -635, -395, -635, -1115, -260, -320, -395, -260, -725, -1205, -320, -1205, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, -25, -25, -10, -25, -10, 65, 65, 20, 65, -25, -10, 65, 20, 65, 35, 35, 40, 35, 40, 65, 65, 125, 125, 10, 55, 50, 55, 95, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, 35, 35, 40, 35, 40, 75, 75, 80, 75, 80, 105, 105, 165, 165, 105, 105, 165, 165, 285, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -100, -100, -85, -100, -85, -10, -10, -55, -10, -100, -85, -10, -55, -10, -40, -40, -35, -40, -35, -10, -10, 50, 50, -65, -20, -25, -20, 20, -100, -85, -10, -55, -10, -40, -35, -10, 50, -65, -20, -25, -20, 20, -25, -25, -10, -25, -10, 65, 65, 20, 65, -25, -10, 65, 20, 65, 35, 35, 40, 35, 40, 65, 65, 125, 125, 10, 55, 50, 55, 95, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, 345, 345, 230, 345, 230, -345, -345, 0, -345, 345, 230, -345, 0, -345, 210, 210, 140, 210, 140, -210, -210, 0, -210, 210, 140, -210, 0, -210, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, 120, 120, 80, 120, 80, -120, -120, 0, -120, 120, 80, -120, 0, -120, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, -265, -265, -260, -265, -260, -425, -425, -420, -425, -420, -130, -130, -125, -130, -125, -425, -425, -420, -425, -420, -290, -290, -285, -290, -285, 35, 35, 40, 35, 40, 75, 75, 80, 75, 80, -40, -40, -35, -40, -35, 35, 35, 40, 35, 40, -375, -375, -370, -375, -370, -240, -240, -235, -240, -235, 75, 75, 80, 75, 80, -150, -150, -145, -150, -145, 75, 75, 80, 75, 80, -345, -345, -585, -585, -345, -345, -585, -585, -1065, -1065, -210, -210, -270, -270, -345, -345, -210, -210, -675, -675, -1155, -1155, -270, -270, -1155, -1155, -750, -750, 105, 105, 165, 165, 105, 105, 165, 165, 285, 285, -120, -120, -60, -60, 105, 105, 165, 165, -345, -345, -210, -210, 105, 105, -120, -120, 105, 105, -735, -735, -1215, -1215, -330, -330, -1215, -1215, -810, -810, 165, 165, 285, 285, -60, -60, 165, 165, -1065, -1065, -660, -660, 285, 285, -390, -390, 285, 285, 10, -170, -150, -170, -330, 170, -250, -150, -310, -250, -410, -250, -410, -730, -35, -80, -75, -80, -120, 170, -250, 125, -160, -210, -370, -75, -370, -235, -250, -410, -250, -410, -730, -160, -200, -250, -160, -470, -790, -200, -790, -520, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -65, -20, -25, -20, 20, 10, 55, 50, 55, 95, 120, -225, 75, -135, -30, 75, 45, -75, -30, 75, -250, -410, -115, -410, -275, 50, 90, -25, 50, -360, -225, 90, -135, 90, -225, -385, -225, -385, -705, -135, -175, -225, -135, -445, -765, -175, -765, -495, 75, 115, 75, 115, 195, -75, -35, 75, 115, -225, -135, 75, -75, 75, -485, -805, -215, -805, -535, 115, 195, -35, 115, -705, -435, 195, -255, 195, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 305, -395, 25, -395, 310, 215, -260, 25, -260, -205, -210, -365, -370, -70, -75, -365, -370, -230, -235, -395, -635, -395, -635, -1115, -260, -320, -395, -260, -725, -1205, -320, -1205, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -100, -85, -10, -55, -10, -40, -35, -10, 50, -65, -20, -25, -20, 20, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, -265, -260, -425, -420, -130, -125, -425, -420, -290, -285, 35, 40, 75, 80, -40, -35, 35, 40, -375, -370, -240, -235, 75, 80, -150, -145, 75, 80, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, 10, -170, -150, -170, -330, 170, -250, -150, -310, -250, -410, -250, -410, -730, -35, -80, -75, -80, -120, 170, -250, 125, -160, -210, -370, -75, -370, -235, -250, -410, -250, -410, -730, -160, -200, -250, -160, -470, -790, -200, -790, -520, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -65, -20, -25, -20, 20, 10, 55, 50, 55, 95, 120, -225, 75, -135, -30, 75, 45, -75, -30, 75, -250, -410, -115, -410, -275, 50, 90, -25, 50, -360, -225, 90, -135, 90, -225, -385, -225, -385, -705, -135, -175, -225, -135, -445, -765, -175, -765, -495, 75, 115, 75, 115, 195, -75, -35, 75, 115, -225, -135, 75, -75, 75, -485, -805, -215, -805, -535, 115, 195, -35, 115, -705, -435, 195, -255, 195, 45, 45, 33, 45, 33, -27, -27, 9, -27, 45, 33, -27, 9, -27, -3, -3, -7, -3, -7, -27, -27, -75, -75, 17, -19, -15, -19, -51, 45, 33, -27, 9, -27, -3, -7, -27, -75, 17, -19, -15, -19, -51, 109, 109, 81, 109, 81, -59, -59, 25, -59, 109, 81, -59, 25, -59, -3, -3, -7, -3, -7, -35, -35, -39, -35, -39, -59, -59, -107, -107, -59, -59, -107, -107, -203, -203, 17, -19, -15, -19, -51, 49, -35, -15, -47, -35, -67, -35, -67, -131, 45, 33, -27, 9, -27, -3, -7, -27, -75, 17, -19, -15, -19, -51, 109, 81, -59, 25, -59, -3, -7, -35, -39, -59, -107, -59, -107, -203, 17, -19, -15, -19, -51, 49, -35, -15, -47, -35, -67, -35, -67, -131, 18, 18, 15, 18, 15, 0, 0, 9, 0, 18, 15, 0, 9, 0, 6, 6, 5, 6, 5, 0, 0, -12, -12, 11, 2, 3, 2, -6, 18, 15, 0, 9, 0, 6, 5, 0, -12, 11, 2, 3, 2, -6, 109, 109, 81, 109, 81, -59, -59, 25, -59, 109, 81, -59, 25, -59, 82, 82, 63, 82, 63, -32, -32, 25, -32, 82, 63, -32, 25, -32, -21, -21, -22, -21, -22, -53, -53, -54, -53, -54, 6, 6, 5, 6, 5, -53, -53, -54, -53, -54, -26, -26, -27, -26, -27, -59, -59, -107, -107, -59, -59, -107, -107, -203, -203, -32, -32, -44, -44, -59, -59, -32, -32, -125, -125, -221, -221, -44, -44, -221, -221, -140, -140, 20, -16, -12, -16, -48, 52, -32, -12, -44, -32, -64, -32, -64, -128, 11, 2, 3, 2, -6, 52, -32, 43, -14, -24, -56, 3, -56, -29, -32, -64, -32, -64, -128, -14, -22, -32, -14, -76, -140, -22, -140, -86, 45, 33, -27, 9, -27, -3, -7, -27, -75, 17, -19, -15, -19, -51, 109, 81, -59, 25, -59, -3, -7, -35, -39, -59, -107, -59, -107, -203, 17, -19, -15, -19, -51, 49, -35, -15, -47, -35, -67, -35, -67, -131, 18, 15, 0, 9, 0, 6, 5, 0, -12, 11, 2, 3, 2, -6, 109, 81, -59, 25, -59, 82, 63, -32, 25, -32, -21, -22, -53, -54, 6, 5, -53, -54, -26, -27, -59, -107, -59, -107, -203, -32, -44, -59, -32, -125, -221, -44, -221, -140, 20, -16, -12, -16, -48, 52, -32, -12, -44, -32, -64, -32, -64, -128, 11, 2, 3, 2, -6, 52, -32, 43, -14, -24, -56, 3, -56, -29, -32, -64, -32, -64, -128, -14, -22, -32, -14, -76, -140, -22, -140, -86, -25, -25, -10, -25, -10, 65, 65, 20, 65, -25, -10, 65, 20, 65, 35, 35, 40, 35, 40, 65, 65, 125, 125, 10, 55, 50, 55, 95, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, 35, 35, 40, 35, 40, 75, 75, 80, 75, 80, 105, 105, 165, 165, 105, 105, 165, 165, 285, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -105, -105, -42, -105, -42, 273, 273, 84, 273, -105, -42, 273, 84, 273, 147, 147, 168, 147, 168, 273, 273, 525, 525, 42, 231, 210, 231, 399, -105, -42, 273, 84, 273, 147, 168, 273, 525, 42, 231, 210, 231, 399, -441, -441, -294, -441, -294, 441, 441, 0, 441, -441, -294, 441, 0, 441, 147, 147, 168, 147, 168, 315, 315, 336, 315, 336, 441, 441, 693, 693, 441, 441, 693, 693, 1197, 1197, 42, 231, 210, 231, 399, -126, 315, 210, 378, 315, 483, 315, 483, 819, -105, -42, 273, 84, 273, 147, 168, 273, 525, 42, 231, 210, 231, 399, -441, -294, 441, 0, 441, 147, 168, 315, 336, 441, 693, 441, 693, 1197, 42, 231, 210, 231, 399, -126, 315, 210, 378, 315, 483, 315, 483, 819, -64, -64, -61, -64, -61, -46, -46, -55, -46, -64, -61, -46, -55, -46, -52, -52, -51, -52, -51, -46, -46, -34, -34, -57, -48, -49, -48, -40, -64, -61, -46, -55, -46, -52, -51, -46, -34, -57, -48, -49, -48, -40, 11, 11, 14, 11, 14, 29, 29, 20, 29, 11, 14, 29, 20, 29, 23, 23, 24, 23, 24, 29, 29, 41, 41, 18, 27, 26, 27, 35, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 0, 0, 3, 0, 3, 18, 18, 9, 18, 0, 3, 18, 9, 18, 12, 12, 13, 12, 13, 18, 18, 30, 30, 7, 16, 15, 16, 24, 0, 3, 18, 9, 18, 12, 13, 18, 30, 7, 16, 15, 16, 24, 11, 11, 14, 11, 14, 29, 29, 20, 29, 11, 14, 29, 20, 29, 23, 23, 24, 23, 24, 29, 29, 41, 41, 18, 27, 26, 27, 35, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 75, 75, 78, 75, 78, 93, 93, 84, 93, 75, 78, 93, 84, 93, 87, 87, 88, 87, 88, 93, 93, 105, 105, 82, 91, 90, 91, 99, 75, 78, 93, 84, 93, 87, 88, 93, 105, 82, 91, 90, 91, 99, 345, 345, 230, 345, 230, -345, -345, 0, -345, 345, 230, -345, 0, -345, 210, 210, 140, 210, 140, -210, -210, 0, -210, 210, 140, -210, 0, -210, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, 120, 120, 80, 120, 80, -120, -120, 0, -120, 120, 80, -120, 0, -120, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, 9, 9, 6, 9, 6, -9, -9, 0, -9, 9, 6, -9, 0, -9, -18, -18, -12, -18, -12, 18, 18, 0, 18, -18, -12, 18, 0, 18, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, -441, -441, -294, -441, -294, 441, 441, 0, 441, -441, -294, 441, 0, 441, 156, 156, 104, 156, 104, -156, -156, 0, -156, 156, 104, -156, 0, -156, -69, -69, -46, -69, -46, 69, 69, 0, 69, -69, -46, 69, 0, 69, -36, -36, -24, -36, -24, 36, 36, 0, 36, -36, -24, 36, 0, 36, -69, -69, -46, -69, -46, 69, 69, 0, 69, -69, -46, 69, 0, 69, -261, -261, -174, -261, -174, 261, 261, 0, 261, -261, -174, 261, 0, 261, -241, -241, -240, -241, -240, -401, -401, -400, -401, -400, -106, -106, -105, -106, -105, -401, -401, -400, -401, -400, -266, -266, -265, -266, -265, 59, 59, 60, 59, 60, 99, 99, 100, 99, 100, -16, -16, -15, -16, -15, 59, 59, 60, 59, 60, -351, -351, -350, -351, -350, -216, -216, -215, -216, -215, 99, 99, 100, 99, 100, -126, -126, -125, -126, -125, 99, 99, 100, 99, 100, -33, -33, -32, -33, -32, -65, -65, -64, -65, -64, -6, -6, -5, -6, -5, -65, -65, -64, -65, -64, -38, -38, -37, -38, -37, 59, 59, 60, 59, 60, 99, 99, 100, 99, 100, 267, 267, 268, 267, 268, 435, 435, 436, 435, 436, -52, -52, -51, -52, -51, 23, 23, 24, 23, 24, 12, 12, 13, 12, 13, 23, 23, 24, 23, 24, 87, 87, 88, 87, 88, -351, -351, -350, -351, -350, -216, -216, -215, -216, -215, 99, 99, 100, 99, 100, -126, -126, -125, -126, -125, 99, 99, 100, 99, 100, -15, -15, -14, -15, -14, 12, 12, 13, 12, 13, 99, 99, 100, 99, 100, 435, 435, 436, 435, 436, -162, -162, -161, -162, -161, 63, 63, 64, 63, 64, 30, 30, 31, 30, 31, 63, 63, 64, 63, 64, 255, 255, 256, 255, 256, -345, -345, -585, -585, -345, -345, -585, -585, -1065, -1065, -210, -210, -270, -270, -345, -345, -210, -210, -675, -675, -1155, -1155, -270, -270, -1155, -1155, -750, -750, 105, 105, 165, 165, 105, 105, 165, 165, 285, 285, -120, -120, -60, -60, 105, 105, 165, 165, -345, -345, -210, -210, 105, 105, -120, -120, 105, 105, -735, -735, -1215, -1215, -330, -330, -1215, -1215, -810, -810, 165, 165, 285, 285, -60, -60, 165, 165, -1065, -1065, -660, -660, 285, 285, -390, -390, 285, 285, -9, -9, -57, -57, -9, -9, -57, -57, -153, -153, 18, 18, 6, 6, -9, -9, 18, 18, -75, -75, -171, -171, 6, 6, -171, -171, -90, -90, 105, 105, 165, 165, 105, 105, 165, 165, 285, 285, 441, 441, 693, 693, 441, 441, 693, 693, 1197, 1197, -156, -156, -144, -144, 69, 69, 81, 81, 36, 36, 48, 48, 69, 69, 81, 81, 261, 261, 273, 273, -345, -345, -210, -210, 105, 105, -120, -120, 105, 105, -9, -9, 18, 18, 105, 105, 441, 441, -156, -156, 69, 69, 36, 36, 69, 69, 261, 261, -711, -711, -1191, -1191, -306, -306, -1191, -1191, -786, -786, 189, 189, 309, 309, -36, -36, 189, 189, -1041, -1041, -636, -636, 309, 309, -366, -366, 309, 309, -87, -87, -183, -183, -6, -6, -183, -183, -102, -102, 189, 189, 309, 309, 813, 813, 1317, 1317, -144, -144, 81, 81, 48, 48, 81, 81, 273, 273, -1041, -1041, -636, -636, 309, 309, -366, -366, 309, 309, -33, -33, 48, 48, 309, 309, 1317, 1317, -474, -474, 201, 201, 102, 102, 201, 201, 777, 777, 6, -174, -154, -174, -334, 166, -254, -154, -314, -254, -414, -254, -414, -734, -39, -84, -79, -84, -124, 166, -254, 121, -164, -214, -374, -79, -374, -239, -254, -414, -254, -414, -734, -164, -204, -254, -164, -474, -794, -204, -794, -524, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, -69, -24, -29, -24, 16, 6, 51, 46, 51, 91, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, -254, -414, -119, -414, -279, 46, 86, -29, 46, -364, -229, 86, -139, 86, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, 22, -14, -10, -14, -46, 54, -30, -10, -42, -30, -62, -30, -62, -126, 13, 4, 5, 4, -4, 54, -30, 45, -12, -22, -54, 5, -54, -27, -30, -62, -30, -62, -126, -12, -20, -30, -12, -74, -138, -20, -138, -84, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, 22, 211, 190, 211, 379, -146, 295, 190, 358, 295, 463, 295, 463, 799, -57, -48, -49, -48, -40, 18, 27, 26, 27, 35, 7, 16, 15, 16, 24, 18, 27, 26, 27, 35, 82, 91, 90, 91, 99, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, 4, -5, -5, 13, -34, 71, -146, 295, 53, -103, -22, 47, -11, 25, -22, 47, -86, 175, -238, -398, -103, -398, -263, 62, 102, -13, 62, -348, -213, 102, -123, 102, -30, -62, -3, -62, -35, 62, 102, 270, 438, -49, 26, 15, 26, 90, -348, -213, 102, -123, 102, -12, 15, 102, 438, -159, 66, 33, 66, 258, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, -5, -37, -5, -37, -101, 13, 5, -5, 13, -49, -113, 5, -113, -59, 71, 111, 71, 111, 191, 295, 463, 295, 463, 799, -103, -95, 47, 55, 25, 33, 47, 55, 175, 183, -229, -139, 71, -79, 71, -5, 13, 71, 295, -103, 47, 25, 47, 175, -473, -793, -203, -793, -523, 127, 207, -23, 127, -693, -423, 207, -243, 207, -57, -121, -3, -121, -67, 127, 207, 543, 879, -95, 55, 33, 55, 183, -693, -423, 207, -243, 207, -21, 33, 207, 879, -315, 135, 69, 135, 519, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 305, -395, 25, -395, 310, 215, -260, 25, -260, -205, -210, -365, -370, -70, -75, -365, -370, -230, -235, -395, -635, -395, -635, -1115, -260, -320, -395, -260, -725, -1205, -320, -1205, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -100, -85, -10, -55, -10, -40, -35, -10, 50, -65, -20, -25, -20, 20, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, -265, -260, -425, -420, -130, -125, -425, -420, -290, -285, 35, 40, 75, 80, -40, -35, 35, 40, -375, -370, -240, -235, 75, 80, -150, -145, 75, 80, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, 10, -170, -150, -170, -330, 170, -250, -150, -310, -250, -410, -250, -410, -730, -35, -80, -75, -80, -120, 170, -250, 125, -160, -210, -370, -75, -370, -235, -250, -410, -250, -410, -730, -160, -200, -250, -160, -470, -790, -200, -790, -520, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -65, -20, -25, -20, 20, 10, 55, 50, 55, 95, 120, -225, 75, -135, -30, 75, 45, -75, -30, 75, -250, -410, -115, -410, -275, 50, 90, -25, 50, -360, -225, 90, -135, 90, -225, -385, -225, -385, -705, -135, -175, -225, -135, -445, -765, -175, -765, -495, 75, 115, 75, 115, 195, -75, -35, 75, 115, -225, -135, 75, -75, 75, -485, -805, -215, -805, -535, 115, 195, -35, 115, -705, -435, 195, -255, 195, 45, 33, -27, 9, -27, -3, -7, -27, -75, 17, -19, -15, -19, -51, 109, 81, -59, 25, -59, -3, -7, -35, -39, -59, -107, -59, -107, -203, 17, -19, -15, -19, -51, 49, -35, -15, -47, -35, -67, -35, -67, -131, 18, 15, 0, 9, 0, 6, 5, 0, -12, 11, 2, 3, 2, -6, 109, 81, -59, 25, -59, 82, 63, -32, 25, -32, -21, -22, -53, -54, 6, 5, -53, -54, -26, -27, -59, -107, -59, -107, -203, -32, -44, -59, -32, -125, -221, -44, -221, -140, 20, -16, -12, -16, -48, 52, -32, -12, -44, -32, -64, -32, -64, -128, 11, 2, 3, 2, -6, 52, -32, 43, -14, -24, -56, 3, -56, -29, -32, -64, -32, -64, -128, -14, -22, -32, -14, -76, -140, -22, -140, -86, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -105, -42, 273, 84, 273, 147, 168, 273, 525, 42, 231, 210, 231, 399, -441, -294, 441, 0, 441, 147, 168, 315, 336, 441, 693, 441, 693, 1197, 42, 231, 210, 231, 399, -126, 315, 210, 378, 315, 483, 315, 483, 819, -64, -61, -46, -55, -46, -52, -51, -46, -34, -57, -48, -49, -48, -40, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 0, 3, 18, 9, 18, 12, 13, 18, 30, 7, 16, 15, 16, 24, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 75, 78, 93, 84, 93, 87, 88, 93, 105, 82, 91, 90, 91, 99, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, 9, 6, -9, 0, -9, -18, -12, 18, 0, 18, -105, -70, 105, 0, 105, -441, -294, 441, 0, 441, 156, 104, -156, 0, -156, -69, -46, 69, 0, 69, -36, -24, 36, 0, 36, -69, -46, 69, 0, 69, -261, -174, 261, 0, 261, -241, -240, -401, -400, -106, -105, -401, -400, -266, -265, 59, 60, 99, 100, -16, -15, 59, 60, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -33, -32, -65, -64, -6, -5, -65, -64, -38, -37, 59, 60, 99, 100, 267, 268, 435, 436, -52, -51, 23, 24, 12, 13, 23, 24, 87, 88, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -15, -14, 12, 13, 99, 100, 435, 436, -162, -161, 63, 64, 30, 31, 63, 64, 255, 256, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, -9, -57, -9, -57, -153, 18, 6, -9, 18, -75, -171, 6, -171, -90, 105, 165, 105, 165, 285, 441, 693, 441, 693, 1197, -156, -144, 69, 81, 36, 48, 69, 81, 261, 273, -345, -210, 105, -120, 105, -9, 18, 105, 441, -156, 69, 36, 69, 261, -711, -1191, -306, -1191, -786, 189, 309, -36, 189, -1041, -636, 309, -366, 309, -87, -183, -6, -183, -102, 189, 309, 813, 1317, -144, 81, 48, 81, 273, -1041, -636, 309, -366, 309, -33, 48, 309, 1317, -474, 201, 102, 201, 777, 6, -174, -154, -174, -334, 166, -254, -154, -314, -254, -414, -254, -414, -734, -39, -84, -79, -84, -124, 166, -254, 121, -164, -214, -374, -79, -374, -239, -254, -414, -254, -414, -734, -164, -204, -254, -164, -474, -794, -204, -794, -524, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, -69, -24, -29, -24, 16, 6, 51, 46, 51, 91, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, -254, -414, -119, -414, -279, 46, 86, -29, 46, -364, -229, 86, -139, 86, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, 22, -14, -10, -14, -46, 54, -30, -10, -42, -30, -62, -30, -62, -126, 13, 4, 5, 4, -4, 54, -30, 45, -12, -22, -54, 5, -54, -27, -30, -62, -30, -62, -126, -12, -20, -30, -12, -74, -138, -20, -138, -84, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, 22, 211, 190, 211, 379, -146, 295, 190, 358, 295, 463, 295, 463, 799, -57, -48, -49, -48, -40, 18, 27, 26, 27, 35, 7, 16, 15, 16, 24, 18, 27, 26, 27, 35, 82, 91, 90, 91, 99, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, 4, -5, -5, 13, -34, 71, -146, 295, 53, -103, -22, 47, -11, 25, -22, 47, -86, 175, -238, -398, -103, -398, -263, 62, 102, -13, 62, -348, -213, 102, -123, 102, -30, -62, -3, -62, -35, 62, 102, 270, 438, -49, 26, 15, 26, 90, -348, -213, 102, -123, 102, -12, 15, 102, 438, -159, 66, 33, 66, 258, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, -5, -37, -5, -37, -101, 13, 5, -5, 13, -49, -113, 5, -113, -59, 71, 111, 71, 111, 191, 295, 463, 295, 463, 799, -103, -95, 47, 55, 25, 33, 47, 55, 175, 183, -229, -139, 71, -79, 71, -5, 13, 71, 295, -103, 47, 25, 47, 175, -473, -793, -203, -793, -523, 127, 207, -23, 127, -693, -423, 207, -243, 207, -57, -121, -3, -121, -67, 127, 207, 543, 879, -95, 55, 33, 55, 183, -693, -423, 207, -243, 207, -21, 33, 207, 879, -315, 135, 69, 135, 519])\n assert answers_match(candidate(expression='10-5+3-2+1*2*3-4*5'), [-30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -100, -28, -40, -28, 32, -66, -18, -100, -28, -10, -10, 0, -6, 0, 2, 22, 2, 22, 22, -28, 32, -18, -28, 22, 22, 72, 42, 72, 38, 14, 18, 14, -6, 38, 14, 18, 18, 14, -6, 14, -6, -6, 5, 5, 5, 5, 5, 73, 25, 33, 25, -15, -12, 0, -46, -10, 56, 20, 5, 5, 73, 25, 30, 30, 40, 34, 40, 18, 18, 25, 13, 28, 34, 16, 25, 13, -10, 10, -10, 10, 10, -40, 20, -30, -40, 10, 10, 60, 30, 60, 10, -10, 10, -10, -10, 5, 5, 25, -15, 0, -10, 20, 5, 25, 50, 50, 100, 70, 100, -10, -10, 25, -35, 40, 70, -20, 25, -35, -30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -100, -28, -40, -28, 32, -66, -18, -100, -28, -10, -10, 0, -6, 0, 2, 22, 2, 22, 22, -28, 32, -18, -28, 22, 22, 72, 42, 72, 38, 14, 18, 14, -6, 38, 14, 18, 18, 14, -6, 14, -6, -6, 38, 14, 18, 14, -6, 38, 14, 18, 18, 14, -6, 14, -6, -6, 180, 60, 80, 60, -40, 248, 80, 108, 80, -60, 180, 60, 80, 60, -40, 248, 80, 108, 80, -60, 248, 80, 108, 80, -60, 78, 30, 44, 20, 146, 50, 95, 35, 163, 55, 78, 30, 44, 20, 146, 50, 146, 50, 180, 60, 248, 80, 180, 60, 248, 80, 248, 80, 30, 30, 40, 34, 40, 18, 18, 25, 13, 28, 34, 16, 25, 13, 30, 30, 40, 34, 40, 18, 18, 18, 18, 0, -12, 0, -12, -12, 18, 24, 6, 15, 3, 18, 24, 6, 6, 0, -12, 0, -12, -12, -30, -10, -30, -10, -10, -60, 0, -50, -60, -10, -10, 40, 10, 40, -10, -30, -10, -30, -30, -15, -15, 5, -35, -20, -30, 0, -15, 5, 30, 30, 80, 50, 80, -30, -30, 5, -55, 20, 50, -40, 5, -55, -30, -10, -30, -10, -10, -60, 0, -50, -60, -10, -10, 40, 10, 40, -10, -30, -10, -30, -30, -10, -30, -10, -30, -30, 60, -40, 80, -60, 60, -40, 80, -60, 80, -60, 30, 20, 50, 35, 55, 30, 20, 50, 50, 60, 80, 60, 80, 80, 30, 30, 80, 50, 80, -30, -30, 5, -55, 20, 50, -40, 5, -55, 30, 30, 80, 50, 80, -30, -30, -30, -30, -120, -180, -120, -180, -180, -30, 0, -90, -45, -105, -30, 0, -90, -90, -120, -180, -120, -180, -180, 40, 16, 20, 16, -4, 40, 16, 20, 20, 16, -4, 16, -4, -4, 110, 38, 50, 38, -22, 76, 28, 110, 38, 20, 20, 10, 16, 10, 8, -12, 8, -12, -12, 38, -22, 28, 38, -12, -12, -62, -32, -62, -28, -4, -8, -4, 16, -28, -4, -8, -8, -4, 16, -4, 16, 16, 5, 5, 5, 5, 5, -63, -15, -23, -15, 25, 22, 10, 56, 20, -46, -10, 5, 5, -63, -15, -20, -20, -30, -24, -30, -8, -8, -15, -3, -18, -24, -6, -15, -3, 20, 0, 20, 0, 0, 50, -10, 40, 50, 0, 0, -50, -20, -50, 0, 20, 0, 20, 20, 5, 5, -15, 25, 10, 20, -10, 5, -15, -40, -40, -90, -60, -90, 20, 20, -15, 45, -30, -60, 30, -15, 45, 34, 10, 14, 10, -10, 34, 10, 14, 14, 10, -10, 10, -10, -10, 104, 32, 44, 32, -28, 70, 22, 104, 32, 14, 14, 4, 10, 4, 2, -18, 2, -18, -18, 32, -28, 22, 32, -18, -18, -68, -38, -68, 40, 16, 20, 16, -4, 40, 16, 20, 20, 16, -4, 16, -4, -4, 110, 38, 50, 38, -22, 76, 28, 110, 38, 20, 20, 10, 16, 10, 8, -12, 8, -12, -12, 38, -22, 28, 38, -12, -12, -62, -32, -62, -30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -28, -4, -8, -4, 16, -28, -4, -8, -8, -4, 16, -4, 16, 16, -34, -10, -14, -10, 10, -34, -10, -14, -14, -10, 10, -10, 10, 10, -28, -4, -8, -4, 16, -28, -4, -8, -8, -4, 16, -4, 16, 16, -170, -50, -70, -50, 50, -102, -30, -42, -30, 30, -170, -50, -70, -50, 50, -102, -30, -42, -30, 30, -102, -30, -42, -30, 30, -170, -50, -70, -50, 50, -238, -70, -98, -70, 70, 34, 10, 14, 10, -10, -170, -50, -70, -50, 50, -170, -50, -70, -50, 50, -170, -50, -70, -50, 50, -238, -70, -98, -70, 70, -34, -10, -14, -10, 10, -238, -70, -98, -70, 70, -102, -30, -136, -40, -34, -10, -85, -25, -17, -5, -102, -30, -136, -40, -34, -10, -34, -10, 0, 0, 68, 20, 0, 0, 68, 20, 68, 20, -68, -20, -34, -10, -136, -40, -85, -25, -153, -45, 34, 10, 68, 20, -68, -20, -34, -10, -102, -30, -102, -30, -136, -40, -34, -10, -136, -40, -170, -50, -102, -30, -170, -50, -102, -30, -102, -30, -170, -50, -238, -70, 34, 10, -170, -50, -170, -50, -170, -50, -238, -70, -34, -10, -238, -70, -10, -10, 0, -6, 0, -22, -22, -15, -27, -12, -6, -24, -15, -27, -10, -10, 0, -6, 0, -22, -22, -22, -22, -40, -52, -40, -52, -52, -22, -16, -34, -25, -37, -22, -16, -34, -34, -40, -52, -40, -52, -52, -20, -20, -30, -24, -30, -8, -8, -15, -3, -18, -24, -6, -15, -3, -26, -26, -36, -30, -36, -20, -20, -30, -24, -30, -10, -10, -10, -10, -8, -8, -14, -14, -8, -8, 10, -2, 10, -2, -2, 10, 22, -26, 10, 10, 10, 22, -14, 22, -2, 4, -14, -5, -17, -2, 4, -14, -14, -20, -32, -20, -32, -32, -8, -14, 4, -5, 7, -26, -32, -8, -14, -2, -2, 4, -14, 4, 10, -2, 10, -2, -2, 10, 22, -26, 10, 10, 10, 22, -14, 22, 10, 30, 10, 30, 30, -20, 40, -10, -20, 30, 30, 80, 50, 80, 30, 10, 30, 10, 10, 25, 25, 45, 5, 20, 10, 40, 25, 45, 70, 70, 120, 90, 120, 10, 10, 45, -15, 60, 90, 0, 45, -15, 10, 30, 10, 30, 30, -20, 40, -10, -20, 30, 30, 80, 50, 80, 30, 10, 30, 10, 10, 30, 10, 30, 10, 10, 100, 0, 120, -20, 100, 0, 120, -20, 120, -20, 70, 60, 90, 75, 95, 70, 60, 90, 90, 100, 120, 100, 120, 120, 70, 70, 120, 90, 120, 10, 10, 45, -15, 60, 90, 0, 45, -15, 70, 70, 120, 90, 120, 10, 10, 10, 10, -80, -140, -80, -140, -140, 10, 40, -50, -5, -65, 10, 40, -50, -50, -80, -140, -80, -140, -140, 40, 20, 40, 20, 20, 70, 10, 60, 70, 20, 20, -30, 0, -30, 20, 40, 20, 40, 40, 25, 25, 5, 45, 30, 40, 10, 25, 5, -20, -20, -70, -40, -70, 40, 40, 5, 65, -10, -40, 50, 5, 65, 10, -10, 10, -10, -10, 40, -20, 30, 40, -10, -10, -60, -30, -60, 40, 20, 40, 20, 20, 70, 10, 60, 70, 20, 20, -30, 0, -30, 10, 30, 10, 30, 30, 10, 30, 10, 30, 30, 20, 40, 20, 40, 40, -10, 10, -10, 10, 10, 20, 40, 20, 40, 40, -50, 50, -30, 30, -50, 50, -30, 30, -30, 30, -50, 50, -70, 70, 10, -10, -50, 50, -50, 50, -50, 50, -70, 70, -10, 10, -70, 70, -30, -40, -10, -25, -5, -30, -40, -10, -10, 0, 20, 0, 20, 20, -20, -10, -40, -25, -45, 10, 20, -20, -10, -30, -30, -40, -10, -40, -50, -30, -50, -30, -30, -50, -70, 10, -50, -50, -50, -70, -10, -70, 30, 30, 80, 50, 80, -30, -30, 5, -55, 20, 50, -40, 5, -55, 30, 30, 80, 50, 80, -30, -30, -30, -30, -120, -180, -120, -180, -180, -30, 0, -90, -45, -105, -30, 0, -90, -90, -120, -180, -120, -180, -180, -20, -20, -70, -40, -70, 40, 40, 5, 65, -10, -40, 50, 5, 65, -50, -50, -100, -70, -100, -20, -20, -70, -40, -70, 30, 30, 30, 30, 40, 40, 10, 10, 40, 40, 130, 70, 130, 70, 70, 130, 190, -50, 130, 130, 130, 190, 10, 190, 70, 100, 10, 55, -5, 70, 100, 10, 10, -20, -80, -20, -80, -80, 40, 10, 100, 55, 115, -50, -80, 40, 10, 70, 70, 100, 10, 100, 130, 70, 130, 70, 70, 130, 190, -50, 130, 130, 130, 190, 10, 190])\n assert answers_match(candidate(expression='1*2+3-4*5+6*7-8*9+10'), [3465, 1785, 441, 1305, -39, 425, 145, 441, -2599, 1505, 161, 65, 161, -1279, 6385, 3305, 841, 2425, -39, 425, 145, 305, 25, 81, -2959, 841, -2959, -5239, 1505, 161, 65, 161, -1279, 2825, 361, 65, -55, 1, -1439, 361, -1439, -2519, 855, 435, 99, 315, -21, 95, 25, 99, -661, 365, 29, 5, 29, -331, 6385, 3305, 841, 2425, -39, 3775, 1955, 499, 1435, -21, -31, -101, -151, -221, 95, 25, -151, -221, -25, -95, 81, -2959, 841, -2959, -5239, -261, -1021, 841, 499, -3415, -5695, -1021, -5695, -3301, 1535, 191, 95, 191, -1249, 2855, 391, 95, -25, 31, -1409, 391, -1409, -2489, 365, 29, 5, 29, -331, 2855, 391, 1685, 229, -121, -241, 5, -241, -115, 31, -1409, 391, -1409, -2489, -131, -491, 391, 229, -1625, -2705, -491, -2705, -1571, 867, 447, 111, 327, -9, 107, 37, 111, -649, 377, 41, 17, 41, -319, 1597, 827, 211, 607, -9, 107, 37, 77, 7, 21, -739, 211, -739, -1309, 377, 41, 17, 41, -319, 707, 91, 17, -13, 1, -359, 91, -359, -629, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -873, -453, -117, -333, 3, -113, -43, -117, 643, -383, -47, -23, -47, 313, 5947, 3077, 781, 2257, -39, 3337, 1727, 439, 1267, -21, 1597, 827, 211, 607, -9, 1597, 827, 211, 607, -9, -143, -73, -17, -53, 3, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -197, -127, -227, -157, -125, -55, -113, -43, -437, -367, -311, -241, -227, -157, -227, -157, -143, -73, 135, -2905, 895, -2905, -5185, -207, -967, 895, 553, -3361, -5641, -967, -5641, -3247, 21, -739, 211, -739, -1309, -435, 325, -207, 553, 781, 439, 211, 211, -17, -3665, -5945, -1271, -5945, -3551, -1043, -1613, 325, 553, -5603, -3209, -1613, -1613, -17, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, 397, 61, 37, 61, -299, 727, 111, 37, 7, 21, -339, 111, -339, -609, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, 2677, 381, 1507, 219, 727, 111, 727, 111, -53, 3, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, 75, -1365, 435, -1365, -2445, -87, -447, 435, 273, -1581, -2661, -447, -2661, -1527, 21, -339, 111, -339, -609, -195, 165, -87, 273, 381, 219, 111, 111, 3, -1725, -2805, -591, -2805, -1671, -483, -753, 165, 273, -2643, -1509, -753, -753, 3, 3465, 1785, 441, 1305, -39, 425, 145, 441, -2599, 1505, 161, 65, 161, -1279, 6385, 3305, 841, 2425, -39, 425, 145, 305, 25, 81, -2959, 841, -2959, -5239, 1505, 161, 65, 161, -1279, 2825, 361, 65, -55, 1, -1439, 361, -1439, -2519, 855, 435, 99, 315, -21, 95, 25, 99, -661, 365, 29, 5, 29, -331, 6385, 3305, 841, 2425, -39, 3775, 1955, 499, 1435, -21, -31, -101, -151, -221, 95, 25, -151, -221, -25, -95, 81, -2959, 841, -2959, -5239, -261, -1021, 841, 499, -3415, -5695, -1021, -5695, -3301, 1535, 191, 95, 191, -1249, 2855, 391, 95, -25, 31, -1409, 391, -1409, -2489, 365, 29, 5, 29, -331, 2855, 391, 1685, 229, -121, -241, 5, -241, -115, 31, -1409, 391, -1409, -2489, -131, -491, 391, 229, -1625, -2705, -491, -2705, -1571, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -873, -453, -117, -333, 3, -113, -43, -117, 643, -383, -47, -23, -47, 313, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, 1305, 675, 171, 495, -9, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 1305, 675, 171, 495, -9, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -197, -127, -227, -157, -125, -55, -113, -43, -437, -367, -311, -241, -227, -157, -227, -157, -143, -73, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -105, -35, -75, -5, -105, -35, -75, -5, -125, -55, -113, -43, -125, -55, -105, -35, -105, -35, -425, -355, -299, -229, -215, -145, -215, -145, -131, -61, -425, -355, -299, -229, -75, -5, -75, -5, -215, -145, -131, -61, -215, -145, -75, -5, -75, -5, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, 57, -703, 247, -703, -1273, -399, 361, -171, 589, 817, 475, 247, 247, 19, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -399, 361, -171, 589, -399, 361, -19, 741, -19, 741, 741, 399, 171, 171, -57, 741, 399, -209, -209, 171, -57, 171, -209, -209, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, -3629, -5909, -1235, -5909, -3515, 741, 1311, 741, 1311, 361, 589, 361, 741, 741, -5339, -2945, -1349, -1349, 247, -5339, -2945, 1311, 1311, -1349, 247, -1349, 1311, 1311, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, 397, 61, 37, 61, -299, 727, 111, 37, 7, 21, -339, 111, -339, -609, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, 2677, 381, 1507, 219, 727, 111, 727, 111, -53, 3, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, 75, -1365, 435, -1365, -2445, -87, -447, 435, 273, -1581, -2661, -447, -2661, -1527, 21, -339, 111, -339, -609, -195, 165, -87, 273, 381, 219, 111, 111, 3, -1725, -2805, -591, -2805, -1671, -483, -753, 165, 273, -2643, -1509, -753, -753, 3, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, -395, -59, -35, -59, 301, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, 2545, 361, 1375, 199, 595, 91, 595, 91, -185, -17, 2545, 361, 1375, 199, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, -705, -89, -705, -89, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, -245, -365, -119, -365, -239, -15, 15, -15, 15, -35, -23, -35, -15, -15, -335, -209, -125, -125, -41, -335, -209, 15, 15, -125, -41, -125, 15, 15, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 37, -323, 127, -323, -593, -179, 181, -71, 289, 397, 235, 127, 127, 19, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, -179, 181, -71, 289, -179, 181, 1, 361, 1, 361, 361, 199, 91, 91, -17, 361, 199, -89, -89, 91, -17, 91, -89, -89, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 181, 289, 181, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, 3465, 1785, 441, 1305, -39, 425, 145, 441, -2599, 1505, 161, 65, 161, -1279, 6385, 3305, 841, 2425, -39, 425, 145, 305, 25, 81, -2959, 841, -2959, -5239, 1505, 161, 65, 161, -1279, 2825, 361, 65, -55, 1, -1439, 361, -1439, -2519, 855, 435, 99, 315, -21, 95, 25, 99, -661, 365, 29, 5, 29, -331, 6385, 3305, 841, 2425, -39, 3775, 1955, 499, 1435, -21, -31, -101, -151, -221, 95, 25, -151, -221, -25, -95, 81, -2959, 841, -2959, -5239, -261, -1021, 841, 499, -3415, -5695, -1021, -5695, -3301, 1535, 191, 95, 191, -1249, 2855, 391, 95, -25, 31, -1409, 391, -1409, -2489, 365, 29, 5, 29, -331, 2855, 391, 1685, 229, -121, -241, 5, -241, -115, 31, -1409, 391, -1409, -2489, -131, -491, 391, 229, -1625, -2705, -491, -2705, -1571, 867, 447, 111, 327, -9, 107, 37, 111, -649, 377, 41, 17, 41, -319, 1597, 827, 211, 607, -9, 107, 37, 77, 7, 21, -739, 211, -739, -1309, 377, 41, 17, 41, -319, 707, 91, 17, -13, 1, -359, 91, -359, -629, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -873, -453, -117, -333, 3, -113, -43, -117, 643, -383, -47, -23, -47, 313, 5947, 3077, 781, 2257, -39, 3337, 1727, 439, 1267, -21, 1597, 827, 211, 607, -9, 1597, 827, 211, 607, -9, -143, -73, -17, -53, 3, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -197, -127, -227, -157, -125, -55, -113, -43, -437, -367, -311, -241, -227, -157, -227, -157, -143, -73, 135, -2905, 895, -2905, -5185, -207, -967, 895, 553, -3361, -5641, -967, -5641, -3247, 21, -739, 211, -739, -1309, -435, 325, -207, 553, 781, 439, 211, 211, -17, -3665, -5945, -1271, -5945, -3551, -1043, -1613, 325, 553, -5603, -3209, -1613, -1613, -17, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, 397, 61, 37, 61, -299, 727, 111, 37, 7, 21, -339, 111, -339, -609, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, 2677, 381, 1507, 219, 727, 111, 727, 111, -53, 3, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, 75, -1365, 435, -1365, -2445, -87, -447, 435, 273, -1581, -2661, -447, -2661, -1527, 21, -339, 111, -339, -609, -195, 165, -87, 273, 381, 219, 111, 111, 3, -1725, -2805, -591, -2805, -1671, -483, -753, 165, 273, -2643, -1509, -753, -753, 3, 3465, 1785, 441, 1305, -39, 425, 145, 441, -2599, 1505, 161, 65, 161, -1279, 6385, 3305, 841, 2425, -39, 425, 145, 305, 25, 81, -2959, 841, -2959, -5239, 1505, 161, 65, 161, -1279, 2825, 361, 65, -55, 1, -1439, 361, -1439, -2519, 855, 435, 99, 315, -21, 95, 25, 99, -661, 365, 29, 5, 29, -331, 6385, 3305, 841, 2425, -39, 3775, 1955, 499, 1435, -21, -31, -101, -151, -221, 95, 25, -151, -221, -25, -95, 81, -2959, 841, -2959, -5239, -261, -1021, 841, 499, -3415, -5695, -1021, -5695, -3301, 1535, 191, 95, 191, -1249, 2855, 391, 95, -25, 31, -1409, 391, -1409, -2489, 365, 29, 5, 29, -331, 2855, 391, 1685, 229, -121, -241, 5, -241, -115, 31, -1409, 391, -1409, -2489, -131, -491, 391, 229, -1625, -2705, -491, -2705, -1571, 3465, 1785, 441, 1305, -39, 425, 145, 441, -2599, 1505, 161, 65, 161, -1279, 6385, 3305, 841, 2425, -39, 425, 145, 305, 25, 81, -2959, 841, -2959, -5239, 1505, 161, 65, 161, -1279, 2825, 361, 65, -55, 1, -1439, 361, -1439, -2519, 855, 435, 99, 315, -21, 95, 25, 99, -661, 365, 29, 5, 29, -331, 6385, 3305, 841, 2425, -39, 3775, 1955, 499, 1435, -21, -31, -101, -151, -221, 95, 25, -151, -221, -25, -95, 81, -2959, 841, -2959, -5239, -261, -1021, 841, 499, -3415, -5695, -1021, -5695, -3301, 1535, 191, 95, 191, -1249, 2855, 391, 95, -25, 31, -1409, 391, -1409, -2489, 365, 29, 5, 29, -331, 2855, 391, 1685, 229, -121, -241, 5, -241, -115, 31, -1409, 391, -1409, -2489, -131, -491, 391, 229, -1625, -2705, -491, -2705, -1571, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -1595, -825, -209, -605, 11, -105, -35, -75, -5, -19, 741, -209, 741, 1311, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -873, -453, -117, -333, 3, -113, -43, -117, 643, -383, -47, -23, -47, 313, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -873, -453, -117, -333, 3, -113, -43, -117, 643, -383, -47, -23, -47, 313, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, -865, -445, -109, -325, 11, -105, -35, -109, 651, -375, -39, -15, -39, 321, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, 1305, 675, 171, 495, -9, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 1305, 675, 171, 495, -9, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, 1305, 675, 171, 495, -9, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, 5655, 2925, 741, 2145, -39, 3045, 1575, 399, 1155, -21, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 1305, 675, 171, 495, -9, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, 1305, 675, 171, 495, -9, -435, -225, -57, -165, 3, 1305, 675, 171, 495, -9, 1305, 675, 171, 495, -9, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -1595, -825, -209, -605, 11, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -197, -127, -227, -157, -125, -55, -113, -43, -437, -367, -311, -241, -227, -157, -227, -157, -143, -73, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -105, -35, -75, -5, -105, -35, -75, -5, -125, -55, -113, -43, -125, -55, -105, -35, -105, -35, -425, -355, -299, -229, -215, -145, -215, -145, -131, -61, -425, -355, -299, -229, -75, -5, -75, -5, -215, -145, -131, -61, -215, -145, -75, -5, -75, -5, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -197, -127, -227, -157, -125, -55, -113, -43, -437, -367, -311, -241, -227, -157, -227, -157, -143, -73, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -335, -265, -455, -385, -209, -139, -455, -385, -329, -259, -105, -35, -75, -5, -105, -35, -75, -5, -105, -35, -75, -5, -105, -35, -75, -5, -105, -35, -75, -5, -125, -55, -113, -43, -125, -55, -105, -35, -105, -35, -125, -55, -113, -43, -125, -55, -125, -55, -105, -35, -105, -35, -105, -35, -105, -35, -105, -35, -425, -355, -299, -229, -215, -145, -215, -145, -131, -61, -425, -355, -299, -229, -75, -5, -75, -5, -215, -145, -131, -61, -215, -145, -75, -5, -75, -5, -425, -355, -299, -229, -215, -145, -215, -145, -131, -61, -425, -355, -299, -229, -425, -355, -299, -229, -75, -5, -75, -5, -75, -5, -75, -5, -75, -5, -215, -145, -131, -61, -215, -145, -75, -5, -75, -5, -215, -145, -131, -61, -215, -145, -215, -145, -75, -5, -75, -5, -75, -5, -75, -5, -75, -5, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, 57, -703, 247, -703, -1273, -399, 361, -171, 589, 817, 475, 247, 247, 19, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -399, 361, -171, 589, -399, 361, -19, 741, -19, 741, 741, 399, 171, 171, -57, 741, 399, -209, -209, 171, -57, 171, -209, -209, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, -3629, -5909, -1235, -5909, -3515, 741, 1311, 741, 1311, 361, 589, 361, 741, 741, -5339, -2945, -1349, -1349, 247, -5339, -2945, 1311, 1311, -1349, 247, -1349, 1311, 1311, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, 57, -703, 247, -703, -1273, -399, 361, -171, 589, 817, 475, 247, 247, 19, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -399, 361, -171, 589, -399, 361, -19, 741, -19, 741, -399, 361, -171, 589, -399, 361, -399, 361, -19, 741, -19, 741, -19, 741, -19, 741, -19, 741, 741, 399, 171, 171, -57, 741, 399, -209, -209, 171, -57, 171, -209, -209, 741, 399, 171, 171, -57, 741, 399, 741, 399, -209, -209, -209, -209, -209, 171, -57, 171, -209, -209, 171, -57, 171, 171, -209, -209, -209, -209, -209, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, -3629, -5909, -1235, -5909, -3515, 741, 1311, 741, 1311, 361, 589, 361, 741, 741, -5339, -2945, -1349, -1349, 247, -5339, -2945, 1311, 1311, -1349, 247, -1349, 1311, 1311, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, -3629, -5909, -1235, -5909, -3515, -3629, -5909, -1235, -5909, -3515, 741, 1311, 741, 1311, 741, 1311, 741, 1311, 741, 1311, 361, 589, 361, 741, 741, 361, 589, 361, 361, 741, 741, 741, 741, 741, -5339, -2945, -1349, -1349, 247, -5339, -2945, 1311, 1311, -1349, 247, -1349, 1311, 1311, -5339, -2945, -1349, -1349, 247, -5339, -2945, -5339, -2945, 1311, 1311, 1311, 1311, 1311, -1349, 247, -1349, 1311, 1311, -1349, 247, -1349, -1349, 1311, 1311, 1311, 1311, 1311, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, 397, 61, 37, 61, -299, 727, 111, 37, 7, 21, -339, 111, -339, -609, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, 2677, 381, 1507, 219, 727, 111, 727, 111, -53, 3, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, 75, -1365, 435, -1365, -2445, -87, -447, 435, 273, -1581, -2661, -447, -2661, -1527, 21, -339, 111, -339, -609, -195, 165, -87, 273, 381, 219, 111, 111, 3, -1725, -2805, -591, -2805, -1671, -483, -753, 165, 273, -2643, -1509, -753, -753, 3, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, -395, -59, -35, -59, 301, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, 2545, 361, 1375, 199, 595, 91, 595, 91, -185, -17, 2545, 361, 1375, 199, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, -705, -89, -705, -89, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, -245, -365, -119, -365, -239, -15, 15, -15, 15, -35, -23, -35, -15, -15, -335, -209, -125, -125, -41, -335, -209, 15, 15, -125, -41, -125, 15, 15, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 37, -323, 127, -323, -593, -179, 181, -71, 289, 397, 235, 127, 127, 19, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, -179, 181, -71, 289, -179, 181, 1, 361, 1, 361, 361, 199, 91, 91, -17, 361, 199, -89, -89, 91, -17, 91, -89, -89, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 181, 289, 181, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, 397, 61, 37, 61, -299, 727, 111, 37, 7, 21, -339, 111, -339, -609, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, 2677, 381, 1507, 219, 727, 111, 727, 111, -53, 3, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, 75, -1365, 435, -1365, -2445, -87, -447, 435, 273, -1581, -2661, -447, -2661, -1527, 21, -339, 111, -339, -609, -195, 165, -87, 273, 381, 219, 111, 111, 3, -1725, -2805, -591, -2805, -1671, -483, -753, 165, 273, -2643, -1509, -753, -753, 3, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, 1555, 211, 115, 211, -1229, 2875, 411, 115, -5, 51, -1389, 411, -1389, -2469, 385, 49, 25, 49, -311, 2875, 411, 1705, 249, -101, -221, 25, -221, -95, 51, -1389, 411, -1389, -2469, -111, -471, 411, 249, -1605, -2685, -471, -2685, -1551, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -375, -39, -15, -39, 321, -705, -89, -15, 15, 1, 361, -89, 361, 631, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, -395, -59, -35, -59, 301, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, -395, -59, -35, -59, 301, -395, -59, -35, -59, 301, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, 2545, 361, 1375, 199, 595, 91, 595, 91, -185, -17, 2545, 361, 1375, 199, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, -705, -89, -705, -89, 2545, 361, 1375, 199, 595, 91, 595, 91, -185, -17, 2545, 361, 1375, 199, 2545, 361, 1375, 199, -705, -89, -705, -89, -705, -89, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, 595, 91, -705, -89, -705, -89, -705, -89, -705, -89, -705, -89, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, -245, -365, -119, -365, -239, -15, 15, -15, 15, -35, -23, -35, -15, -15, -335, -209, -125, -125, -41, -335, -209, 15, 15, -125, -41, -125, 15, 15, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, -245, -365, -119, -365, -239, -245, -365, -119, -365, -239, -15, 15, -15, 15, -15, 15, -15, 15, -15, 15, -35, -23, -35, -15, -15, -35, -23, -35, -35, -15, -15, -15, -15, -15, -335, -209, -125, -125, -41, -335, -209, 15, 15, -125, -41, -125, 15, 15, -335, -209, -125, -125, -41, -335, -209, -335, -209, 15, 15, 15, 15, 15, -125, -41, -125, 15, 15, -125, -41, -125, -125, 15, 15, 15, 15, 15, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 37, -323, 127, -323, -593, -179, 181, -71, 289, 397, 235, 127, 127, 19, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, -179, 181, -71, 289, -179, 181, 1, 361, 1, 361, 361, 199, 91, 91, -17, 361, 199, -89, -89, 91, -17, 91, -89, -89, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 181, 289, 181, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 37, -323, 127, -323, -593, -179, 181, -71, 289, 397, 235, 127, 127, 19, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, -179, 181, -71, 289, -179, 181, 1, 361, 1, 361, -179, 181, -71, 289, -179, 181, -179, 181, 1, 361, 1, 361, 1, 361, 1, 361, 1, 361, 361, 199, 91, 91, -17, 361, 199, -89, -89, 91, -17, 91, -89, -89, 361, 199, 91, 91, -17, 361, 199, 361, 199, -89, -89, -89, -89, -89, 91, -17, 91, -89, -89, 91, -17, 91, 91, -89, -89, -89, -89, -89, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 181, 289, 181, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 361, 631, 361, 631, 361, 631, 181, 289, 181, 361, 361, 181, 289, 181, 181, 361, 361, 361, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, -2519, -1385, -629, -629, 127, -2519, -1385, -2519, -1385, 631, 631, 631, 631, 631, -629, 127, -629, 631, 631, -629, 127, -629, -629, 631, 631, 631, 631, 631])\n assert answers_match(candidate(expression='1*2*3+4*5*6-7*8*9'), [-19914, -19914, -2874, -17994, -2874, -3786, -3786, -2874, 13254, -17994, -2874, -1866, -2874, 13254, -19914, -19914, -2874, -17994, -2874, -762, -762, -762, -762, -2874, 13254, -2874, 16278, 16278, -17994, -2874, -1866, -2874, 13254, -17994, -2874, 1158, 1158, -2874, 13254, -2874, 16278, 16278, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -762, -762, -762, -762, -588, -588, -732, -732, -588, -588, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -9954, -9954, -1434, -8994, -1434, -1890, -1890, -1434, 6630, -8994, -1434, -930, -1434, 6630, -9954, -9954, -1434, -8994, -1434, -378, -378, -378, -378, -1434, 6630, -1434, 8142, 8142, -8994, -1434, -930, -1434, 6630, -8994, -1434, 582, 582, -1434, 6630, -1434, 8142, 8142, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -12948, -12948, -1872, -11700, -1872, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -258, -258, -258, -258, -84, -84, -228, -228, -84, -84, -378, -378, -378, -378, -84, -84, -204, -204, -228, -228, -84, -84, -348, -348, -84, -84, -204, -204, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -20700, -3312, -31500, -5040, -11700, -1872, -31500, -5040, -22500, -3600, 1710, 1710, 3276, 1980, 3276, 630, 630, 3276, 2196, 1980, 3276, 900, 3276, 2196, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -19914, -19914, -2874, -17994, -2874, -3786, -3786, -2874, 13254, -17994, -2874, -1866, -2874, 13254, -19914, -19914, -2874, -17994, -2874, -762, -762, -762, -762, -2874, 13254, -2874, 16278, 16278, -17994, -2874, -1866, -2874, 13254, -17994, -2874, 1158, 1158, -2874, 13254, -2874, 16278, 16278, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -762, -762, -762, -762, -588, -588, -732, -732, -588, -588, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -9954, -9954, -1434, -8994, -1434, -1890, -1890, -1434, 6630, -8994, -1434, -930, -1434, 6630, -9954, -9954, -1434, -8994, -1434, -378, -378, -378, -378, -1434, 6630, -1434, 8142, 8142, -8994, -1434, -930, -1434, 6630, -8994, -1434, 582, 582, -1434, 6630, -1434, 8142, 8142, -9954, -9954, -1434, -8994, -1434, -1890, -1890, -1434, 6630, -8994, -1434, -930, -1434, 6630, -9954, -9954, -1434, -8994, -1434, -378, -378, -378, -378, -1434, 6630, -1434, 8142, 8142, -8994, -1434, -930, -1434, 6630, -8994, -1434, 582, 582, -1434, 6630, -1434, 8142, 8142, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -12948, -12948, -1872, -11700, -1872, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -12948, -12948, -1872, -11700, -1872, -12948, -12948, -1872, -11700, -1872, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -24900, -24900, -3600, -22500, -3600, -258, -258, -258, -258, -84, -84, -228, -228, -84, -84, -378, -378, -378, -378, -84, -84, -204, -204, -228, -228, -84, -84, -348, -348, -84, -84, -204, -204, -258, -258, -258, -258, -84, -84, -228, -228, -84, -84, -378, -378, -378, -378, -378, -378, -378, -378, -84, -84, -204, -204, -84, -84, -204, -204, -204, -204, -228, -228, -84, -84, -348, -348, -84, -84, -204, -204, -228, -228, -84, -84, -348, -348, -348, -348, -84, -84, -204, -204, -84, -84, -204, -204, -204, -204, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -5040, 23184, -3600, 16560, -3600, 16560, -3312, -5040, -1872, -5040, -3600, -3312, -5040, -1872, -1872, -5040, -3600, -5040, -3600, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 8568, 8568, 29736, 21096, 29736, 21096, 21096, 19368, 29736, 10728, 29736, 21096, 19368, 29736, 10728, 10728, 29736, 21096, 29736, 21096, 21096, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -20700, -3312, -31500, -5040, -11700, -1872, -31500, -5040, -22500, -3600, 1710, 1710, 3276, 1980, 3276, 630, 630, 3276, 2196, 1980, 3276, 900, 3276, 2196, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -20700, -3312, -31500, -5040, -11700, -1872, -31500, -5040, -22500, -3600, -20700, -3312, -31500, -5040, -11700, -1872, -11700, -1872, -31500, -5040, -22500, -3600, -31500, -5040, -22500, -3600, -22500, -3600, 1710, 1710, 3276, 1980, 3276, 630, 630, 3276, 2196, 1980, 3276, 900, 3276, 2196, 1710, 1710, 3276, 1980, 3276, 630, 630, 630, 630, 3276, 2196, 3276, 2196, 2196, 1980, 3276, 900, 3276, 2196, 1980, 3276, 900, 900, 3276, 2196, 3276, 2196, 2196, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -5040, 23184, -3600, 16560, -3600, 16560, -3312, -5040, -1872, -5040, -3600, -3312, -5040, -1872, -1872, -5040, -3600, -5040, -3600, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 8568, 8568, 29736, 21096, 29736, 21096, 21096, 19368, 29736, 10728, 29736, 21096, 19368, 29736, 10728, 10728, 29736, 21096, 29736, 21096, 21096])\n assert answers_match(candidate(expression='1*2+3*4-5*6+7*8-9*10'), [8534, 974, 434, 974, -7126, 16004, 1964, 434, -196, 164, -7936, 1964, -7936, -14236, 1646, 134, 26, 134, -1486, 16004, 1964, 9116, 1124, -646, -1276, 26, -1276, -604, 164, -7936, 1964, -7936, -14236, -676, -2296, 1964, 1124, -9016, -15316, -2296, -15316, -8596, 1706, 194, 86, 194, -1426, 3200, 392, 86, -40, 32, -1588, 392, -1588, -2848, -1798, -286, -178, -286, 1334, -1738, -226, -118, -226, 1394, 15008, 1832, 8120, 992, 3200, 392, 4676, 572, -244, -28, -1186, -1816, -514, -1816, -1144, -454, -580, -178, -118, -1732, -1060, -580, -724, -244, 272, -7828, 2072, -7828, -14128, -568, -2188, 2072, 1232, -8908, -15208, -2188, -15208, -8488, 32, -1588, 392, -1588, -2848, -988, 632, -388, 1232, 1832, 992, 392, 572, -28, -9448, -15748, -2728, -15748, -9028, -2128, -3388, 632, 1232, -14908, -8188, -3388, -4828, -28, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 1706, 194, 86, 194, -1426, 3200, 392, 86, -40, 32, -1588, 392, -1588, -2848, -3974, -446, -194, -446, 3334, -7460, -908, -194, 100, -68, 3712, -908, 3712, 6652, -650, -146, -110, -146, 394, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -530, -26, 10, -26, 514, 15008, 1832, 8120, 992, 3200, 392, 4676, 572, -244, -28, 4348, 532, 2052, 252, 3200, 392, -7460, -908, 5824, 712, 904, 112, 904, 112, 904, 112, -4016, -488, -1006, -1636, -334, -1636, -964, -274, -400, 2, 62, -1552, -880, -400, -544, -64, -386, -596, -162, -596, -372, -274, -400, 346, 640, -110, -50, -50, -50, 10, -1552, -880, -400, -544, -64, -512, -288, -400, 640, -656, -176, -176, -176, 304, 272, -7828, 2072, -7828, -14128, -568, -2188, 2072, 1232, -8908, -15208, -2188, -15208, -8488, 32, -1588, 392, -1588, -2848, -988, 632, -388, 1232, 1832, 992, 392, 572, -28, -9448, -15748, -2728, -15748, -9028, -2128, -3388, 632, 1232, -14908, -8188, -3388, -4828, -28, 172, -2528, 772, -2528, -4628, -108, -648, 772, 492, -2888, -4988, -648, -4988, -2748, 32, -1588, 392, -1588, -2848, -68, 3712, -908, 3712, 6652, -848, -308, -248, 292, -248, 292, -248, 292, 352, 892, 1832, 992, 392, 572, -28, 532, 252, 392, -908, 712, 112, 112, 112, -488, -9268, -15568, -2548, -15568, -8848, -1948, -3208, 812, 1412, -14728, -8008, -3208, -4648, 152, -3068, -5168, -828, -5168, -2928, -1948, -3208, 4252, 7192, -308, 292, 292, 292, 892, -14728, -8008, -3208, -4648, 152, -4328, -2088, -3208, 7192, -5768, -968, -968, -968, 3832, 14220, 1620, 720, 1620, -11880, 26670, 3270, 720, -330, 270, -13230, 3270, -13230, -23730, 2740, 220, 40, 220, -2480, 26670, 3270, 15190, 1870, -1080, -2130, 40, -2130, -1010, 270, -13230, 3270, -13230, -23730, -1130, -3830, 3270, 1870, -15030, -25530, -3830, -25530, -14330, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -3000, -480, -300, -480, 2220, -2900, -380, -200, -380, 2320, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, -1980, -3030, -860, -3030, -1910, -760, -970, -300, -200, -2890, -1770, -970, -1210, -410, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 2860, 340, 160, 340, -2360, 5350, 670, 160, -50, 70, -2630, 670, -2630, -4730, 564, 60, 24, 60, -480, 5350, 670, 3054, 390, -200, -410, 24, -410, -186, 70, -2630, 670, -2630, -4730, -210, -750, 670, 390, -2990, -5090, -750, -5090, -2850, 568, 64, 28, 64, -476, 1066, 130, 28, -14, 10, -530, 130, -530, -950, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, -8520, -960, -420, -960, 7140, -15990, -1950, -420, 210, -150, 7950, -1950, 7950, 14250, -650, -146, -110, -146, 394, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -530, -26, 10, -26, 514, -704, -200, -164, -200, 340, -604, -100, -64, -100, 440, -590, -86, -50, -86, 454, -584, -80, -44, -80, 460, -580, -76, -40, -76, 464, -520, -16, 20, -16, 524, -604, -100, -64, -100, 440, -520, -16, 20, -16, 524, -484, 20, 56, 20, 560, 14842, 1810, 7954, 970, 3034, 370, 4510, 550, -410, -50, 4182, 510, 1886, 230, 3034, 370, -7626, -930, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, 4182, 510, 1886, 230, 3690, 450, 1394, 170, 1066, 130, -9594, -1170, 5330, 650, -9594, -1170, -15990, -1950, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 10086, 1230, 1886, 230, 738, 90, 246, 30, -82, -10, -5002, -610, 1886, 230, -5002, -610, -7954, -970, -1006, -1636, -334, -1636, -964, -274, -400, 2, 62, -1552, -880, -400, -544, -64, -386, -596, -162, -596, -372, -274, -400, 346, 640, -110, -50, -50, -50, 10, -1552, -880, -400, -544, -64, -512, -288, -400, 640, -656, -176, -176, -176, 304, -1620, -2670, -500, -2670, -1550, -400, -610, 60, 160, -2530, -1410, -610, -850, -50, -386, -596, -162, -596, -372, -380, -590, -156, -590, -366, -152, -194, 468, 846, -400, -610, 468, 846, 840, 1470, -110, -50, -50, -50, 10, -164, -64, -50, -44, -40, 20, -64, 20, 56, -1538, -866, -386, -530, -50, -498, -274, -386, 654, -642, -162, -162, -162, 318, -2530, -1410, -610, -850, -50, -498, -274, -450, -226, -194, 846, -610, 846, 1470, -642, -162, -162, -162, 318, -1074, -274, -162, -114, -82, 398, -274, 398, 686, 290, -7810, 2090, -7810, -14110, -550, -2170, 2090, 1250, -8890, -15190, -2170, -15190, -8470, 50, -1570, 410, -1570, -2830, -970, 650, -370, 1250, 1850, 1010, 410, 590, -10, -9430, -15730, -2710, -15730, -9010, -2110, -3370, 650, 1250, -14890, -8170, -3370, -4810, -10, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 50, -1570, 410, -1570, -2830, -50, 3730, -890, 3730, 6670, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, 1850, 1010, 410, 590, -10, 550, 270, 410, -890, 730, 130, 130, 130, -470, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 250, -2450, 850, -2450, -4550, -30, -570, 850, 570, -2810, -4910, -570, -4910, -2670, 10, -530, 130, -530, -950, -90, 4770, -1170, 4770, 8550, 50, -2650, 650, -2650, -4750, -90, 4770, -1170, 4770, 8550, -150, 7950, -1950, 7950, 14250, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, -1370, -830, -370, 170, -230, 310, -170, 370, -130, 410, 470, 1010, -370, 170, 470, 1010, 830, 1370, 1810, 970, 370, 550, -50, 510, 230, 370, -930, 690, 90, 90, 90, -510, 3050, 1650, 650, 950, -50, 510, 230, 450, 170, 130, -1170, 650, -1170, -1950, 690, 90, 90, 90, -510, 1230, 230, 90, 30, -10, -610, 230, -610, -970, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -710, -1130, 5490, 9270, -3190, -5290, 5490, 9270, 9210, 15510, -290, 310, 310, 310, 910, -830, 170, 310, 370, 410, 1010, 170, 1010, 1370, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, 8534, 974, 434, 974, -7126, 16004, 1964, 434, -196, 164, -7936, 1964, -7936, -14236, 1646, 134, 26, 134, -1486, 16004, 1964, 9116, 1124, -646, -1276, 26, -1276, -604, 164, -7936, 1964, -7936, -14236, -676, -2296, 1964, 1124, -9016, -15316, -2296, -15316, -8596, 1706, 194, 86, 194, -1426, 3200, 392, 86, -40, 32, -1588, 392, -1588, -2848, -1798, -286, -178, -286, 1334, -1738, -226, -118, -226, 1394, 15008, 1832, 8120, 992, 3200, 392, 4676, 572, -244, -28, -1186, -1816, -514, -1816, -1144, -454, -580, -178, -118, -1732, -1060, -580, -724, -244, 272, -7828, 2072, -7828, -14128, -568, -2188, 2072, 1232, -8908, -15208, -2188, -15208, -8488, 32, -1588, 392, -1588, -2848, -988, 632, -388, 1232, 1832, 992, 392, 572, -28, -9448, -15748, -2728, -15748, -9028, -2128, -3388, 632, 1232, -14908, -8188, -3388, -4828, -28, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 1706, 194, 86, 194, -1426, 3200, 392, 86, -40, 32, -1588, 392, -1588, -2848, -3974, -446, -194, -446, 3334, -7460, -908, -194, 100, -68, 3712, -908, 3712, 6652, -650, -146, -110, -146, 394, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -530, -26, 10, -26, 514, 15008, 1832, 8120, 992, 3200, 392, 4676, 572, -244, -28, 4348, 532, 2052, 252, 3200, 392, -7460, -908, 5824, 712, 904, 112, 904, 112, 904, 112, -4016, -488, -1006, -1636, -334, -1636, -964, -274, -400, 2, 62, -1552, -880, -400, -544, -64, -386, -596, -162, -596, -372, -274, -400, 346, 640, -110, -50, -50, -50, 10, -1552, -880, -400, -544, -64, -512, -288, -400, 640, -656, -176, -176, -176, 304, 272, -7828, 2072, -7828, -14128, -568, -2188, 2072, 1232, -8908, -15208, -2188, -15208, -8488, 32, -1588, 392, -1588, -2848, -988, 632, -388, 1232, 1832, 992, 392, 572, -28, -9448, -15748, -2728, -15748, -9028, -2128, -3388, 632, 1232, -14908, -8188, -3388, -4828, -28, 172, -2528, 772, -2528, -4628, -108, -648, 772, 492, -2888, -4988, -648, -4988, -2748, 32, -1588, 392, -1588, -2848, -68, 3712, -908, 3712, 6652, -848, -308, -248, 292, -248, 292, -248, 292, 352, 892, 1832, 992, 392, 572, -28, 532, 252, 392, -908, 712, 112, 112, 112, -488, -9268, -15568, -2548, -15568, -8848, -1948, -3208, 812, 1412, -14728, -8008, -3208, -4648, 152, -3068, -5168, -828, -5168, -2928, -1948, -3208, 4252, 7192, -308, 292, 292, 292, 892, -14728, -8008, -3208, -4648, 152, -4328, -2088, -3208, 7192, -5768, -968, -968, -968, 3832, 14220, 1620, 720, 1620, -11880, 26670, 3270, 720, -330, 270, -13230, 3270, -13230, -23730, 2740, 220, 40, 220, -2480, 26670, 3270, 15190, 1870, -1080, -2130, 40, -2130, -1010, 270, -13230, 3270, -13230, -23730, -1130, -3830, 3270, 1870, -15030, -25530, -3830, -25530, -14330, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -3000, -480, -300, -480, 2220, -2900, -380, -200, -380, 2320, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, -1980, -3030, -860, -3030, -1910, -760, -970, -300, -200, -2890, -1770, -970, -1210, -410, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 14220, 1620, 720, 1620, -11880, 26670, 3270, 720, -330, 270, -13230, 3270, -13230, -23730, 2740, 220, 40, 220, -2480, 26670, 3270, 15190, 1870, -1080, -2130, 40, -2130, -1010, 270, -13230, 3270, -13230, -23730, -1130, -3830, 3270, 1870, -15030, -25530, -3830, -25530, -14330, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -3000, -480, -300, -480, 2220, -2900, -380, -200, -380, 2320, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, -1980, -3030, -860, -3030, -1910, -760, -970, -300, -200, -2890, -1770, -970, -1210, -410, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 2860, 340, 160, 340, -2360, 5350, 670, 160, -50, 70, -2630, 670, -2630, -4730, 564, 60, 24, 60, -480, 5350, 670, 3054, 390, -200, -410, 24, -410, -186, 70, -2630, 670, -2630, -4730, -210, -750, 670, 390, -2990, -5090, -750, -5090, -2850, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 2860, 340, 160, 340, -2360, 5350, 670, 160, -50, 70, -2630, 670, -2630, -4730, 564, 60, 24, 60, -480, 5350, 670, 3054, 390, -200, -410, 24, -410, -186, 70, -2630, 670, -2630, -4730, -210, -750, 670, 390, -2990, -5090, -750, -5090, -2850, 2860, 340, 160, 340, -2360, 5350, 670, 160, -50, 70, -2630, 670, -2630, -4730, 564, 60, 24, 60, -480, 5350, 670, 3054, 390, -200, -410, 24, -410, -186, 70, -2630, 670, -2630, -4730, -210, -750, 670, 390, -2990, -5090, -750, -5090, -2850, 568, 64, 28, 64, -476, 1066, 130, 28, -14, 10, -530, 130, -530, -950, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, -8520, -960, -420, -960, 7140, -15990, -1950, -420, 210, -150, 7950, -1950, 7950, 14250, 568, 64, 28, 64, -476, 1066, 130, 28, -14, 10, -530, 130, -530, -950, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, -8520, -960, -420, -960, 7140, -15990, -1950, -420, 210, -150, 7950, -1950, 7950, 14250, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, -8520, -960, -420, -960, 7140, -15990, -1950, -420, 210, -150, 7950, -1950, 7950, 14250, -8520, -960, -420, -960, 7140, -15990, -1950, -420, 210, -150, 7950, -1950, 7950, 14250, -650, -146, -110, -146, 394, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -530, -26, 10, -26, 514, -704, -200, -164, -200, 340, -604, -100, -64, -100, 440, -590, -86, -50, -86, 454, -584, -80, -44, -80, 460, -580, -76, -40, -76, 464, -520, -16, 20, -16, 524, -604, -100, -64, -100, 440, -520, -16, 20, -16, 524, -484, 20, 56, 20, 560, -650, -146, -110, -146, 394, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -530, -26, 10, -26, 514, -704, -200, -164, -200, 340, -604, -100, -64, -100, 440, -704, -200, -164, -200, 340, -604, -100, -64, -100, 440, -590, -86, -50, -86, 454, -584, -80, -44, -80, 460, -590, -86, -50, -86, 454, -584, -80, -44, -80, 460, -584, -80, -44, -80, 460, -580, -76, -40, -76, 464, -520, -16, 20, -16, 524, -604, -100, -64, -100, 440, -520, -16, 20, -16, 524, -484, 20, 56, 20, 560, -580, -76, -40, -76, 464, -520, -16, 20, -16, 524, -604, -100, -64, -100, 440, -604, -100, -64, -100, 440, -520, -16, 20, -16, 524, -484, 20, 56, 20, 560, -520, -16, 20, -16, 524, -484, 20, 56, 20, 560, -484, 20, 56, 20, 560, 14842, 1810, 7954, 970, 3034, 370, 4510, 550, -410, -50, 4182, 510, 1886, 230, 3034, 370, -7626, -930, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, 4182, 510, 1886, 230, 3690, 450, 1394, 170, 1066, 130, -9594, -1170, 5330, 650, -9594, -1170, -15990, -1950, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 10086, 1230, 1886, 230, 738, 90, 246, 30, -82, -10, -5002, -610, 1886, 230, -5002, -610, -7954, -970, 14842, 1810, 7954, 970, 3034, 370, 4510, 550, -410, -50, 4182, 510, 1886, 230, 3034, 370, -7626, -930, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, 4182, 510, 1886, 230, 3690, 450, 1394, 170, 4182, 510, 1886, 230, 3690, 450, 1394, 170, 3690, 450, 1394, 170, 1066, 130, -9594, -1170, 5330, 650, -9594, -1170, -15990, -1950, 1066, 130, -9594, -1170, 5330, 650, 5330, 650, -9594, -1170, -15990, -1950, -9594, -1170, -15990, -1950, -15990, -1950, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 10086, 1230, 1886, 230, 738, 90, 246, 30, -82, -10, -5002, -610, 1886, 230, -5002, -610, -7954, -970, 5658, 690, 738, 90, 738, 90, 738, 90, -4182, -510, 10086, 1230, 1886, 230, 10086, 1230, 1886, 230, 738, 90, 246, 30, 738, 90, 246, 30, 246, 30, -82, -10, -5002, -610, 1886, 230, -5002, -610, -7954, -970, -82, -10, -5002, -610, 1886, 230, 1886, 230, -5002, -610, -7954, -970, -5002, -610, -7954, -970, -7954, -970, -1006, -1636, -334, -1636, -964, -274, -400, 2, 62, -1552, -880, -400, -544, -64, -386, -596, -162, -596, -372, -274, -400, 346, 640, -110, -50, -50, -50, 10, -1552, -880, -400, -544, -64, -512, -288, -400, 640, -656, -176, -176, -176, 304, -1620, -2670, -500, -2670, -1550, -400, -610, 60, 160, -2530, -1410, -610, -850, -50, -386, -596, -162, -596, -372, -380, -590, -156, -590, -366, -152, -194, 468, 846, -400, -610, 468, 846, 840, 1470, -110, -50, -50, -50, 10, -164, -64, -50, -44, -40, 20, -64, 20, 56, -1538, -866, -386, -530, -50, -498, -274, -386, 654, -642, -162, -162, -162, 318, -2530, -1410, -610, -850, -50, -498, -274, -450, -226, -194, 846, -610, 846, 1470, -642, -162, -162, -162, 318, -1074, -274, -162, -114, -82, 398, -274, 398, 686, -1006, -1636, -334, -1636, -964, -274, -400, 2, 62, -1552, -880, -400, -544, -64, -386, -596, -162, -596, -372, -274, -400, 346, 640, -110, -50, -50, -50, 10, -1552, -880, -400, -544, -64, -512, -288, -400, 640, -656, -176, -176, -176, 304, -1620, -2670, -500, -2670, -1550, -400, -610, 60, 160, -2530, -1410, -610, -850, -50, -1620, -2670, -500, -2670, -1550, -400, -610, 60, 160, -2530, -1410, -610, -850, -50, -386, -596, -162, -596, -372, -380, -590, -156, -590, -366, -386, -596, -162, -596, -372, -380, -590, -156, -590, -366, -380, -590, -156, -590, -366, -152, -194, 468, 846, -400, -610, 468, 846, 840, 1470, -152, -194, 468, 846, -400, -610, -400, -610, 468, 846, 840, 1470, 468, 846, 840, 1470, 840, 1470, -110, -50, -50, -50, 10, -164, -64, -50, -44, -40, 20, -64, 20, 56, -110, -50, -50, -50, 10, -164, -64, -164, -64, -50, -44, -50, -44, -44, -40, 20, -64, 20, 56, -40, 20, -64, -64, 20, 56, 20, 56, 56, -1538, -866, -386, -530, -50, -498, -274, -386, 654, -642, -162, -162, -162, 318, -2530, -1410, -610, -850, -50, -498, -274, -450, -226, -194, 846, -610, 846, 1470, -642, -162, -162, -162, 318, -1074, -274, -162, -114, -82, 398, -274, 398, 686, -1538, -866, -386, -530, -50, -498, -274, -386, 654, -642, -162, -162, -162, 318, -2530, -1410, -610, -850, -50, -2530, -1410, -610, -850, -50, -498, -274, -450, -226, -498, -274, -450, -226, -450, -226, -194, 846, -610, 846, 1470, -194, 846, -610, -610, 846, 1470, 846, 1470, 1470, -642, -162, -162, -162, 318, -1074, -274, -162, -114, -82, 398, -274, 398, 686, -642, -162, -162, -162, 318, -1074, -274, -1074, -274, -162, -114, -162, -114, -114, -82, 398, -274, 398, 686, -82, 398, -274, -274, 398, 686, 398, 686, 686, 290, -7810, 2090, -7810, -14110, -550, -2170, 2090, 1250, -8890, -15190, -2170, -15190, -8470, 50, -1570, 410, -1570, -2830, -970, 650, -370, 1250, 1850, 1010, 410, 590, -10, -9430, -15730, -2710, -15730, -9010, -2110, -3370, 650, 1250, -14890, -8170, -3370, -4810, -10, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 50, -1570, 410, -1570, -2830, -50, 3730, -890, 3730, 6670, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, 1850, 1010, 410, 590, -10, 550, 270, 410, -890, 730, 130, 130, 130, -470, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 250, -2450, 850, -2450, -4550, -30, -570, 850, 570, -2810, -4910, -570, -4910, -2670, 10, -530, 130, -530, -950, -90, 4770, -1170, 4770, 8550, 50, -2650, 650, -2650, -4750, -90, 4770, -1170, 4770, 8550, -150, 7950, -1950, 7950, 14250, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, -1370, -830, -370, 170, -230, 310, -170, 370, -130, 410, 470, 1010, -370, 170, 470, 1010, 830, 1370, 1810, 970, 370, 550, -50, 510, 230, 370, -930, 690, 90, 90, 90, -510, 3050, 1650, 650, 950, -50, 510, 230, 450, 170, 130, -1170, 650, -1170, -1950, 690, 90, 90, 90, -510, 1230, 230, 90, 30, -10, -610, 230, -610, -970, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -710, -1130, 5490, 9270, -3190, -5290, 5490, 9270, 9210, 15510, -290, 310, 310, 310, 910, -830, 170, 310, 370, 410, 1010, 170, 1010, 1370, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, 290, -7810, 2090, -7810, -14110, -550, -2170, 2090, 1250, -8890, -15190, -2170, -15190, -8470, 50, -1570, 410, -1570, -2830, -970, 650, -370, 1250, 1850, 1010, 410, 590, -10, -9430, -15730, -2710, -15730, -9010, -2110, -3370, 650, 1250, -14890, -8170, -3370, -4810, -10, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 50, -1570, 410, -1570, -2830, -50, 3730, -890, 3730, 6670, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, 1850, 1010, 410, 590, -10, 550, 270, 410, -890, 730, 130, 130, 130, -470, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 250, -2450, 850, -2450, -4550, -30, -570, 850, 570, -2810, -4910, -570, -4910, -2670, 190, -2510, 790, -2510, -4610, -90, -630, 790, 510, -2870, -4970, -630, -4970, -2730, 250, -2450, 850, -2450, -4550, -30, -570, 850, 570, -2810, -4910, -570, -4910, -2670, 250, -2450, 850, -2450, -4550, -30, -570, 850, 570, -2810, -4910, -570, -4910, -2670, 10, -530, 130, -530, -950, -90, 4770, -1170, 4770, 8550, 50, -2650, 650, -2650, -4750, -90, 4770, -1170, 4770, 8550, -150, 7950, -1950, 7950, 14250, 10, -530, 130, -530, -950, -90, 4770, -1170, 4770, 8550, 50, -2650, 650, -2650, -4750, 50, -2650, 650, -2650, -4750, -90, 4770, -1170, 4770, 8550, -150, 7950, -1950, 7950, 14250, -90, 4770, -1170, 4770, 8550, -150, 7950, -1950, 7950, 14250, -150, 7950, -1950, 7950, 14250, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, -1370, -830, -370, 170, -230, 310, -170, 370, -130, 410, 470, 1010, -370, 170, 470, 1010, 830, 1370, -830, -290, -230, 310, -230, 310, -230, 310, 370, 910, -1370, -830, -370, 170, -1370, -830, -370, 170, -230, 310, -170, 370, -230, 310, -170, 370, -170, 370, -130, 410, 470, 1010, -370, 170, 470, 1010, 830, 1370, -130, 410, 470, 1010, -370, 170, -370, 170, 470, 1010, 830, 1370, 470, 1010, 830, 1370, 830, 1370, 1810, 970, 370, 550, -50, 510, 230, 370, -930, 690, 90, 90, 90, -510, 3050, 1650, 650, 950, -50, 510, 230, 450, 170, 130, -1170, 650, -1170, -1950, 690, 90, 90, 90, -510, 1230, 230, 90, 30, -10, -610, 230, -610, -970, 1810, 970, 370, 550, -50, 510, 230, 370, -930, 690, 90, 90, 90, -510, 3050, 1650, 650, 950, -50, 3050, 1650, 650, 950, -50, 510, 230, 450, 170, 510, 230, 450, 170, 450, 170, 130, -1170, 650, -1170, -1950, 130, -1170, 650, 650, -1170, -1950, -1170, -1950, -1950, 690, 90, 90, 90, -510, 1230, 230, 90, 30, -10, -610, 230, -610, -970, 690, 90, 90, 90, -510, 1230, 230, 1230, 230, 90, 30, 90, 30, 30, -10, -610, 230, -610, -970, -10, -610, 230, 230, -610, -970, -610, -970, -970, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -710, -1130, 5490, 9270, -3190, -5290, 5490, 9270, 9210, 15510, -290, 310, 310, 310, 910, -830, 170, 310, 370, 410, 1010, 170, 1010, 1370, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, -9250, -15550, -2530, -15550, -8830, -1930, -3190, 830, 1430, -14710, -7990, -3190, -4630, 170, -3050, -5150, -810, -5150, -2910, -1930, -3190, 4270, 7210, -290, 310, 310, 310, 910, -14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -2990, -5090, -750, -5090, -2850, -710, -1130, 5490, 9270, -3190, -5290, 5490, 9270, 9210, 15510, -710, -1130, 5490, 9270, -3190, -5290, -3190, -5290, 5490, 9270, 9210, 15510, 5490, 9270, 9210, 15510, 9210, 15510, -290, 310, 310, 310, 910, -830, 170, 310, 370, 410, 1010, 170, 1010, 1370, -290, 310, 310, 310, 910, -830, 170, -830, 170, 310, 370, 310, 370, 370, 410, 1010, 170, 1010, 1370, 410, 1010, 170, 170, 1010, 1370, 1010, 1370, 1370, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -4170, -1930, -3690, -1450, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -1130, 9270, -5290, -5290, 9270, 15510, 9270, 15510, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, -5610, -810, -810, -810, 3990, -9930, -1930, -9930, -1930, -810, -330, -810, -330, -330, -10, 4790, -1930, 4790, 7670, -10, 4790, -1930, -1930, 4790, 7670, 4790, 7670, 7670])\n assert answers_match(candidate(expression='2*3-4+5*6-7+8*9-10'), [-72, 628, -212, 628, 1188, 88, -612, -92, 68, 828, 1388, -612, 908, -532, -64, 76, -92, 76, 188, 24, -116, -32, -172, -92, 68, 28, 4, 60, 748, 1308, -692, 828, -612, 116, 228, -116, -172, 828, -612, -252, -36, -540, -120, 1140, -372, 1140, 2148, 168, -1092, -156, 132, 1500, 2508, -1092, 1644, -948, -64, 76, -92, 76, 188, -104, 36, -132, 36, 148, 24, -116, -32, -172, 40, -100, -32, -172, -72, -212, -76, 84, 44, 20, 76, -156, 132, 44, 84, 20, 76, 4, 76, 116, 748, 1308, -692, 828, -612, 116, 228, -116, -172, 828, -612, -252, -36, -540, 1340, 2348, -1252, 1484, -1108, 116, 228, 76, 188, -116, -172, -100, -172, -212, 764, -676, -316, -100, -604, 1484, -1108, -316, -676, -100, -604, 44, -604, -964, 68, -632, 208, -632, -1192, -92, 608, 88, -72, -832, -1392, 608, -912, 528, 60, -80, 88, -80, -192, -28, 112, 28, 168, 88, -72, -32, -8, -64, -752, -1312, 688, -832, 608, -120, -232, 112, 168, -832, 608, 248, 32, 536, -84, 756, -252, 756, 1428, 108, -732, -108, 84, 996, 1668, -732, 1092, -636, 56, -504, 168, -504, -952, -72, 488, 72, -56, -664, -1112, 488, -728, 424, -60, -200, -32, -200, -312, -100, -240, -72, -240, -352, 60, -80, 88, -80, -192, -70, -210, -42, -210, -322, 50, -90, 78, -90, -202, -8, 132, -64, 76, 8, 148, -64, 76, -104, 36, -28, 112, 28, 168, -4, 136, -24, 116, -92, 48, -132, 8, 28, 168, -102, 38, 18, 158, -88, 72, 32, 8, 64, -168, 120, 32, 72, 8, 64, -8, 64, 104, 92, -68, -28, -4, -60, -108, 84, 72, -56, 92, 132, -28, 102, -18, -24, 32, -40, 32, 72, -4, -60, -28, -8, 60, 100, -60, 70, -50, 708, 1268, -732, 788, -652, 76, 188, -156, -212, 788, -652, -292, -76, -580, 1300, 2308, -1292, 1444, -1148, 76, 188, 36, 148, -156, -212, -140, -212, -252, 724, -716, -356, -140, -644, 1444, -1148, -356, -716, -140, -644, 4, -644, -1004, -752, -1312, 688, -832, 608, -120, -232, 112, 168, -832, 608, 248, 32, 536, 856, 1528, -872, 952, -776, -604, -1052, 548, -668, 484, -240, -352, -280, -392, -120, -232, -250, -362, -130, -242, 132, 76, 148, 76, 36, 112, 168, 136, 116, 48, 8, 168, 38, 158, 772, -668, -308, -92, -596, 1492, -1100, -308, -668, -92, -596, 52, -596, -956, -848, 592, 232, 16, 520, 952, -776, -668, 484, -848, -1208, 232, -938, 142, 196, -308, 340, -308, -668, 16, 520, 232, 52, -560, -920, 520, -650, 430, -33, 317, -103, 317, 597, 47, -303, -43, 37, 417, 697, -303, 457, -263, -29, 41, -43, 41, 97, 15, -55, -13, -83, -43, 37, 17, 5, 33, 377, 657, -343, 417, -303, 61, 117, -55, -83, 417, -303, -123, -15, -267, -57, 573, -183, 573, 1077, 87, -543, -75, 69, 753, 1257, -543, 825, -471, -29, 41, -43, 41, 97, -49, 21, -63, 21, 77, 15, -55, -13, -83, 23, -47, -13, -83, -33, -103, -35, 45, 25, 13, 41, -75, 69, 25, 45, 13, 41, 5, 41, 61, 377, 657, -343, 417, -303, 61, 117, -55, -83, 417, -303, -123, -15, -267, 673, 1177, -623, 745, -551, 61, 117, 41, 97, -55, -83, -47, -83, -103, 385, -335, -155, -47, -299, 745, -551, -155, -335, -47, -299, 25, -299, -479, 33, -317, 103, -317, -597, -47, 303, 43, -37, -417, -697, 303, -457, 263, 29, -41, 43, -41, -97, -15, 55, 13, 83, 43, -37, -17, -5, -33, -377, -657, 343, -417, 303, -61, -117, 55, 83, -417, 303, 123, 15, 267, 37, -313, 107, -313, -593, -43, 307, 47, -33, -413, -693, 307, -453, 267, 33, -37, 47, -37, -93, -11, 59, 17, 87, 47, -33, -13, -1, -29, -373, -653, 347, -413, 307, -57, -113, 59, 87, -413, 307, 127, 19, 271, -84, 756, -252, 756, 1428, 108, -732, -108, 84, 996, 1668, -732, 1092, -636, 56, -504, 168, -504, -952, -72, 488, 72, -56, -664, -1112, 488, -728, 424, -21, 189, -63, 189, 357, 27, -183, -27, 21, 249, 417, -183, 273, -159, 21, -189, 63, -189, -357, -27, 183, 27, -21, -249, -417, 183, -273, 159, 49, -441, 147, -441, -833, -63, 427, 63, -49, -581, -973, 427, -637, 371, -61, -131, -47, -131, -187, -101, -171, -87, -171, -227, 59, -11, 73, -11, -67, -71, -141, -57, -141, -197, 49, -21, 63, -21, -77, -27, -97, -13, -97, -153, -47, -117, -33, -117, -173, 29, -41, 43, -41, -97, 33, -37, 47, -37, -93, -71, -141, -57, -141, -197, 49, -21, 63, -21, -77, -17, -87, -3, -87, -143, 19, -51, 33, -51, -107, 43, -27, 57, -27, -83, 0, 70, -56, 14, 16, 86, -56, 14, -96, -26, -20, 50, 36, 106, 4, 74, -16, 54, -84, -14, -124, -54, 36, 106, -94, -24, 26, 96, -1, 69, -29, 41, 7, 77, -29, 41, -49, 21, -15, 55, 13, 83, -11, 59, 17, 87, 4, 74, -16, 54, -5, 65, -11, 59, -15, 55, -77, -7, -117, -47, 43, 113, -87, -17, 33, 103, -43, 27, -63, 7, 13, 83, 17, 87, -87, -17, 33, 103, -33, 37, 3, 73, 27, 97, -88, 72, 32, 8, 64, -168, 120, 32, 72, 8, 64, -8, 64, 104, 92, -68, -28, -4, -60, -108, 84, 72, -56, 92, 132, -28, 102, -18, -24, 32, -40, 32, 72, -4, -60, -28, -8, 60, 100, -60, 70, -50, -47, 33, 13, 1, 29, -87, 57, 13, 33, 1, 29, -7, 29, 49, 47, -33, -13, -1, -29, 43, -37, -17, -5, -33, -108, 84, 72, -56, -27, 21, 27, -21, 63, -49, 77, 117, -43, 87, -33, 43, 63, -13, -17, 87, -33, 33, -3, -27, -16, 40, -32, 40, 80, 4, -52, -20, 0, 68, 108, -52, 78, -42, -15, 13, -23, 13, 33, -1, -29, -5, -33, -20, 0, -11, -5, -1, 61, 101, -59, 71, -49, 27, 47, -29, -33, 71, -49, 17, -19, -43, 718, 1278, -722, 798, -642, 86, 198, -146, -202, 798, -642, -282, -66, -570, 1310, 2318, -1282, 1454, -1138, 86, 198, 46, 158, -146, -202, -130, -202, -242, 734, -706, -346, -130, -634, 1454, -1138, -346, -706, -130, -634, 14, -634, -994, -742, -1302, 698, -822, 618, -110, -222, 122, 178, -822, 618, 258, 42, 546, 866, 1538, -862, 962, -766, -594, -1042, 558, -658, 494, -230, -342, -270, -382, -110, -222, -240, -352, -120, -232, 142, 86, 158, 86, 46, 122, 178, 146, 126, 58, 18, 178, 48, 168, 782, -658, -298, -82, -586, 1502, -1090, -298, -658, -82, -586, 62, -586, -946, -838, 602, 242, 26, 530, 962, -766, -658, 494, -838, -1198, 242, -928, 152, 206, -298, 350, -298, -658, 26, 530, 242, 62, -550, -910, 530, -640, 440, 357, 637, -363, 397, -323, 41, 97, -75, -103, 397, -323, -143, -35, -287, 653, 1157, -643, 725, -571, 41, 97, 21, 77, -75, -103, -67, -103, -123, 365, -355, -175, -67, -319, 725, -571, -175, -355, -67, -319, 5, -319, -499, -377, -657, 343, -417, 303, -61, -117, 55, 83, -417, 303, 123, 15, 267, -373, -653, 347, -413, 307, -57, -113, 59, 87, -413, 307, 127, 19, 271, 866, 1538, -862, 962, -766, -594, -1042, 558, -658, 494, 209, 377, -223, 233, -199, -229, -397, 203, -253, 179, -521, -913, 487, -577, 431, -151, -207, -191, -247, -31, -87, -161, -217, -41, -97, -117, -173, -137, -193, -61, -117, -57, -113, -161, -217, -41, -97, -107, -163, -71, -127, -47, -103, 70, 14, 86, 14, -26, 50, 106, 74, 54, -14, -54, 106, -24, 96, 69, 41, 77, 41, 21, 55, 83, 59, 87, 74, 54, 65, 59, 55, -7, -47, 113, -17, 103, 27, 7, 83, 87, -17, 103, 37, 73, 97, 782, -658, -298, -82, -586, 1502, -1090, -298, -658, -82, -586, 62, -586, -946, -838, 602, 242, 26, 530, 962, -766, -658, 494, -838, -1198, 242, -928, 152, 206, -298, 350, -298, -658, 26, 530, 242, 62, -550, -910, 530, -640, 440, 413, -307, -127, -19, -271, 773, -523, -127, -307, -19, -271, 53, -271, -451, -433, 287, 107, -1, 251, -397, 323, 143, 35, 287, 962, -766, -658, 494, 233, -199, -253, 179, -577, 431, -703, -1063, 377, -793, 287, -397, -577, 107, 143, -793, 287, -307, 17, 233, 134, -370, 278, -370, -730, -46, 458, 170, -10, -622, -982, 458, -712, 368, 125, -127, 197, -127, -307, -1, 251, 35, 287, 170, -10, 89, 35, -1, -559, -919, 521, -649, 431, -253, -433, 251, 287, -649, 431, -163, 161, 377])\n assert answers_match(candidate(expression='9*8-7*6+5*4-3*2'), [324, -936, -1188, -936, -2448, 1458, -1314, -1188, -2322, -1314, -2826, -1314, -2826, -5094, -216, -396, -432, -396, -612, 1458, -1314, 918, -774, -1512, -2646, -432, -2646, -1566, -1314, -2826, -1314, -2826, -5094, -774, -990, -1314, -774, -3150, -5418, -990, -5418, -3258, -36, 144, 180, 144, 360, -198, 198, 180, 342, 198, 414, 198, 414, 738, -396, -216, -180, -216, 0, -36, 144, 180, 144, 360, 1242, -1242, 702, -702, -198, 198, 522, -522, -198, 198, -1620, -2754, -540, -2754, -1674, 180, 342, -180, 180, -2538, -1458, 342, -1098, 342, -1242, -2754, -1242, -2754, -5022, -702, -918, -1242, -702, -3078, -5346, -918, -5346, -3186, 198, 414, 198, 414, 738, -522, -306, 198, 414, -1242, -702, 198, -522, 198, -3186, -5454, -1026, -5454, -3294, 414, 738, -306, 414, -5022, -2862, 738, -2142, 738, 100, -40, -68, -40, -208, 226, -82, -68, -194, -82, -250, -82, -250, -502, 40, 20, 16, 20, -4, 226, -82, 166, -22, -104, -230, 16, -230, -110, -82, -250, -82, -250, -502, -22, -46, -82, -22, -286, -538, -46, -538, -298, -36, 144, 180, 144, 360, -198, 198, 180, 342, 198, 414, 198, 414, 738, -260, 1040, 1300, 1040, 2600, -1430, 1430, 1300, 2470, 1430, 2990, 1430, 2990, 5330, -316, -296, -292, -296, -272, 44, 64, 68, 64, 88, 20, 40, 44, 40, 64, 44, 64, 68, 64, 88, 380, 400, 404, 400, 424, 1242, -1242, 702, -702, -198, 198, 522, -522, -198, 198, 10, -10, -50, 50, -198, 198, -1430, 1430, 602, -602, -118, 118, -70, 70, -118, 118, -790, 790, -1572, -2706, -492, -2706, -1626, 228, 390, -132, 228, -2490, -1410, 390, -1050, 390, -116, -242, 4, -242, -122, 228, 390, 1684, 2854, -292, 68, 44, 68, 404, -2490, -1410, 390, -1050, 390, -26, 94, 390, 2854, -1210, 230, 134, 230, 1574, -1242, -2754, -1242, -2754, -5022, -702, -918, -1242, -702, -3078, -5346, -918, -5346, -3186, 198, 414, 198, 414, 738, -522, -306, 198, 414, -1242, -702, 198, -522, 198, -3186, -5454, -1026, -5454, -3294, 414, 738, -306, 414, -5022, -2862, 738, -2142, 738, -10, -178, -10, -178, -430, 50, 26, -10, 50, -214, -466, 26, -466, -226, 198, 414, 198, 414, 738, 1430, 2990, 1430, 2990, 5330, -602, -578, 118, 142, 70, 94, 118, 142, 790, 814, -1242, -702, 198, -522, 198, -10, 50, 198, 1430, -602, 118, 70, 118, 790, -3138, -5406, -978, -5406, -3246, 462, 786, -258, 462, -4974, -2814, 786, -2094, 786, -226, -478, 14, -478, -238, 462, 786, 3374, 5714, -578, 142, 94, 142, 814, -4974, -2814, 786, -2094, 786, -46, 194, 786, 5714, -2414, 466, 274, 466, 3154])\n assert answers_match(candidate(expression='7*8-9+2*3-1+4'), [21, -91, -14, -63, -70, 210, -406, -14, -140, -63, -70, -126, -70, -196, -35, 77, 0, 49, 56, 42, -126, -14, 42, -84, -210, 0, -98, -14, -7, -14, -70, -14, -140, 49, 56, -14, 42, -28, -154, 56, -42, 42, 51, 35, 46, 39, 38, 78, -10, 46, 28, 39, 38, 30, 38, 20, -11, 5, -6, 1, 2, 43, 59, 48, 55, 56, 42, -126, -14, 42, -90, 270, 10, -30, -98, 294, -54, -180, 30, -68, 16, 36, 18, -6, 48, -68, 16, 130, -20, 142, -31, -38, -94, -38, -164, 25, 32, -38, 18, -52, -178, 32, -66, 18, 47, 46, 38, 46, 28, 1, 2, 55, 56, -38, 18, 94, -6, 102, -46, -172, 38, -60, 24, 44, 26, 2, 56, -60, 24, 138, -12, 150])\n assert answers_match(candidate(expression='20*3+5-4*7+6-8*1'), [-240, -240, -240, -240, -240, -360, -360, -720, -360, -240, -240, -360, -720, -360, 160, 160, 160, 160, 160, -440, -440, 160, 160, -1040, -680, 160, -440, 160, -240, -240, -360, -720, -360, 160, 160, -440, 160, -1040, -680, 160, -440, 160, -240, -240, -240, -240, -240, -360, -360, -720, -360, -240, -240, -360, -720, -360, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, -440, -440, 160, 160, -440, -440, 520, 520, 520, 520, -1040, -680, 160, -440, 160, -1040, -680, 880, 880, -440, 160, -440, 520, 520, -240, -240, -360, -720, -360, 160, 160, -440, 160, -1040, -680, 160, -440, 160, -240, -240, -360, -720, -360, 400, 400, 400, 400, -440, 160, -440, 520, 520, -1040, -680, 160, -440, 160, -1040, -680, 880, 880, -440, 160, -440, 520, 520, 45, 45, 45, 45, 45, 39, 39, 21, 39, 45, 45, 39, 21, 39, 65, 65, 65, 65, 65, 35, 35, 65, 65, 5, 23, 65, 35, 65, 45, 45, 39, 21, 39, 65, 65, 35, 65, 5, 23, 65, 35, 65, 140, 140, 140, 140, 140, 134, 134, 116, 134, 140, 140, 134, 116, 134, 45, 45, 45, 45, 45, 39, 39, 21, 39, 45, 45, 39, 21, 39, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 305, 305, 305, 305, 305, 780, 780, 780, 780, 780, 305, 305, 305, 305, 305, -402, -402, 198, 198, -402, -402, 558, 558, 558, 558, 35, 35, 65, 65, 130, 130, 35, 35, 558, 558, 558, 558, 425, 425, 1090, 1090, 425, 425, -888, -528, 312, -288, 312, -888, -528, 1032, 1032, -288, 312, -288, 672, 672, 5, 23, 65, 35, 65, 100, 118, 5, 23, 1032, 1032, 785, 2020, 785, -402, 198, -402, 558, 558, 35, 65, 130, 35, 558, 558, 425, 1090, 425, -240, -240, -360, -720, -360, 160, 160, -440, 160, -1040, -680, 160, -440, 160, -240, -240, -360, -720, -360, 400, 400, 400, 400, -440, 160, -440, 520, 520, -1040, -680, 160, -440, 160, -1040, -680, 880, 880, -440, 160, -440, 520, 520, 45, 45, 39, 21, 39, 65, 65, 35, 65, 5, 23, 65, 35, 65, 140, 140, 134, 116, 134, 45, 45, 39, 21, 39, 400, 400, 400, 400, 305, 305, 780, 780, 305, 305, -402, 198, -402, 558, 558, 35, 65, 130, 35, 558, 558, 425, 1090, 425, -888, -528, 312, -288, 312, -888, -528, 1032, 1032, -288, 312, -288, 672, 672, 5, 23, 65, 35, 65, 100, 118, 5, 23, 1032, 1032, 785, 2020, 785, -402, 198, -402, 558, 558, 35, 65, 130, 35, 558, 558, 425, 1090, 425])\n assert answers_match(candidate(expression='7-2*3+1*4-5'), [3, 3, 15, 3, -15, 2, 2, 15, 14, -2, -20, 2, -20, -16, 10, 10, -20, 10, 55, 0, 0, 14, 14, 1, 0, -20, -2, -16, -12, -30, -8, -30, -26, 30, 75, 0, 14, -9, -5, 75, 3, 59])\n assert answers_match(candidate(expression='9+8*7-6+5*4-3+2*1'), [57, 57, -103, 57, -103, -103, -103, -39, -135, 57, -103, -103, -39, -135, 153, 153, -199, 153, -199, -103, -103, -247, -247, -39, -135, -39, -135, -279, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, -23, 137, -23, 137, 137, 137, 73, 169, -23, 137, 137, 73, 169, 41, 41, -87, 41, -87, -39, -39, 153, -39, 153, -183, -183, -327, -327, 137, 137, -159, -159, 161, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, 137, 137, 73, 169, 41, -87, -39, 153, -183, -327, 137, -159, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 64, 64, 44, 64, 44, 44, 44, 52, 40, 64, 44, 44, 52, 40, 76, 76, 32, 76, 32, 44, 44, 26, 26, 52, 40, 52, 40, 22, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 12, 12, 32, 12, 32, 32, 32, 24, 36, 12, 32, 32, 24, 36, 54, 54, 74, 54, 74, 74, 74, 66, 78, 54, 74, 74, 66, 78, 41, 41, -87, 41, -87, -39, -39, 153, -39, 153, -36, -36, 144, -36, 144, -4, -4, 48, -4, 48, -46, -46, 174, -46, 174, -148, -148, -292, -292, 172, 172, -124, -124, 196, 196, 34, 34, 16, 16, 32, 32, 74, 74, -124, -124, 196, 196, 184, 184, 56, 56, 224, 224, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, 137, 137, 73, 169, 41, -87, -39, 153, -183, -327, 137, -159, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 41, -87, -39, 153, -36, 144, -4, 48, -46, 174, -148, -292, 172, -124, 196, 34, 16, 32, 74, -124, 196, 184, 56, 224, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, 102, 102, -238, 102, -238, -238, -238, -102, -306, 102, -238, -238, -102, -306, 306, 306, -442, 306, -442, -238, -238, -544, -544, -102, -306, -102, -306, -612, 102, -238, -238, -102, -306, 306, -442, -238, -544, -102, -306, -102, -306, -612, -68, -68, 272, -68, 272, 272, 272, 136, 340, -68, 272, 272, 136, 340, 68, 68, -204, 68, -204, -102, -102, 306, -102, 306, -408, -408, -714, -714, 272, 272, -357, -357, 323, 323, -34, -238, -34, -238, -544, 136, 340, -34, 136, -340, -646, 340, -289, 391, 102, -238, -238, -102, -306, 306, -442, -238, -544, -102, -306, -102, -306, -612, -68, 272, 272, 136, 340, 68, -204, -102, 306, -408, -714, 272, -357, 323, -34, -238, -34, -238, -544, 136, 340, -34, 136, -340, -646, 340, -289, 391, 64, 64, 44, 64, 44, 44, 44, 52, 40, 64, 44, 44, 52, 40, 76, 76, 32, 76, 32, 44, 44, 26, 26, 52, 40, 52, 40, 22, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 118, 118, 98, 118, 98, 98, 98, 106, 94, 118, 98, 98, 106, 94, 130, 130, 86, 130, 86, 98, 98, 80, 80, 106, 94, 106, 94, 76, 118, 98, 98, 106, 94, 130, 86, 98, 80, 106, 94, 106, 94, 76, 12, 12, 32, 12, 32, 32, 32, 24, 36, 12, 32, 32, 24, 36, 54, 54, 74, 54, 74, 74, 74, 66, 78, 54, 74, 74, 66, 78, 12, 12, 32, 12, 32, 32, 32, 24, 36, 12, 32, 32, 24, 36, 54, 54, 74, 54, 74, 74, 74, 66, 78, 54, 74, 74, 66, 78, 108, 108, 128, 108, 128, 128, 128, 120, 132, 108, 128, 128, 120, 132, 23, 23, -69, 23, -69, -57, -57, 171, -57, 171, -54, -54, 162, -54, 162, -22, -22, 66, -22, 66, -64, -64, 192, -64, 192, 68, 68, -204, 68, -204, -102, -102, 306, -102, 306, -54, -54, 162, -54, 162, -108, -108, 324, -108, 324, -22, -22, 66, -22, 66, -64, -64, 192, -64, 192, -22, -22, 66, -22, 66, -64, -64, 192, -64, 192, -118, -118, 354, -118, 354, -148, -148, -292, -292, 172, 172, -124, -124, 196, 196, 34, 34, 16, 16, 32, 32, 74, 74, -124, -124, 196, 196, 184, 184, 56, 56, 224, 224, -328, -328, -634, -634, 352, 352, -277, -277, 403, 403, 34, 34, 16, 16, 88, 88, 70, 70, 32, 32, 74, 74, 32, 32, 74, 74, 128, 128, -97, -97, 223, 223, 211, 211, 83, 83, 251, 251, -277, -277, 403, 403, 211, 211, 427, 427, 83, 83, 251, 251, 83, 83, 251, 251, 467, 467, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -66, -270, -66, -270, -576, 104, 308, -66, 104, -372, -678, 308, -321, 359, 56, 44, 56, 44, 26, 110, 98, 110, 98, 80, 24, 36, 66, 78, 24, 36, 66, 78, 120, 132, -21, 59, 56, 24, 66, -66, 104, 56, 110, 24, 66, 24, 66, 120, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -324, -630, 356, -273, 407, 38, 20, 92, 74, 36, 78, 36, 78, 132, -93, 227, 215, 87, 255, -273, 407, 215, 431, 87, 255, 87, 255, 471, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, 137, 137, 73, 169, 41, -87, -39, 153, -183, -327, 137, -159, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 41, -87, -39, 153, -36, 144, -4, 48, -46, 174, -148, -292, 172, -124, 196, 34, 16, 32, 74, -124, 196, 184, 56, 224, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, 102, -238, -238, -102, -306, 306, -442, -238, -544, -102, -306, -102, -306, -612, -68, 272, 272, 136, 340, 68, -204, -102, 306, -408, -714, 272, -357, 323, -34, -238, -34, -238, -544, 136, 340, -34, 136, -340, -646, 340, -289, 391, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 118, 98, 98, 106, 94, 130, 86, 98, 80, 106, 94, 106, 94, 76, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 108, 128, 128, 120, 132, 23, -69, -57, 171, -54, 162, -22, 66, -64, 192, 68, -204, -102, 306, -54, 162, -108, 324, -22, 66, -64, 192, -22, 66, -64, 192, -118, 354, -148, -292, 172, -124, 196, 34, 16, 32, 74, -124, 196, 184, 56, 224, -328, -634, 352, -277, 403, 34, 16, 88, 70, 32, 74, 32, 74, 128, -97, 223, 211, 83, 251, -277, 403, 211, 427, 83, 251, 83, 251, 467, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -66, -270, -66, -270, -576, 104, 308, -66, 104, -372, -678, 308, -321, 359, 56, 44, 56, 44, 26, 110, 98, 110, 98, 80, 24, 36, 66, 78, 24, 36, 66, 78, 120, 132, -21, 59, 56, 24, 66, -66, 104, 56, 110, 24, 66, 24, 66, 120, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -324, -630, 356, -273, 407, 38, 20, 92, 74, 36, 78, 36, 78, 132, -93, 227, 215, 87, 255, -273, 407, 215, 431, 87, 255, 87, 255, 471])\n assert answers_match(candidate(expression='7*6-5*4+3*2-1*0'), [-308, -98, -308, -98, -98, -448, 42, -308, -448, 42, 42, 42, 42, 42, -140, -98, -140, -98, -98, -448, 42, -280, 42, -308, -448, -140, -448, -280, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 70, 28, 70, 28, 28, 98, 0, 70, 98, 0, 0, 0, 0, 0, -56, -98, -56, -98, -98, 70, 28, 70, 28, 28, -406, 0, -238, 0, 98, 0, -154, 0, 98, 0, -308, -448, -140, -448, -280, 70, 98, -56, 70, -406, -238, 98, -154, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 22, -8, 22, 22, -28, 42, -8, -28, 42, 42, 42, 42, 42, 16, 22, 16, 22, 22, -28, 42, -4, 42, -8, -28, 16, -28, -4, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 70, 28, 70, 28, 28, 98, 0, 70, 98, 0, 0, 0, 0, 0, 370, 148, 370, 148, 148, 518, 0, 370, 518, 0, 0, 0, 0, 0, -92, -98, -92, -98, -98, 34, 28, 34, 28, 28, 28, 22, 28, 22, 22, 34, 28, 34, 28, 28, 154, 148, 154, 148, 148, -406, 0, -238, 0, 98, 0, -154, 0, 98, 0, 14, 0, 38, 0, 98, 0, 518, 0, -190, 0, 62, 0, 50, 0, 62, 0, 302, 0, -308, -448, -140, -448, -280, 70, 98, -56, 70, -406, -238, 98, -154, 98, -8, -28, 16, -28, -4, 70, 98, 370, 518, -92, 34, 28, 34, 154, -406, -238, 98, -154, 98, 14, 38, 98, 518, -190, 62, 50, 62, 302, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n assert answers_match(candidate(expression='99-98+97-96+95-94'), [1, 1, -1, 189, -1, 1, 1, -1, -1, 189, -1, 189, -1, -1, 1, 1, 3, -187, 3, -193, -193, 1, 1, 1, 1, 3, -191, 3, 1, -189, 1, -189, -189, -187, 3, -381, -187, 1, 1, 3, -191, 3])\n assert answers_match(candidate(expression='1*1*1*1*1*1*1*1*1*1'), [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n assert answers_match(candidate(expression='9*8*7-6*5+4*3-2*1'), [-3384, -3384, -5976, -3384, -5976, -3384, -3384, -5976, -10296, -3384, -5976, -3384, -5976, -10296, -1944, -1944, -2376, -1944, -2376, -3384, -3384, -1944, -1944, -6696, -11016, -2376, -11016, -6696, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 648, 1080, 648, 1080, 648, 648, 1080, 1800, 648, 1080, 648, 1080, 1800, -1368, -1368, -936, -1368, -936, 648, 648, 1080, 648, 1080, -3384, -3384, -1944, -1944, 648, 648, -1368, -1368, 648, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 18, 18, -306, 18, -306, 18, 18, -306, -846, 18, -306, 18, -306, -846, 198, 198, 144, 198, 144, 18, 18, 198, 198, -396, -936, 144, -936, -396, 18, -306, 18, -306, -846, 198, 144, 18, 198, -396, -936, 144, -936, -396, 648, 648, 1080, 648, 1080, 648, 648, 1080, 1800, 648, 1080, 648, 1080, 1800, 4050, 4050, 6750, 4050, 6750, 4050, 4050, 6750, 11250, 4050, 6750, 4050, 6750, 11250, -1620, -1620, -1566, -1620, -1566, 396, 396, 450, 396, 450, 270, 270, 324, 270, 324, 396, 396, 450, 396, 450, 2286, 2286, 2340, 2286, 2340, -3384, -3384, -1944, -1944, 648, 648, -1368, -1368, 648, 648, 18, 18, 198, 198, 648, 648, 4050, 4050, -1620, -1620, 396, 396, 270, 270, 396, 396, 2286, 2286, -6858, -11178, -2538, -11178, -6858, 1206, 1926, -810, 1206, -10170, -5850, 1926, -4122, 1926, -432, -972, 108, -972, -432, 1206, 1926, 7632, 12132, -1566, 450, 324, 450, 2340, -10170, -5850, 1926, -4122, 1926, 36, 576, 1926, 12132, -4878, 1170, 792, 1170, 6840, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 18, -306, 18, -306, -846, 198, 144, 18, 198, -396, -936, 144, -936, -396, 648, 1080, 648, 1080, 1800, 4050, 6750, 4050, 6750, 11250, -1620, -1566, 396, 450, 270, 324, 396, 450, 2286, 2340, -3384, -1944, 648, -1368, 648, 18, 198, 648, 4050, -1620, 396, 270, 396, 2286, -6858, -11178, -2538, -11178, -6858, 1206, 1926, -810, 1206, -10170, -5850, 1926, -4122, 1926, -432, -972, 108, -972, -432, 1206, 1926, 7632, 12132, -1566, 450, 324, 450, 2340, -10170, -5850, 1926, -4122, 1926, 36, 576, 1926, 12132, -4878, 1170, 792, 1170, 6840, -3384, -3384, -5976, -3384, -5976, -3384, -3384, -5976, -10296, -3384, -5976, -3384, -5976, -10296, -1944, -1944, -2376, -1944, -2376, -3384, -3384, -1944, -1944, -6696, -11016, -2376, -11016, -6696, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 648, 1080, 648, 1080, 648, 648, 1080, 1800, 648, 1080, 648, 1080, 1800, -1368, -1368, -936, -1368, -936, 648, 648, 1080, 648, 1080, -3384, -3384, -1944, -1944, 648, 648, -1368, -1368, 648, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 450, 450, 414, 450, 414, 450, 450, 414, 354, 450, 414, 450, 414, 354, 470, 470, 464, 470, 464, 450, 450, 470, 470, 404, 344, 464, 344, 404, 450, 414, 450, 414, 354, 470, 464, 450, 470, 404, 344, 464, 344, 404, 450, 450, 414, 450, 414, 450, 450, 414, 354, 450, 414, 450, 414, 354, 470, 470, 464, 470, 464, 450, 450, 470, 470, 404, 344, 464, 344, 404, 450, 414, 450, 414, 354, 470, 464, 450, 470, 404, 344, 464, 344, 404, 648, 648, 1080, 648, 1080, 648, 648, 1080, 1800, 648, 1080, 648, 1080, 1800, 4050, 4050, 6750, 4050, 6750, 4050, 4050, 6750, 11250, 4050, 6750, 4050, 6750, 11250, 648, 648, 1080, 648, 1080, 648, 648, 1080, 1800, 648, 1080, 648, 1080, 1800, 4482, 4482, 7470, 4482, 7470, 4482, 4482, 7470, 12450, 4482, 7470, 4482, 7470, 12450, 4482, 4482, 7470, 4482, 7470, 4482, 4482, 7470, 12450, 4482, 7470, 4482, 7470, 12450, -1652, -1652, -1646, -1652, -1646, 364, 364, 370, 364, 370, 238, 238, 244, 238, 244, 364, 364, 370, 364, 370, 2254, 2254, 2260, 2254, 2260, -1652, -1652, -1646, -1652, -1646, 364, 364, 370, 364, 370, 478, 478, 484, 478, 484, 478, 478, 484, 478, 484, 364, 364, 370, 364, 370, 2254, 2254, 2260, 2254, 2260, 364, 364, 370, 364, 370, 2494, 2494, 2500, 2494, 2500, 2494, 2494, 2500, 2494, 2500, -3384, -3384, -1944, -1944, 648, 648, -1368, -1368, 648, 648, 18, 18, 198, 198, 648, 648, 4050, 4050, -1620, -1620, 396, 396, 270, 270, 396, 396, 2286, 2286, -3384, -3384, -1944, -1944, 648, 648, -1368, -1368, 648, 648, 450, 450, 470, 470, 450, 450, 470, 470, 648, 648, 4050, 4050, 648, 648, 4482, 4482, 4482, 4482, -1652, -1652, 364, 364, 238, 238, 364, 364, 2254, 2254, -1652, -1652, 364, 364, 478, 478, 478, 478, 364, 364, 2254, 2254, 364, 364, 2494, 2494, 2494, 2494, -6842, -11162, -2522, -11162, -6842, 1222, 1942, -794, 1222, -10154, -5834, 1942, -4106, 1942, -416, -956, 124, -956, -416, 1222, 1942, 7648, 12148, -1550, 466, 340, 466, 2356, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -6842, -11162, -2522, -11162, -6842, 1222, 1942, -794, 1222, -10154, -5834, 1942, -4106, 1942, 400, 340, 460, 340, 400, 400, 340, 460, 340, 400, 1222, 1942, 7648, 12148, 1222, 1942, 8464, 13444, 8464, 13444, -1646, 370, 244, 370, 2260, -1646, 370, 484, 484, 370, 2260, 370, 2500, 2500, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -10154, -5834, 1942, -4106, 1942, 1348, 1408, 1348, 1408, 1942, 12148, 1942, 13444, 13444, -4958, 1090, 712, 1090, 6760, -4958, 1090, 1432, 1432, 1090, 6760, 1090, 7480, 7480, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 18, -306, 18, -306, -846, 198, 144, 18, 198, -396, -936, 144, -936, -396, 648, 1080, 648, 1080, 1800, 4050, 6750, 4050, 6750, 11250, -1620, -1566, 396, 450, 270, 324, 396, 450, 2286, 2340, -3384, -1944, 648, -1368, 648, 18, 198, 648, 4050, -1620, 396, 270, 396, 2286, -6858, -11178, -2538, -11178, -6858, 1206, 1926, -810, 1206, -10170, -5850, 1926, -4122, 1926, -432, -972, 108, -972, -432, 1206, 1926, 7632, 12132, -1566, 450, 324, 450, 2340, -10170, -5850, 1926, -4122, 1926, 36, 576, 1926, 12132, -4878, 1170, 792, 1170, 6840, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 450, 414, 450, 414, 354, 470, 464, 450, 470, 404, 344, 464, 344, 404, 450, 414, 450, 414, 354, 470, 464, 450, 470, 404, 344, 464, 344, 404, 648, 1080, 648, 1080, 1800, 4050, 6750, 4050, 6750, 11250, 648, 1080, 648, 1080, 1800, 4482, 7470, 4482, 7470, 12450, 4482, 7470, 4482, 7470, 12450, -1652, -1646, 364, 370, 238, 244, 364, 370, 2254, 2260, -1652, -1646, 364, 370, 478, 484, 478, 484, 364, 370, 2254, 2260, 364, 370, 2494, 2500, 2494, 2500, -3384, -1944, 648, -1368, 648, 18, 198, 648, 4050, -1620, 396, 270, 396, 2286, -3384, -1944, 648, -1368, 648, 450, 470, 450, 470, 648, 4050, 648, 4482, 4482, -1652, 364, 238, 364, 2254, -1652, 364, 478, 478, 364, 2254, 364, 2494, 2494, -6842, -11162, -2522, -11162, -6842, 1222, 1942, -794, 1222, -10154, -5834, 1942, -4106, 1942, -416, -956, 124, -956, -416, 1222, 1942, 7648, 12148, -1550, 466, 340, 466, 2356, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -6842, -11162, -2522, -11162, -6842, 1222, 1942, -794, 1222, -10154, -5834, 1942, -4106, 1942, 400, 340, 460, 340, 400, 400, 340, 460, 340, 400, 1222, 1942, 7648, 12148, 1222, 1942, 8464, 13444, 8464, 13444, -1646, 370, 244, 370, 2260, -1646, 370, 484, 484, 370, 2260, 370, 2500, 2500, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -10154, -5834, 1942, -4106, 1942, 1348, 1408, 1348, 1408, 1942, 12148, 1942, 13444, 13444, -4958, 1090, 712, 1090, 6760, -4958, 1090, 1432, 1432, 1090, 6760, 1090, 7480, 7480])\n assert answers_match(candidate(expression='1*2*3*4*5-6*7+8'), [-2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -60, 20, -60, 20, -360, 1260, -360, 1620, 1620, -872, -152, -116, -152, 604, -872, -152, 52, 52, -152, 604, -152, 772, 772, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, -360, 1260, -360, 1620, 1620, -360, 1260, -360, -360, 1710, 1710, 1710, 1710, 1710, -880, -160, -124, -160, 596, -880, -160, 44, 44, -160, 596, -160, 764, 764, -880, -160, -124, -160, 596, -880, -160, -880, -160, 86, 86, 86, 86, 86, -160, 596, -160, 764, 764, -160, 596, -160, -160, 806, 806, 806, 806, 806, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -60, 20, -60, 20, -360, 1260, -360, 1620, 1620, -872, -152, -116, -152, 604, -872, -152, 52, 52, -152, 604, -152, 772, 772, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, -360, 1260, -360, 1620, 1620, -360, 1260, -360, -360, 1710, 1710, 1710, 1710, 1710, -360, 1260, -360, 1620, 1620, -360, 1260, -360, 1260, -360, -360, -360, -360, -360, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, -880, -160, -124, -160, 596, -880, -160, 44, 44, -160, 596, -160, 764, 764, -880, -160, -124, -160, 596, -880, -160, -880, -160, 86, 86, 86, 86, 86, -160, 596, -160, 764, 764, -160, 596, -160, -160, 806, 806, 806, 806, 806, -880, -160, -124, -160, 596, -880, -160, 44, 44, -160, 596, -160, 764, 764, -880, -160, -124, -160, 596, -880, -160, -124, -160, 596, -880, -160, -880, -160, -880, -160, -880, -160, -880, -160, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, -160, 596, -160, 764, 764, -160, 596, -160, -160, 806, 806, 806, 806, 806, -160, 596, -160, 764, 764, -160, 596, -160, 596, -160, -160, -160, -160, -160, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806])\n assert answers_match(candidate(expression='3+3*3-3*3+3*3-3*3'), [147, -15, -15, -15, -177, 336, 12, -15, -69, -69, -231, 12, -231, -393, 39, -15, -15, -15, -69, 336, 12, 228, 12, -69, -123, -15, -123, -69, -69, -231, 12, -231, -393, -69, -123, 12, 12, -285, -447, -123, -447, -285, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -69, -15, -15, -15, 39, -51, 3, 3, 3, 57, 273, 3, 165, 3, 3, 3, 57, 3, -51, 3, -123, -177, -69, -177, -123, -24, -24, -15, 3, -159, -105, -24, -51, 3, -51, -213, 30, -213, -375, -51, -105, 30, 30, -267, -429, -105, -429, -267, 3, 3, 3, 3, 3, -51, 3, 3, 57, 3, 3, 3, 3, 3, -321, -483, -159, -483, -321, -24, -24, 3, 57, -429, -267, -24, -105, 57, 57, 3, 3, 3, -51, 120, 12, 3, -15, -15, -69, 12, -69, -123, 21, 3, 3, 3, -15, 120, 12, 84, 12, -15, -33, 3, -33, -15, -15, -69, 12, -69, -123, -15, -33, 12, 12, -87, -141, -33, -141, -87, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -87, 21, 21, 21, 129, -213, 3, 21, 57, 57, 165, 3, 165, 273, -33, -15, -15, -15, 3, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, 3, 21, 21, 21, 39, 273, 3, 165, 3, 3, 3, 57, 3, -51, 3, 57, 3, 21, 3, 3, 3, -213, 3, 93, 3, -15, 3, -15, 3, -15, 3, -123, 3, -105, -159, -51, -159, -105, -6, -6, 3, 21, -141, -87, -6, -33, 21, -33, -51, -15, -51, -33, -6, -6, 66, 102, -15, 3, 3, 3, 21, -141, -87, -6, -33, 21, -33, -15, -6, 102, -51, 3, 3, 3, 57, -51, -213, 30, -213, -375, -51, -105, 30, 30, -267, -429, -105, -429, -267, 3, 3, 3, 3, 3, -51, 3, 3, 57, 3, 3, 3, 3, 3, -321, -483, -159, -483, -321, -24, -24, 3, 57, -429, -267, -24, -105, 57, 3, -51, 30, -51, -105, 3, -15, 30, 30, -69, -123, -15, -123, -69, 3, 3, 3, 3, 3, 57, 165, 3, 165, 273, -51, -33, 3, 21, 3, 21, 3, 21, 57, 75, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -303, -465, -141, -465, -303, -6, -6, 21, 75, -411, -249, -6, -87, 75, -87, -141, -33, -141, -87, -6, -6, 210, 318, -33, 21, 21, 21, 75, -411, -249, -6, -87, 75, -87, -33, -6, 318, -141, 21, 21, 21, 183, 288, -36, -36, -36, -360, 666, 18, -36, -144, -144, -468, 18, -468, -792, 72, -36, -36, -36, -144, 666, 18, 450, 18, -144, -252, -36, -252, -144, -144, -468, 18, -468, -792, -144, -252, 18, 18, -576, -900, -252, -900, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, -36, -36, -36, 72, -108, 0, 0, 0, 108, 540, 0, 324, 0, 0, 0, 108, 0, -108, 0, -252, -360, -144, -360, -252, -54, -54, -36, 0, -324, -216, -54, -108, 0, -108, -432, 54, -432, -756, -108, -216, 54, 54, -540, -864, -216, -864, -540, 0, 0, 0, 0, 0, -108, 0, 0, 108, 0, 0, 0, 0, 0, -648, -972, -324, -972, -648, -54, -54, 0, 108, -864, -540, -54, -216, 108, 57, 3, 3, 3, -51, 120, 12, 3, -15, -15, -69, 12, -69, -123, 21, 3, 3, 3, -15, 120, 12, 84, 12, -15, -33, 3, -33, -15, -15, -69, 12, -69, -123, -15, -33, 12, 12, -87, -141, -33, -141, -87, 63, 9, 9, 9, -45, 126, 18, 9, -9, -9, -63, 18, -63, -117, 27, 9, 9, 9, -9, 126, 18, 90, 18, -9, -27, 9, -27, -9, -9, -63, 18, -63, -117, -9, -27, 18, 18, -81, -135, -27, -135, -81, -45, 9, 9, 9, 63, -108, 0, 9, 27, 27, 81, 0, 81, 135, -135, 27, 27, 27, 189, -324, 0, 27, 81, 81, 243, 0, 243, 405, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -135, 27, 27, 27, 189, -324, 0, 27, 81, 81, 243, 0, 243, 405, -225, 45, 45, 45, 315, -540, 0, 45, 135, 135, 405, 0, 405, 675, -33, -15, -15, -15, 3, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, 3, 21, 21, 21, 39, -54, -36, -36, -36, -18, -18, 0, 0, 0, 18, -15, 3, 3, 3, 21, -9, 9, 9, 9, 27, -9, 9, 9, 9, 27, 9, 27, 27, 27, 45, -18, 0, 0, 0, 18, 9, 27, 27, 27, 45, 27, 45, 45, 45, 63, 252, 0, 144, 0, -18, 0, 36, 0, -72, 0, 36, 0, 0, 0, -18, 0, -234, 0, 72, 0, -36, 0, -36, 0, -36, 0, -144, 0, 540, 0, 324, 0, 0, 0, 108, 0, -108, 0, 36, 0, 0, 0, 0, 0, -36, 0, -108, 0, -324, 0, 0, 0, -324, 0, -540, 0, 72, 0, -36, 0, -36, 0, -36, 0, -144, 0, 198, 0, -18, 0, -36, 0, -72, 0, -72, 0, -180, 0, -18, 0, -180, 0, -288, 0, -105, -159, -51, -159, -105, -6, -6, 3, 21, -141, -87, -6, -33, 21, -33, -51, -15, -51, -33, -6, -6, 66, 102, -15, 3, 3, 3, 21, -141, -87, -6, -33, 21, -33, -15, -6, 102, -51, 3, 3, 3, 57, -207, -315, -99, -315, -207, -9, -9, 9, 45, -279, -171, -9, -63, 45, -33, -51, -15, -51, -33, -27, -45, -9, -45, -27, 27, 45, 99, 153, -9, -9, 99, 153, 171, 261, -15, 3, 3, 3, 21, -36, 0, 3, 9, 9, 27, 0, 27, 45, -135, -81, 0, -27, 27, -27, -9, 0, 108, -45, 9, 9, 9, 63, -279, -171, -9, -63, 45, -27, -9, -9, 9, 45, 153, -9, 153, 261, -45, 9, 9, 9, 63, -108, 0, 9, 27, 27, 81, 0, 81, 135, -45, -207, 36, -207, -369, -45, -99, 36, 36, -261, -423, -99, -423, -261, 9, 9, 9, 9, 9, -45, 9, 9, 63, 9, 9, 9, 9, 9, -315, -477, -153, -477, -315, -18, -18, 9, 63, -423, -261, -18, -99, 63, 9, -45, 36, -45, -99, 9, -9, 36, 36, -63, -117, -9, -117, -63, 9, 9, 9, 9, 9, 63, 171, 9, 171, 279, -45, -27, 9, 27, 9, 27, 9, 27, 63, 81, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -297, -459, -135, -459, -297, 0, 0, 27, 81, -405, -243, 0, -81, 81, -81, -135, -27, -135, -81, 0, 0, 216, 324, -27, 27, 27, 27, 81, -405, -243, 0, -81, 81, -81, -27, 0, 324, -135, 27, 27, 27, 189, -108, -432, 54, -432, -756, -108, -216, 54, 54, -540, -864, -216, -864, -540, 0, 0, 0, 0, 0, -108, 0, 0, 108, 0, 0, 0, 0, 0, -648, -972, -324, -972, -648, -54, -54, 0, 108, -864, -540, -54, -216, 108, 9, -45, 36, -45, -99, 9, -9, 36, 36, -63, -117, -9, -117, -63, 27, -27, 54, -27, -81, 27, 9, 54, 54, -45, -99, 9, -99, -45, 27, 81, 0, 81, 135, 81, 243, 0, 243, 405, 0, 0, 0, 0, 0, 81, 243, 0, 243, 405, 135, 405, 0, 405, 675, -45, -27, 9, 27, 9, 27, 9, 27, 63, 81, -108, -90, 0, 18, 9, 27, 27, 45, 27, 45, 81, 99, 0, 18, 81, 99, 135, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -297, -459, -135, -459, -297, 0, 0, 27, 81, -405, -243, 0, -81, 81, -81, -135, -27, -135, -81, 0, 0, 216, 324, -27, 27, 27, 27, 81, -405, -243, 0, -81, 81, -81, -27, 0, 324, -135, 27, 27, 27, 189, -603, -927, -279, -927, -603, -9, -9, 45, 153, -819, -495, -9, -171, 153, -81, -135, -27, -135, -81, -63, -117, -9, -117, -63, 99, 153, 315, 477, -9, -9, 315, 477, 531, 801, -27, 27, 27, 27, 81, -90, 18, 27, 45, 45, 99, 18, 99, 153, -387, -225, 18, -63, 99, -63, -9, 18, 342, -117, 45, 45, 45, 207, -819, -495, -9, -171, 153, -63, -9, -9, 45, 153, 477, -9, 477, 801, -117, 45, 45, 45, 207, -306, 18, 45, 99, 99, 261, 18, 261, 423])\n assert answers_match(candidate(expression='1+2+3*4-5*6+7-8*9'), [900, 60, 900, -660, -660, 120, -48, 36, 120, -660, -660, -768, -1524, -768, 180, 12, 180, -132, -132, -270, -102, -210, -42, -396, -312, -252, -270, -210, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 180, 12, 180, -132, -132, -410, -18, -410, 318, 318, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, -114, -114, -150, -402, -150, -132, -132, 318, 318, -708, -168, -168, -168, 372, -1716, -960, -420, -582, -42, -546, -294, -420, 750, -708, -168, -168, -168, 372, 1496, 96, 1496, -1104, -1104, 196, -84, 56, 196, -1104, -1104, -1284, -2544, -1284, 296, 16, 296, -224, -224, -454, -174, -354, -74, -664, -524, -424, -454, -354, -944, -944, -1124, -2384, -1124, -224, -224, -1214, -314, -3104, -1844, -944, -1214, -314, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 316, 36, 316, -204, -204, 56, 0, 28, 56, -204, -204, -240, -492, -240, 60, 4, 60, -44, -44, -530, -26, -530, 406, 406, 296, 16, 296, -224, -224, -530, -26, -530, 406, 406, -884, -44, -884, 676, 676, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -194, -138, -94, -38, -80, -24, -74, -18, -70, -14, -10, 46, -94, -38, -10, 46, 26, 82, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -376, -236, -136, -166, -66, -122, -94, -116, -88, -84, 46, -136, 46, 124, -140, -80, -80, -80, -20, -194, -94, -80, -74, -70, -10, -94, -10, 26, -548, -548, -656, -1412, -656, -116, -116, -710, -170, -1844, -1088, -548, -710, -170, -98, -98, -134, -386, -134, -116, -116, 334, 334, -692, -152, -152, -152, 388, -1700, -944, -404, -566, -26, -530, -278, -404, 766, -692, -152, -152, -152, 388, -944, -944, -1124, -2384, -1124, -224, -224, -1214, -314, -3104, -1844, -944, -1214, -314, -98, -98, -134, -386, -134, -44, -44, -80, -332, -80, -44, -44, 406, 406, -224, -224, 406, 406, 676, 676, -692, -152, -152, -152, 388, -1178, -278, -152, -98, -62, 478, -278, 478, 802, -1700, -944, -404, -566, -26, -530, -278, -404, 766, -692, -152, -152, -152, 388, -2816, -1556, -656, -926, -26, -530, -278, -476, -224, -188, 982, -656, 982, 1684, -692, -152, -152, -152, 388, -1178, -278, -152, -98, -62, 478, -278, 478, 802, 900, 60, 900, -660, -660, 120, -48, 36, 120, -660, -660, -768, -1524, -768, 180, 12, 180, -132, -132, -270, -102, -210, -42, -396, -312, -252, -270, -210, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 180, 12, 180, -132, -132, -410, -18, -410, 318, 318, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, -114, -114, -150, -402, -150, -132, -132, 318, 318, -708, -168, -168, -168, 372, -1716, -960, -420, -582, -42, -546, -294, -420, 750, -708, -168, -168, -168, 372, 1794, 114, 1794, -1326, -1326, 234, -102, 66, 234, -1326, -1326, -1542, -3054, -1542, 354, 18, 354, -270, -270, -546, -210, -426, -90, -798, -630, -510, -546, -426, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, 1794, 114, 1794, -1326, -1326, 234, -102, 66, 234, -1326, -1326, -1542, -3054, -1542, 354, 18, 354, -270, -270, -546, -210, -426, -90, -798, -630, -510, -546, -426, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 316, 36, 316, -204, -204, 56, 0, 28, 56, -204, -204, -240, -492, -240, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 319, 39, 319, -201, -201, 59, 3, 31, 59, -201, -201, -237, -489, -237, 319, 39, 319, -201, -201, 59, 3, 31, 59, -201, -201, -237, -489, -237, 0, 0, 0, 0, 0, -590, -30, -590, 450, 450, 236, 12, 236, -180, -180, -590, -30, -590, 450, 450, -944, -48, -944, 720, 720, 0, 0, 0, 0, 0, -590, -30, -590, 450, 450, 354, 18, 354, -270, -270, 354, 18, 354, -270, -270, -590, -30, -590, 450, 450, -944, -48, -944, 720, 720, -590, -30, -590, 450, 450, -1121, -57, -1121, 855, 855, -1121, -57, -1121, 855, 855, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -194, -138, -94, -38, -80, -24, -74, -18, -70, -14, -10, 46, -94, -38, -10, 46, 26, 82, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -221, -165, -101, -45, -221, -165, -101, -45, -80, -24, -74, -18, -80, -24, -71, -15, -71, -15, -65, -9, -5, 51, -89, -33, -5, 51, 31, 87, -65, -9, -5, 51, -101, -45, -101, -45, -5, 51, 31, 87, -5, 51, 49, 105, 49, 105, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -376, -236, -136, -166, -66, -122, -94, -116, -88, -84, 46, -136, 46, 124, -140, -80, -80, -80, -20, -194, -94, -80, -74, -70, -10, -94, -10, 26, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -438, -270, -150, -186, -66, -438, -270, -150, -186, -66, -122, -94, -116, -88, -122, -94, -113, -85, -113, -85, -72, 58, -124, 58, 136, -72, 58, -150, -150, 58, 136, 58, 175, 175, -140, -80, -80, -80, -20, -194, -94, -80, -74, -70, -10, -94, -10, 26, -140, -80, -80, -80, -20, -221, -101, -221, -101, -80, -74, -80, -71, -71, -65, -5, -89, -5, 31, -65, -5, -101, -101, -5, 31, -5, 49, 49, -540, -540, -648, -1404, -648, -108, -108, -702, -162, -1836, -1080, -540, -702, -162, -90, -90, -126, -378, -126, -108, -108, 342, 342, -684, -144, -144, -144, 396, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -936, -936, -1116, -2376, -1116, -216, -216, -1206, -306, -3096, -1836, -936, -1206, -306, -90, -90, -126, -378, -126, -36, -36, -72, -324, -72, -36, -36, 414, 414, -216, -216, 414, 414, 684, 684, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -2808, -1548, -648, -918, -18, -522, -270, -468, -216, -180, 990, -648, 990, 1692, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -540, -540, -648, -1404, -648, -108, -108, -702, -162, -1836, -1080, -540, -702, -162, -90, -90, -126, -378, -126, -108, -108, 342, 342, -684, -144, -144, -144, 396, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, -90, -90, -126, -378, -126, -36, -36, -72, -324, -72, -90, -90, -126, -378, -126, -9, -9, -45, -297, -45, -9, -9, -45, -297, -45, 0, 0, 450, 450, -180, -180, 450, 450, 720, 720, 0, 0, 450, 450, -270, -270, -270, -270, 450, 450, 720, 720, 450, 450, 855, 855, 855, 855, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -684, -144, -144, -144, 396, -1413, -333, -1413, -333, -144, -90, -144, -63, -63, -9, 531, -225, 531, 855, -9, 531, -333, -333, 531, 855, 531, 1017, 1017, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -2808, -1548, -648, -918, -18, -522, -270, -468, -216, -180, 990, -648, 990, 1692, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -3366, -1854, -774, -1098, -18, -3366, -1854, -774, -1098, -18, -522, -270, -468, -216, -522, -270, -441, -189, -441, -189, -72, 1098, -540, 1098, 1800, -72, 1098, -774, -774, 1098, 1800, 1098, 2151, 2151, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -684, -144, -144, -144, 396, -1413, -333, -1413, -333, -144, -90, -144, -63, -63, -9, 531, -225, 531, 855, -9, 531, -333, -333, 531, 855, 531, 1017, 1017])\n assert answers_match(candidate(expression='1*2*3*4*5'), [120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120])\n assert answers_match(candidate(expression='6*7+8-9*10+11-12'), [-396, -396, -444, -972, -444, -12, -12, -456, -24, -1116, -588, -156, -456, -24, -396, -396, -444, -972, -444, 324, 324, 324, 324, -456, -24, -456, 354, 354, -1116, -588, -156, -456, -24, -1116, -588, 684, 684, -456, -24, -456, 354, 354, -31, -31, -39, -127, -39, 33, 33, -41, 31, -151, -63, 9, -41, 31, 9, 9, 1, -87, 1, -31, -31, -39, -127, -39, 324, 324, 324, 324, 369, 369, 729, 729, 369, 369, -451, -19, -451, 359, 359, -41, 31, -1, -41, 359, 359, 409, 809, 409, -1056, -528, -96, -396, 36, -1056, -528, 744, 744, -396, 36, -396, 414, 414, -151, -63, 9, -41, 31, -111, -23, -151, -63, 744, 744, 849, 1689, 849, -451, -19, -451, 359, 359, -41, 31, -1, -41, 359, 359, 409, 809, 409])\n assert answers_match(candidate(expression='8*3+4-2*9+5-1'), [-152, -152, -120, -160, -120, 232, 232, -56, 200, -176, -136, 240, -56, 200, -152, -152, -120, -160, -120, 520, 520, 520, 520, -56, 200, -56, 392, 392, -176, -136, 240, -56, 200, -176, -136, 552, 552, -56, 200, -56, 392, 392, 2, 2, 6, 1, 6, 50, 50, 14, 46, -1, 4, 51, 14, 46, 30, 30, 34, 29, 34, 2, 2, 6, 1, 6, 520, 520, 520, 520, 338, 338, 702, 702, 338, 338, -84, 172, -84, 364, 364, 14, 46, 42, 14, 364, 364, 238, 490, 238, -169, -129, 247, -49, 207, -169, -129, 559, 559, -49, 207, -49, 399, 399, -1, 4, 51, 14, 46, 27, 32, -1, 4, 559, 559, 363, 755, 363, -84, 172, -84, 364, 364, 14, 46, 42, 14, 364, 364, 238, 490, 238])\n assert answers_match(candidate(expression='2*2*2*2-1+1*1*1'), [0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 8, 8, 8, 8, 8, 12, 12, 16, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 10, 10, 14, 14, 10, 10, 16, 16, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 12, 12, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 8, 8, 8, 8, 8, 12, 12, 16, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 9, 9, 13, 13, 9, 9, 15, 15, 15, 15, 9, 9, 13, 13, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 0, 16, 14, 14, 14, 14, 14, 9, 13, 9, 15, 15, 9, 13, 9, 9, 16, 16, 16, 16, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 12, 12, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 0, 0, 16, 0, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 9, 13, 9, 15, 15, 9, 13, 9, 9, 16, 16, 16, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 0, 16, 14, 14, 14, 14, 14, 9, 13, 9, 15, 15, 9, 13, 9, 9, 16, 16, 16, 16, 16])\n assert answers_match(candidate(expression='5*5*5-3*3*3+2*2*2'), [-2350, -2350, -4375, -3025, -4375, -1150, -1150, -4375, -3175, -3025, -4375, -1825, -4375, -3175, -2350, -2350, -4375, -3025, -4375, -750, -750, -750, -750, -4375, -3175, -4375, -2775, -2775, -3025, -4375, -1825, -4375, -3175, -3025, -4375, -1425, -1425, -4375, -3175, -4375, -2775, -2775, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, -350, -350, -350, -350, 650, 650, -100, -100, 650, 650, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -370, -370, -775, -505, -775, -130, -130, -775, -535, -505, -775, -265, -775, -535, -370, -370, -775, -505, -775, -50, -50, -50, -50, -775, -535, -775, -455, -455, -505, -775, -265, -775, -535, -505, -775, -185, -185, -775, -535, -775, -455, -455, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, 3630, 3630, 6600, 4620, 6600, 1870, 1870, 6600, 4840, 4620, 6600, 2860, 6600, 4840, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, 880, 880, 1600, 1120, 1600, 1650, 1650, 3000, 2100, 3000, 3630, 3630, 6600, 4620, 6600, -510, -510, -510, -510, 490, 490, -260, -260, 490, 490, 30, 30, 30, 30, 490, 490, 1030, 1030, -260, -260, 490, 490, 280, 280, 490, 490, 1030, 1030, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -380, -650, -140, -650, -410, -380, -650, -60, -60, -650, -410, -650, -330, -330, 2100, 3000, 1300, 3000, 2200, 4620, 6600, 2860, 6600, 4840, -1400, -2000, 2100, 3000, 1120, 1600, 2100, 3000, 4620, 6600, -1060, -1060, 940, -560, 940, 20, 20, 940, 2020, -560, 940, 520, 940, 2020, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -2350, -2350, -4375, -3025, -4375, -1150, -1150, -4375, -3175, -3025, -4375, -1825, -4375, -3175, -2350, -2350, -4375, -3025, -4375, -750, -750, -750, -750, -4375, -3175, -4375, -2775, -2775, -3025, -4375, -1825, -4375, -3175, -3025, -4375, -1425, -1425, -4375, -3175, -4375, -2775, -2775, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, -350, -350, -350, -350, 650, 650, -100, -100, 650, 650, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 26, 26, -55, -1, -55, 74, 74, -55, -7, -1, -55, 47, -55, -7, 26, 26, -55, -1, -55, 90, 90, 90, 90, -55, -7, -55, 9, 9, -1, -55, 47, -55, -7, -1, -55, 63, 63, -55, -7, -55, 9, 9, 26, 26, -55, -1, -55, 74, 74, -55, -7, -1, -55, 47, -55, -7, 26, 26, -55, -1, -55, 90, 90, 90, 90, -55, -7, -55, 9, 9, -1, -55, 47, -55, -7, -1, -55, 63, 63, -55, -7, -55, 9, 9, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, 3630, 3630, 6600, 4620, 6600, 1870, 1870, 6600, 4840, 4620, 6600, 2860, 6600, 4840, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, 4026, 4026, 7320, 5124, 7320, 2074, 2074, 7320, 5368, 5124, 7320, 3172, 7320, 5368, 4026, 4026, 7320, 5124, 7320, 2074, 2074, 7320, 5368, 5124, 7320, 3172, 7320, 5368, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, 880, 880, 1600, 1120, 1600, 1650, 1650, 3000, 2100, 3000, 3630, 3630, 6600, 4620, 6600, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, 1276, 1276, 2320, 1624, 2320, 1276, 1276, 2320, 1624, 2320, 1650, 1650, 3000, 2100, 3000, 3630, 3630, 6600, 4620, 6600, 1650, 1650, 3000, 2100, 3000, 4026, 4026, 7320, 5124, 7320, 4026, 4026, 7320, 5124, 7320, -542, -542, -542, -542, 458, 458, -292, -292, 458, 458, -2, -2, -2, -2, 458, 458, 998, 998, -292, -292, 458, 458, 248, 248, 458, 458, 998, 998, -542, -542, -542, -542, 458, 458, -292, -292, 458, 458, 106, 106, 106, 106, 106, 106, 106, 106, 458, 458, 998, 998, 458, 458, 1106, 1106, 1106, 1106, -292, -292, 458, 458, 248, 248, 458, 458, 998, 998, -292, -292, 458, 458, 356, 356, 356, 356, 458, 458, 998, 998, 458, 458, 1106, 1106, 1106, 1106, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 320, 368, 320, 384, 384, 320, 368, 320, 384, 384, 3000, 2200, 6600, 4840, 3000, 2200, 7320, 5368, 7320, 5368, -2000, 3000, 1600, 3000, 6600, -2000, 3000, 2320, 2320, 3000, 6600, 3000, 7320, 7320, -2192, -2192, 1808, -1192, 1808, -32, -32, 1808, 3968, -1192, 1808, 968, 1808, 3968, -2192, -2192, 1808, -1192, 1808, 400, 400, 400, 400, 1808, 3968, 1808, 4400, 4400, -1192, 1808, 968, 1808, 3968, -1192, 1808, 1400, 1400, 1808, 3968, 1808, 4400, 4400, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -380, -650, -140, -650, -410, -380, -650, -60, -60, -650, -410, -650, -330, -330, 2100, 3000, 1300, 3000, 2200, 4620, 6600, 2860, 6600, 4840, -1400, -2000, 2100, 3000, 1120, 1600, 2100, 3000, 4620, 6600, -1060, -1060, 940, -560, 940, 20, 20, 940, 2020, -560, 940, 520, 940, 2020, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 124, 70, 172, 70, 118, 124, 70, 188, 188, 70, 118, 70, 134, 134, 124, 70, 172, 70, 118, 124, 70, 188, 188, 70, 118, 70, 134, 134, 2100, 3000, 1300, 3000, 2200, 4620, 6600, 2860, 6600, 4840, 2100, 3000, 1300, 3000, 2200, 5124, 7320, 3172, 7320, 5368, 5124, 7320, 3172, 7320, 5368, -1400, -2000, 2100, 3000, 1120, 1600, 2100, 3000, 4620, 6600, -1400, -2000, 2100, 3000, 1624, 2320, 1624, 2320, 2100, 3000, 4620, 6600, 2100, 3000, 5124, 7320, 5124, 7320, -1092, -1092, 908, -592, 908, -12, -12, 908, 1988, -592, 908, 488, 908, 1988, -1092, -1092, 908, -592, 908, 204, 204, 204, 204, 908, 1988, 908, 2204, 2204, -592, 908, 488, 908, 1988, -592, 908, 704, 704, 908, 1988, 908, 2204, 2204, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 320, 368, 320, 384, 384, 320, 368, 320, 384, 384, 3000, 2200, 6600, 4840, 3000, 2200, 7320, 5368, 7320, 5368, -2000, 3000, 1600, 3000, 6600, -2000, 3000, 2320, 2320, 3000, 6600, 3000, 7320, 7320, -2192, -2192, 1808, -1192, 1808, -32, -32, 1808, 3968, -1192, 1808, 968, 1808, 3968, -2192, -2192, 1808, -1192, 1808, 400, 400, 400, 400, 1808, 3968, 1808, 4400, 4400, -1192, 1808, 968, 1808, 3968, -1192, 1808, 1400, 1400, 1808, 3968, 1808, 4400, 4400])\n assert answers_match(candidate(expression='5*3+10-2*8+4'), [-55, -35, 495, 5, 355, -55, -35, 660, 660, 5, 355, 5, 460, 460, 1, 5, 111, 13, 83, 41, 45, 1, 5, 660, 660, 276, 756, 276, -11, 339, -11, 444, 444, 13, 83, 53, 13, 444, 444, 188, 508, 188])\n assert answers_match(candidate(expression='9*8-7*6+5*4-3*2+1'), [1269, 639, -1251, 9, -1251, -999, -1125, -1251, -3519, 261, -999, -1251, -999, -2511, 3537, 2151, -2007, 765, -2007, -999, -1125, -2133, -2259, -2007, -4275, -2007, -4275, -7677, 261, -999, -1251, -999, -2511, 1395, -1377, -1251, -2385, -1377, -2889, -1377, -2889, -5157, -81, -171, -441, -261, -441, -405, -423, -441, -765, -225, -405, -441, -405, -621, 3537, 2151, -2007, 765, -2007, 2187, 1341, -1197, 495, -1197, -1485, -1503, -2619, -2637, -405, -423, -2619, -2637, -1539, -1557, -2007, -4275, -2007, -4275, -7677, -1197, -1521, -2007, -1197, -4761, -8163, -1521, -8163, -4923, 315, -945, -1197, -945, -2457, 1449, -1323, -1197, -2331, -1323, -2835, -1323, -2835, -5103, -225, -405, -441, -405, -621, 1449, -1323, 909, -783, -1521, -2655, -441, -2655, -1575, -1323, -2835, -1323, -2835, -5103, -783, -999, -1323, -783, -3159, -5427, -999, -5427, -3267, -171, -81, 189, 9, 189, 153, 171, 189, 513, -27, 153, 189, 153, 369, -495, -297, 297, -99, 297, 153, 171, 315, 333, 297, 621, 297, 621, 1107, -27, 153, 189, 153, 369, -189, 207, 189, 351, 207, 423, 207, 423, 747, -531, -441, -171, -351, -171, -207, -189, -171, 153, -387, -207, -171, -207, 9, -171, -81, 189, 9, 189, 153, 171, 189, 513, -27, 153, 189, 153, 369, 3105, 1863, -1863, 621, -1863, 1755, 1053, -1053, 351, -1053, -495, -297, 297, -99, 297, 1305, 783, -783, 261, -783, -495, -297, 297, -99, 297, -1647, -1629, -2781, -2763, -567, -549, -2781, -2763, -1701, -1683, 153, 171, 315, 333, -207, -189, 153, 171, -2565, -2547, -1485, -1467, 315, 333, -1125, -1107, 315, 333, -1863, -4131, -1863, -4131, -7533, -1053, -1377, -1863, -1053, -4617, -8019, -1377, -8019, -4779, 297, 621, 297, 621, 1107, -783, -459, 297, 621, -1863, -1053, 297, -783, 297, -4779, -8181, -1539, -8181, -4941, 621, 1107, -459, 621, -7533, -4293, 1107, -3213, 1107, 333, -927, -1179, -927, -2439, 1467, -1305, -1179, -2313, -1305, -2817, -1305, -2817, -5085, -207, -387, -423, -387, -603, 1467, -1305, 927, -765, -1503, -2637, -423, -2637, -1557, -1305, -2817, -1305, -2817, -5085, -765, -981, -1305, -765, -3141, -5409, -981, -5409, -3249, -27, 153, 189, 153, 369, -189, 207, 189, 351, 207, 423, 207, 423, 747, -387, -207, -171, -207, 9, -27, 153, 189, 153, 369, 1251, -1233, 711, -693, -189, 207, 531, -513, -189, 207, -1611, -2745, -531, -2745, -1665, 189, 351, -171, 189, -2529, -1449, 351, -1089, 351, -1233, -2745, -1233, -2745, -5013, -693, -909, -1233, -693, -3069, -5337, -909, -5337, -3177, 207, 423, 207, 423, 747, -513, -297, 207, 423, -1233, -693, 207, -513, 207, -3177, -5445, -1017, -5445, -3285, 423, 747, -297, 423, -5013, -2853, 747, -2133, 747, 205, 135, -75, 65, -75, -47, -61, -75, -327, 93, -47, -75, -47, -215, 457, 303, -159, 149, -159, -47, -61, -173, -187, -159, -411, -159, -411, -789, 93, -47, -75, -47, -215, 219, -89, -75, -201, -89, -257, -89, -257, -509, 55, 45, 15, 35, 15, 19, 17, 15, -21, 39, 19, 15, 19, -5, 457, 303, -159, 149, -159, 307, 213, -69, 119, -69, -101, -103, -227, -229, 19, 17, -227, -229, -107, -109, -159, -411, -159, -411, -789, -69, -105, -159, -69, -465, -843, -105, -843, -483, 99, -41, -69, -41, -209, 225, -83, -69, -195, -83, -251, -83, -251, -503, 39, 19, 15, 19, -5, 225, -83, 165, -23, -105, -231, 15, -231, -111, -83, -251, -83, -251, -503, -23, -47, -83, -23, -287, -539, -47, -539, -299, -171, -81, 189, 9, 189, 153, 171, 189, 513, -27, 153, 189, 153, 369, -495, -297, 297, -99, 297, 153, 171, 315, 333, 297, 621, 297, 621, 1107, -27, 153, 189, 153, 369, -189, 207, 189, 351, 207, 423, 207, 423, 747, -1235, -585, 1365, 65, 1365, 1105, 1235, 1365, 3705, -195, 1105, 1365, 1105, 2665, -3575, -2145, 2145, -715, 2145, 1105, 1235, 2275, 2405, 2145, 4485, 2145, 4485, 7995, -195, 1105, 1365, 1105, 2665, -1365, 1495, 1365, 2535, 1495, 3055, 1495, 3055, 5395, -331, -321, -291, -311, -291, -295, -293, -291, -255, -315, -295, -291, -295, -271, 29, 39, 69, 49, 69, 65, 67, 69, 105, 45, 65, 69, 65, 89, 5, 15, 45, 25, 45, 41, 43, 45, 81, 21, 41, 45, 41, 65, 29, 39, 69, 49, 69, 65, 67, 69, 105, 45, 65, 69, 65, 89, 365, 375, 405, 385, 405, 401, 403, 405, 441, 381, 401, 405, 401, 425, 3105, 1863, -1863, 621, -1863, 1755, 1053, -1053, 351, -1053, -495, -297, 297, -99, 297, 1305, 783, -783, 261, -783, -495, -297, 297, -99, 297, 25, 15, -15, 5, -15, -125, -75, 75, -25, 75, -495, -297, 297, -99, 297, -3575, -2145, 2145, -715, 2145, 1505, 903, -903, 301, -903, -295, -177, 177, -59, 177, -175, -105, 105, -35, 105, -295, -177, 177, -59, 177, -1975, -1185, 1185, -395, 1185, -1575, -1573, -2709, -2707, -495, -493, -2709, -2707, -1629, -1627, 225, 227, 387, 389, -135, -133, 225, 227, -2493, -2491, -1413, -1411, 387, 389, -1053, -1051, 387, 389, -119, -117, -245, -243, 1, 3, -245, -243, -125, -123, 225, 227, 387, 389, 1681, 1683, 2851, 2853, -295, -293, 65, 67, 41, 43, 65, 67, 401, 403, -2493, -2491, -1413, -1411, 387, 389, -1053, -1051, 387, 389, -29, -27, 91, 93, 387, 389, 2851, 2853, -1213, -1211, 227, 229, 131, 133, 227, 229, 1571, 1573, -1863, -4131, -1863, -4131, -7533, -1053, -1377, -1863, -1053, -4617, -8019, -1377, -8019, -4779, 297, 621, 297, 621, 1107, -783, -459, 297, 621, -1863, -1053, 297, -783, 297, -4779, -8181, -1539, -8181, -4941, 621, 1107, -459, 621, -7533, -4293, 1107, -3213, 1107, -15, -267, -15, -267, -645, 75, 39, -15, 75, -321, -699, 39, -699, -339, 297, 621, 297, 621, 1107, 2145, 4485, 2145, 4485, 7995, -903, -867, 177, 213, 105, 141, 177, 213, 1185, 1221, -1863, -1053, 297, -783, 297, -15, 75, 297, 2145, -903, 177, 105, 177, 1185, -4707, -8109, -1467, -8109, -4869, 693, 1179, -387, 693, -7461, -4221, 1179, -3141, 1179, -339, -717, 21, -717, -357, 693, 1179, 5061, 8571, -867, 213, 141, 213, 1221, -7461, -4221, 1179, -3141, 1179, -69, 291, 1179, 8571, -3621, 699, 411, 699, 4731, 325, -935, -1187, -935, -2447, 1459, -1313, -1187, -2321, -1313, -2825, -1313, -2825, -5093, -215, -395, -431, -395, -611, 1459, -1313, 919, -773, -1511, -2645, -431, -2645, -1565, -1313, -2825, -1313, -2825, -5093, -773, -989, -1313, -773, -3149, -5417, -989, -5417, -3257, -35, 145, 181, 145, 361, -197, 199, 181, 343, 199, 415, 199, 415, 739, -395, -215, -179, -215, 1, -35, 145, 181, 145, 361, 1243, -1241, 703, -701, -197, 199, 523, -521, -197, 199, -1619, -2753, -539, -2753, -1673, 181, 343, -179, 181, -2537, -1457, 343, -1097, 343, -1241, -2753, -1241, -2753, -5021, -701, -917, -1241, -701, -3077, -5345, -917, -5345, -3185, 199, 415, 199, 415, 739, -521, -305, 199, 415, -1241, -701, 199, -521, 199, -3185, -5453, -1025, -5453, -3293, 415, 739, -305, 415, -5021, -2861, 739, -2141, 739, 101, -39, -67, -39, -207, 227, -81, -67, -193, -81, -249, -81, -249, -501, 41, 21, 17, 21, -3, 227, -81, 167, -21, -103, -229, 17, -229, -109, -81, -249, -81, -249, -501, -21, -45, -81, -21, -285, -537, -45, -537, -297, -35, 145, 181, 145, 361, -197, 199, 181, 343, 199, 415, 199, 415, 739, -259, 1041, 1301, 1041, 2601, -1429, 1431, 1301, 2471, 1431, 2991, 1431, 2991, 5331, -315, -295, -291, -295, -271, 45, 65, 69, 65, 89, 21, 41, 45, 41, 65, 45, 65, 69, 65, 89, 381, 401, 405, 401, 425, 1243, -1241, 703, -701, -197, 199, 523, -521, -197, 199, 11, -9, -49, 51, -197, 199, -1429, 1431, 603, -601, -117, 119, -69, 71, -117, 119, -789, 791, -1571, -2705, -491, -2705, -1625, 229, 391, -131, 229, -2489, -1409, 391, -1049, 391, -115, -241, 5, -241, -121, 229, 391, 1685, 2855, -291, 69, 45, 69, 405, -2489, -1409, 391, -1049, 391, -25, 95, 391, 2855, -1209, 231, 135, 231, 1575, -1241, -2753, -1241, -2753, -5021, -701, -917, -1241, -701, -3077, -5345, -917, -5345, -3185, 199, 415, 199, 415, 739, -521, -305, 199, 415, -1241, -701, 199, -521, 199, -3185, -5453, -1025, -5453, -3293, 415, 739, -305, 415, -5021, -2861, 739, -2141, 739, -9, -177, -9, -177, -429, 51, 27, -9, 51, -213, -465, 27, -465, -225, 199, 415, 199, 415, 739, 1431, 2991, 1431, 2991, 5331, -601, -577, 119, 143, 71, 95, 119, 143, 791, 815, -1241, -701, 199, -521, 199, -9, 51, 199, 1431, -601, 119, 71, 119, 791, -3137, -5405, -977, -5405, -3245, 463, 787, -257, 463, -4973, -2813, 787, -2093, 787, -225, -477, 15, -477, -237, 463, 787, 3375, 5715, -577, 143, 95, 143, 815, -4973, -2813, 787, -2093, 787, -45, 195, 787, 5715, -2413, 467, 275, 467, 3155])\n assert answers_match(candidate(expression='5+5+5+5+5+5+5+5+5+5'), [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50])\n assert answers_match(candidate(expression='9*8+7*6-5*4+3*2'), [-2700, -3960, -1188, -3960, -2448, 702, 954, -432, 702, -3582, -2070, 954, -1314, 954, 0, -180, 216, -180, 36, 702, 954, 3402, 4734, -756, 378, 324, 378, 1458, -3582, -2070, 954, -1314, 954, 198, 414, 954, 4734, -1638, 630, 522, 630, 2790, -5940, -8640, -2700, -8640, -5400, 1350, 1890, -1080, 1350, -7830, -4590, 1890, -2970, 1890, 0, -180, 216, -180, 36, 360, 180, 576, 180, 396, 1350, 1890, 4050, 5670, 1350, 1890, 4050, 5670, 7650, 10710, -756, 378, 324, 378, 1458, -1836, 594, 324, 684, 594, 1674, 594, 1674, 3114, -3510, -1998, 1026, -1242, 1026, 270, 486, 1026, 4806, -1566, 702, 594, 702, 2862, -7830, -4590, 1890, -2970, 1890, 270, 486, 990, 1206, 1890, 5670, 1890, 5670, 10710, -1566, 702, 594, 702, 2862, -3726, 1134, 594, 1314, 1134, 3294, 1134, 3294, 6174, -236, -376, -68, -376, -208, 142, 170, 16, 142, -334, -166, 170, -82, 170, 64, 44, 88, 44, 68, 142, 170, 442, 590, -20, 106, 100, 106, 226, -334, -166, 170, -82, 170, 86, 110, 170, 590, -118, 134, 122, 134, 374, -5940, -8640, -2700, -8640, -5400, 1350, 1890, -1080, 1350, -7830, -4590, 1890, -2970, 1890, -3476, -5056, -1580, -5056, -3160, 790, 1106, -632, 790, -4582, -2686, 1106, -1738, 1106, 400, 380, 424, 380, 404, 760, 740, 784, 740, 764, 64, 44, 88, 44, 68, 760, 740, 784, 740, 764, 424, 404, 448, 404, 428, 1350, 1890, 4050, 5670, 1350, 1890, 4050, 5670, 7650, 10710, 790, 1106, 1090, 1526, 1350, 1890, 790, 1106, 4450, 6230, 8050, 11270, 1090, 1526, 8050, 11270, 4690, 6566, -804, 330, 276, 330, 1410, -1884, 546, 276, 636, 546, 1626, 546, 1626, 3066, -20, 106, 100, 106, 226, -1884, 546, -1100, 322, 436, 796, 100, 796, 460, 546, 1626, 546, 1626, 3066, 322, 442, 546, 322, 1786, 3226, 442, 3226, 1882, -3510, -1998, 1026, -1242, 1026, 270, 486, 1026, 4806, -1566, 702, 594, 702, 2862, -7830, -4590, 1890, -2970, 1890, 270, 486, 990, 1206, 1890, 5670, 1890, 5670, 10710, -1566, 702, 594, 702, 2862, -3726, 1134, 594, 1314, 1134, 3294, 1134, 3294, 6174, -262, -94, 242, -10, 242, 158, 182, 242, 662, -46, 206, 194, 206, 446, -7830, -4590, 1890, -2970, 1890, -4582, -2686, 1106, -1738, 1106, 830, 854, 1550, 1574, 158, 182, 1550, 1574, 878, 902, 1890, 5670, 1890, 5670, 10710, 1106, 1526, 1890, 1106, 6230, 11270, 1526, 11270, 6566, -1614, 654, 546, 654, 2814, -3774, 1086, 546, 1266, 1086, 3246, 1086, 3246, 6126, -46, 206, 194, 206, 446, -3774, 1086, -2206, 638, 866, 1586, 194, 1586, 914, 1086, 3246, 1086, 3246, 6126, 638, 878, 1086, 638, 3566, 6446, 878, 6446, 3758])\n assert answers_match(candidate(expression='10*9-8*7+6*5-4*3'), [2890, -1910, -1910, -1910, -6710, 7370, -3030, -1910, -4150, -3030, -7830, -3030, -7830, -14550, -50, -650, -650, -650, -1250, 7370, -3030, 4430, -1770, -2750, -4990, -650, -4990, -2890, -3030, -7830, -3030, -7830, -14550, -1770, -2370, -3030, -1770, -8670, -15390, -2370, -15390, -9090, -350, 250, 250, 250, 850, -910, 390, 250, 530, 390, 990, 390, 990, 1830, -890, -290, -290, -290, 310, -350, 250, 250, 250, 850, 6650, -2850, 3710, -1590, -910, 390, 2870, -1230, -910, 390, -2990, -5230, -890, -5230, -3130, 250, 530, -290, 250, -4870, -2770, 530, -2170, 530, -2850, -7650, -2850, -7650, -14370, -1590, -2190, -2850, -1590, -8490, -15210, -2190, -15210, -8910, 390, 990, 390, 990, 1830, -1230, -630, 390, 990, -2850, -1590, 390, -1230, 390, -8730, -15450, -2430, -15450, -9150, 990, 1830, -630, 990, -14370, -8070, 1830, -6270, 1830, 370, -110, -110, -110, -590, 818, -222, -110, -334, -222, -702, -222, -702, -1374, 76, 16, 16, 16, -44, 818, -222, 524, -96, -194, -418, 16, -418, -208, -222, -702, -222, -702, -1374, -96, -156, -222, -96, -786, -1458, -156, -1458, -828, -350, 250, 250, 250, 850, -910, 390, 250, 530, 390, 990, 390, 990, 1830, -2870, 2050, 2050, 2050, 6970, -7462, 3198, 2050, 4346, 3198, 8118, 3198, 8118, 15006, -512, -452, -452, -452, -392, 28, 88, 88, 88, 148, -8, 52, 52, 52, 112, 28, 88, 88, 88, 148, 532, 592, 592, 592, 652, 6650, -2850, 3710, -1590, -910, 390, 2870, -1230, -910, 390, 98, -42, -196, 84, -910, 390, -7462, 3198, 3248, -1392, -532, 228, -280, 120, -532, 228, -4060, 1740, -2882, -5122, -782, -5122, -3022, 358, 638, -182, 358, -4762, -2662, 638, -2062, 638, -218, -442, -8, -442, -232, 358, 638, 3022, 5318, -452, 88, 52, 88, 592, -4762, -2662, 638, -2062, 638, -82, 128, 638, 5318, -2332, 368, 188, 368, 2888, -2850, -7650, -2850, -7650, -14370, -1590, -2190, -2850, -1590, -8490, -15210, -2190, -15210, -8910, 390, 990, 390, 990, 1830, -1230, -630, 390, 990, -2850, -1590, 390, -1230, 390, -8730, -15450, -2430, -15450, -9150, 990, 1830, -630, 990, -14370, -8070, 1830, -6270, 1830, -42, -522, -42, -522, -1194, 84, 24, -42, 84, -606, -1278, 24, -1278, -648, 390, 990, 390, 990, 1830, 3198, 8118, 3198, 8118, 15006, -1392, -1332, 228, 288, 120, 180, 228, 288, 1740, 1800, -2850, -1590, 390, -1230, 390, -42, 84, 390, 3198, -1392, 228, 120, 228, 1740, -8622, -15342, -2322, -15342, -9042, 1098, 1938, -522, 1098, -14262, -7962, 1938, -6162, 1938, -630, -1302, 0, -1302, -672, 1098, 1938, 9090, 15978, -1332, 288, 180, 288, 1800, -14262, -7962, 1938, -6162, 1938, -222, 408, 1938, 15978, -6972, 1128, 588, 1128, 8688])\n assert answers_match(candidate(expression='9*8-7+6*5-4*3+2'), [819, 495, -261, 279, -261, -81, -135, -261, -1161, 369, -171, -171, -171, -711, 1827, 1125, -513, 657, -513, -81, -135, -333, -387, -513, -1413, -513, -1413, -2673, 369, -171, -171, -171, -711, 873, -297, -171, -423, -297, -837, -297, -837, -1593, -801, -477, 279, -261, 279, 99, 153, 279, 1179, -351, 189, 189, 189, 729, 675, 405, -225, 225, -225, -945, -567, 315, -315, 315, -441, -387, -693, -639, 99, 153, -405, -351, 135, 189, -225, -1125, -225, -1125, -2385, 315, 1215, -225, 315, -1485, -2745, 1215, -1305, 1395, 405, -135, -135, -135, -675, 909, -261, -135, -387, -261, -801, -261, -801, -1557, -351, 189, 189, 189, 729, 333, -117, -423, 207, -351, -603, 189, -315, 225, -117, -657, -117, -657, -1413, 207, 747, -117, 207, -873, -1629, 747, -765, 855, 155, 119, 35, 95, 35, 55, 49, 35, -65, 105, 45, 45, 45, -15, 267, 189, 7, 137, 7, 55, 49, 27, 21, 7, -93, 7, -93, -233, 105, 45, 45, 45, -15, 161, 31, 45, 17, 31, -29, 31, -29, -113, -81, -45, 39, -21, 39, 19, 25, 39, 139, -31, 29, 29, 29, 89, -25, 11, 95, 35, 95, 75, 81, 95, 195, 25, 85, 85, 85, 145, 675, 405, -225, 225, -225, -945, -567, 315, -315, 315, -885, -531, 295, -295, 295, -225, -135, 75, -75, 75, -1065, -639, 355, -355, 355, -281, -275, -533, -527, 259, 265, -245, -239, 295, 301, 15, 21, -13, -7, 19, 25, 75, 81, -245, -239, 295, 301, 275, 281, 55, 61, 335, 341, -225, -1125, -225, -1125, -2385, 315, 1215, -225, 315, -1485, -2745, 1215, -1305, 1395, 295, 195, 295, 195, 55, 75, 175, 355, 455, -225, 315, 295, 75, 355, -1325, -2585, 1375, -1145, 1555, 155, 15, 175, 455, -1145, 1555, 1455, 355, 1755, 389, -151, -151, -151, -691, 893, -277, -151, -403, -277, -817, -277, -817, -1573, -367, 173, 173, 173, 713, 317, -133, -439, 191, -367, -619, 173, -331, 209, -133, -673, -133, -673, -1429, 191, 731, -133, 191, -889, -1645, 731, -781, 839, 109, 49, 49, 49, -11, 165, 35, 49, 21, 35, -25, 35, -25, -109, -31, 29, 29, 29, 89, 25, 85, 85, 85, 145, 317, -133, -439, 191, -411, 179, -103, 47, -495, 215, -271, -523, 269, -235, 305, 25, -3, 29, 85, -235, 305, 285, 65, 345, -133, -673, -133, -673, -1429, 191, 731, -133, 191, -889, -1645, 731, -781, 839, 179, 119, 179, 119, 35, 47, 107, 215, 275, -133, 191, 179, 47, 215, -793, -1549, 827, -685, 935, 95, 11, 107, 275, -685, 935, 875, 215, 1055])\n assert answers_match(candidate(expression='8*9-2*3+5*2'), [-136, -184, -56, -184, -104, 728, 896, 104, 248, -112, -32, 896, 128, 416, 46, 40, 56, 40, 50, 728, 896, 910, 1120, 34, 178, 76, 178, 220, -112, -32, 896, 128, 416, 112, 122, 896, 1120, 58, 346, 142, 346, 430])\n assert answers_match(candidate(expression='8*7-6*5+4*3-2*1'), [-376, -376, -664, -376, -664, -376, -376, -664, -1144, -376, -664, -376, -664, -1144, -216, -216, -264, -216, -264, -376, -376, -216, -216, -744, -1224, -264, -1224, -744, -376, -664, -376, -664, -1144, -216, -264, -376, -216, -744, -1224, -264, -1224, -744, 72, 72, 120, 72, 120, 72, 72, 120, 200, 72, 120, 72, 120, 200, -152, -152, -104, -152, -104, 72, 72, 120, 72, 120, -376, -376, -216, -216, 72, 72, -152, -152, 72, 72, -776, -1256, -296, -1256, -776, 120, 200, -104, 120, -1144, -664, 200, -472, 200, -376, -664, -376, -664, -1144, -216, -264, -376, -216, -744, -1224, -264, -1224, -744, 72, 120, 72, 120, 200, -152, -104, 72, 120, -376, -216, 72, -152, 72, -776, -1256, -296, -1256, -776, 120, 200, -104, 120, -1144, -664, 200, -472, 200, 2, 2, -34, 2, -34, 2, 2, -34, -94, 2, -34, 2, -34, -94, 22, 22, 16, 22, 16, 2, 2, 22, 22, -44, -104, 16, -104, -44, 2, -34, 2, -34, -94, 22, 16, 2, 22, -44, -104, 16, -104, -44, 72, 72, 120, 72, 120, 72, 72, 120, 200, 72, 120, 72, 120, 200, 450, 450, 750, 450, 750, 450, 450, 750, 1250, 450, 750, 450, 750, 1250, -180, -180, -174, -180, -174, 44, 44, 50, 44, 50, 30, 30, 36, 30, 36, 44, 44, 50, 44, 50, 254, 254, 260, 254, 260, -376, -376, -216, -216, 72, 72, -152, -152, 72, 72, 2, 2, 22, 22, 72, 72, 450, 450, -180, -180, 44, 44, 30, 30, 44, 44, 254, 254, -762, -1242, -282, -1242, -762, 134, 214, -90, 134, -1130, -650, 214, -458, 214, -48, -108, 12, -108, -48, 134, 214, 848, 1348, -174, 50, 36, 50, 260, -1130, -650, 214, -458, 214, 4, 64, 214, 1348, -542, 130, 88, 130, 760, -376, -664, -376, -664, -1144, -216, -264, -376, -216, -744, -1224, -264, -1224, -744, 72, 120, 72, 120, 200, -152, -104, 72, 120, -376, -216, 72, -152, 72, -776, -1256, -296, -1256, -776, 120, 200, -104, 120, -1144, -664, 200, -472, 200, 2, -34, 2, -34, -94, 22, 16, 2, 22, -44, -104, 16, -104, -44, 72, 120, 72, 120, 200, 450, 750, 450, 750, 1250, -180, -174, 44, 50, 30, 36, 44, 50, 254, 260, -376, -216, 72, -152, 72, 2, 22, 72, 450, -180, 44, 30, 44, 254, -762, -1242, -282, -1242, -762, 134, 214, -90, 134, -1130, -650, 214, -458, 214, -48, -108, 12, -108, -48, 134, 214, 848, 1348, -174, 50, 36, 50, 260, -1130, -650, 214, -458, 214, 4, 64, 214, 1348, -542, 130, 88, 130, 760])\n assert answers_match(candidate(expression='3+3*3-3+3*3-3+3'), [30, -24, -6, -6, -24, 66, -42, -6, -24, -6, -24, 3, -24, -42, -24, 30, 12, 12, 30, 30, -24, -24, 30, -42, -60, 12, -42, 12, 12, -6, 21, -6, -24, 12, 30, 12, 12, -24, -42, 30, -24, 30, 18, 0, 6, 6, 0, 30, -6, 6, 0, 6, 0, 9, 0, -6, -6, 12, 6, 6, 12, 0, 18, 12, 12, 18, 30, -24, -24, 30, -6, 12, -6, 12, -24, 30, -30, -48, 24, -30, 24, -6, -12, 6, 12, -30, 24, 6, 6, 24, 6, -12, 15, -12, -30, 6, 24, 6, 6, -30, -48, 24, -30, 24, 12, 6, 15, 6, 0, 6, 12, 12, 18, 6, 6, 6, 6, 6, -24, -42, 30, -24, 30, 0, -6, 12, 18, -24, 30, 12, 12, 30, 54, -54, -18, -18, -54, 126, -90, -18, -54, -18, -54, 0, -54, -90, -54, 54, 18, 18, 54, 54, -54, -54, 54, -90, -126, 18, -90, 18, 18, -18, 36, -18, -54, 18, 54, 18, 18, -54, -90, 54, -54, 54, 18, 0, 6, 6, 0, 30, -6, 6, 0, 6, 0, 9, 0, -6, 24, 6, 12, 12, 6, 36, 0, 12, 6, 12, 6, 15, 6, 0, -6, 12, 6, 6, 12, 0, 18, 12, 12, 18, -9, 9, 3, 3, 9, 0, 18, 12, 12, 18, 6, 24, 18, 18, 24, 18, -18, -36, 36, -18, 18, -18, 18, -36, 36, 54, -54, -54, 54, -18, 18, -36, 36, -18, 18, -36, 36, -9, 9, -36, 36, -54, 54, -30, -48, 24, -30, 24, -6, -12, 6, 12, -30, 24, 6, 6, 24, -60, -96, 48, -60, 48, -6, -12, 0, -6, 6, 12, 3, 12, 18, -24, 30, 12, 12, 30, -60, 48, 12, 30, 12, 30, 3, 30, 48, 6, -12, 15, -12, -30, 6, 24, 6, 6, -30, -48, 24, -30, 24, 12, 6, 15, 6, 0, 6, 12, 12, 18, 6, 6, 6, 6, 6, -24, -42, 30, -24, 30, 0, -6, 12, 18, -24, 30, 12, 12, 30, 3, -33, 21, -33, -69, 3, 39, 3, 3, -69, -105, 39, -69, 39, 12, 6, 15, 6, 0, 18, 12, 21, 12, 6, 6, 12, 12, 18, 3, 9, 12, 18, 18, 24, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -24, -42, 30, -24, 30, 0, -6, 12, 18, -24, 30, 12, 12, 30, -54, -90, 54, -54, 54, 0, -6, 6, 0, 12, 18, 9, 18, 24, -18, 36, 18, 18, 36, -54, 54, 18, 36, 18, 36, 9, 36, 54])\n assert answers_match(candidate(expression='5*6-7+8-9*10+11'), [900, 460, 100, 350, -10, 900, 460, -600, -600, 350, -10, 350, -325, -325, -910, -470, -110, -360, 0, -990, -550, -910, -470, 0, 0, -210, -1890, -210, 460, 100, 460, -215, -215, -360, 0, -440, -360, 55, 55, -45, -845, -45, 204, 116, 44, 94, 22, 204, 116, -96, -96, 94, 22, 94, -41, -41, -186, -98, -26, -76, -4, -158, -70, 2, -48, 24, -234, -146, -154, -66, -174, -86, -186, -98, -158, -70, 0, 0, -210, -1890, -210, 504, 504, -126, 462, -1134, 546, 126, -126, 462, 416, 56, 416, -259, -259, -404, -44, -484, -404, 11, 11, -89, -889, -89, 116, 44, 116, -19, -19, -76, -4, -48, 24, -124, -44, -64, -76, -48, 11, 11, -89, -889, -89, 251, 251, -49, 231, -529, 271, 71, -49, 231])\n assert answers_match(candidate(expression='5*5-4*4+3*3-2*2+1'), [125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 305, -395, 25, -395, 310, 215, -260, 25, -260, -205, -210, -365, -370, -70, -75, -365, -370, -230, -235, -395, -635, -395, -635, -1115, -260, -320, -395, -260, -725, -1205, -320, -1205, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -100, -85, -10, -55, -10, -40, -35, -10, 50, -65, -20, -25, -20, 20, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, -265, -260, -425, -420, -130, -125, -425, -420, -290, -285, 35, 40, 75, 80, -40, -35, 35, 40, -375, -370, -240, -235, 75, 80, -150, -145, 75, 80, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, 10, -170, -150, -170, -330, 170, -250, -150, -310, -250, -410, -250, -410, -730, -35, -80, -75, -80, -120, 170, -250, 125, -160, -210, -370, -75, -370, -235, -250, -410, -250, -410, -730, -160, -200, -250, -160, -470, -790, -200, -790, -520, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -65, -20, -25, -20, 20, 10, 55, 50, 55, 95, 120, -225, 75, -135, -30, 75, 45, -75, -30, 75, -250, -410, -115, -410, -275, 50, 90, -25, 50, -360, -225, 90, -135, 90, -225, -385, -225, -385, -705, -135, -175, -225, -135, -445, -765, -175, -765, -495, 75, 115, 75, 115, 195, -75, -35, 75, 115, -225, -135, 75, -75, 75, -485, -805, -215, -805, -535, 115, 195, -35, 115, -705, -435, 195, -255, 195, 45, 33, -27, 9, -27, -3, -7, -27, -75, 17, -19, -15, -19, -51, 109, 81, -59, 25, -59, -3, -7, -35, -39, -59, -107, -59, -107, -203, 17, -19, -15, -19, -51, 49, -35, -15, -47, -35, -67, -35, -67, -131, 18, 15, 0, 9, 0, 6, 5, 0, -12, 11, 2, 3, 2, -6, 109, 81, -59, 25, -59, 82, 63, -32, 25, -32, -21, -22, -53, -54, 6, 5, -53, -54, -26, -27, -59, -107, -59, -107, -203, -32, -44, -59, -32, -125, -221, -44, -221, -140, 20, -16, -12, -16, -48, 52, -32, -12, -44, -32, -64, -32, -64, -128, 11, 2, 3, 2, -6, 52, -32, 43, -14, -24, -56, 3, -56, -29, -32, -64, -32, -64, -128, -14, -22, -32, -14, -76, -140, -22, -140, -86, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -105, -42, 273, 84, 273, 147, 168, 273, 525, 42, 231, 210, 231, 399, -441, -294, 441, 0, 441, 147, 168, 315, 336, 441, 693, 441, 693, 1197, 42, 231, 210, 231, 399, -126, 315, 210, 378, 315, 483, 315, 483, 819, -64, -61, -46, -55, -46, -52, -51, -46, -34, -57, -48, -49, -48, -40, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 0, 3, 18, 9, 18, 12, 13, 18, 30, 7, 16, 15, 16, 24, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 75, 78, 93, 84, 93, 87, 88, 93, 105, 82, 91, 90, 91, 99, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, 9, 6, -9, 0, -9, -18, -12, 18, 0, 18, -105, -70, 105, 0, 105, -441, -294, 441, 0, 441, 156, 104, -156, 0, -156, -69, -46, 69, 0, 69, -36, -24, 36, 0, 36, -69, -46, 69, 0, 69, -261, -174, 261, 0, 261, -241, -240, -401, -400, -106, -105, -401, -400, -266, -265, 59, 60, 99, 100, -16, -15, 59, 60, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -33, -32, -65, -64, -6, -5, -65, -64, -38, -37, 59, 60, 99, 100, 267, 268, 435, 436, -52, -51, 23, 24, 12, 13, 23, 24, 87, 88, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -15, -14, 12, 13, 99, 100, 435, 436, -162, -161, 63, 64, 30, 31, 63, 64, 255, 256, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, -9, -57, -9, -57, -153, 18, 6, -9, 18, -75, -171, 6, -171, -90, 105, 165, 105, 165, 285, 441, 693, 441, 693, 1197, -156, -144, 69, 81, 36, 48, 69, 81, 261, 273, -345, -210, 105, -120, 105, -9, 18, 105, 441, -156, 69, 36, 69, 261, -711, -1191, -306, -1191, -786, 189, 309, -36, 189, -1041, -636, 309, -366, 309, -87, -183, -6, -183, -102, 189, 309, 813, 1317, -144, 81, 48, 81, 273, -1041, -636, 309, -366, 309, -33, 48, 309, 1317, -474, 201, 102, 201, 777, 6, -174, -154, -174, -334, 166, -254, -154, -314, -254, -414, -254, -414, -734, -39, -84, -79, -84, -124, 166, -254, 121, -164, -214, -374, -79, -374, -239, -254, -414, -254, -414, -734, -164, -204, -254, -164, -474, -794, -204, -794, -524, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, -69, -24, -29, -24, 16, 6, 51, 46, 51, 91, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, -254, -414, -119, -414, -279, 46, 86, -29, 46, -364, -229, 86, -139, 86, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, 22, -14, -10, -14, -46, 54, -30, -10, -42, -30, -62, -30, -62, -126, 13, 4, 5, 4, -4, 54, -30, 45, -12, -22, -54, 5, -54, -27, -30, -62, -30, -62, -126, -12, -20, -30, -12, -74, -138, -20, -138, -84, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, 22, 211, 190, 211, 379, -146, 295, 190, 358, 295, 463, 295, 463, 799, -57, -48, -49, -48, -40, 18, 27, 26, 27, 35, 7, 16, 15, 16, 24, 18, 27, 26, 27, 35, 82, 91, 90, 91, 99, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, 4, -5, -5, 13, -34, 71, -146, 295, 53, -103, -22, 47, -11, 25, -22, 47, -86, 175, -238, -398, -103, -398, -263, 62, 102, -13, 62, -348, -213, 102, -123, 102, -30, -62, -3, -62, -35, 62, 102, 270, 438, -49, 26, 15, 26, 90, -348, -213, 102, -123, 102, -12, 15, 102, 438, -159, 66, 33, 66, 258, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, -5, -37, -5, -37, -101, 13, 5, -5, 13, -49, -113, 5, -113, -59, 71, 111, 71, 111, 191, 295, 463, 295, 463, 799, -103, -95, 47, 55, 25, 33, 47, 55, 175, 183, -229, -139, 71, -79, 71, -5, 13, 71, 295, -103, 47, 25, 47, 175, -473, -793, -203, -793, -523, 127, 207, -23, 127, -693, -423, 207, -243, 207, -57, -121, -3, -121, -67, 127, 207, 543, 879, -95, 55, 33, 55, 183, -693, -423, 207, -243, 207, -21, 33, 207, 879, -315, 135, 69, 135, 519])\n assert answers_match(candidate(expression='7-6+5*4-3'), [-4, -16, -4, -16, -34, 6, 18, -4, 6, -22, -40, 18, -19, 21])\n assert answers_match(candidate(expression='10-5*2+3*2-1'), [-15, -25, -15, -25, -35, -3, -5, -15, -3, -29, -39, -5, -39, -15, 25, 35, 25, 35, 45, 3, 5, 13, 15, -15, -3, 25, 3, 13, -31, -41, -7, -41, -17, 39, 49, 5, 15, -31, -7, 49, 5, 25])\n assert answers_match(candidate(expression='5-3*2+4*3'), [-37, -49, -13, -49, -25, 28, 36, 11, 16, -39, -15, 36, 9, 24])\n assert answers_match(candidate(expression='3-2*2+1+4*5'), [-43, -51, -43, -67, -67, -22, -26, -23, -22, -67, -67, -42, -47, -42, 23, 27, 23, 35, 35, 20, 24, 23, 27, 17, 18, 23, 20, 23, -55, -55, -30, -35, -30, 35, 35, 20, 35, 5, 10, 35, 20, 35])\n assert answers_match(candidate(expression='1+2+3+4+5+6+7+8+9+0'), [45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45])\n assert answers_match(candidate(expression='9+8*7+6-5*4+3-2*1+0'), [-87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -55, -55, -55, -55, -55, -151, -151, -55, -55, -87, -87, -55, -151, -55, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, -39, -39, -39, -39, -39, 105, 105, 105, 105, 105, -183, -183, -87, -87, 105, 105, -39, -39, 105, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, -39, -39, 105, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -55, -55, -55, -55, -55, -151, -151, -55, -55, -87, -87, -55, -151, -55, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, -39, -39, -39, -39, -39, 105, 105, 105, 105, 105, -39, -39, -39, -39, -39, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, -183, -183, -87, -87, 105, 105, -39, -39, 105, 105, -183, -183, -87, -87, 441, 441, 441, 441, -39, -39, 105, 105, -39, -39, 273, 273, 273, 273, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, -39, -39, 105, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, -39, -39, 105, 105, -39, -39, 273, 273, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 52, 52, 70, 70, 34, 46, 70, 52, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 92, 92, 92, 92, 92, 80, 80, 92, 92, 88, 88, 92, 80, 92, 88, 88, 88, 88, 88, 92, 92, 80, 92, 88, 88, 92, 80, 92, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, -46, -46, -46, -46, -46, 98, 98, 98, 98, 98, -46, -46, -46, -46, -46, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 94, 94, 94, 94, 94, 52, 52, 52, 52, 52, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 238, 238, 238, 238, 238, 406, 406, 406, 406, 406, 238, 238, 238, 238, 238, -169, -169, -73, -73, 119, 119, -25, -25, 119, 119, -169, -169, -73, -73, 455, 455, 455, 455, -25, -25, 119, 119, -25, -25, 287, 287, 287, 287, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 76, 76, 88, 88, 34, 34, 46, 46, 455, 455, 455, 455, 406, 406, 700, 700, 406, 406, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 329, 329, 329, 329, 294, 294, 504, 504, 294, 294, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, -39, -39, 105, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, -39, -39, 105, 105, -39, -39, 273, 273, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 52, 52, 70, 70, 34, 46, 70, 52, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 88, 88, 88, 92, 92, 80, 92, 88, 88, 92, 80, 92, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 294, 294, 294, 294, 294, 504, 504, 504, 504, 504, 294, 294, 294, 294, 294, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 329, 329, 329, 329, 294, 294, 504, 504, 294, 294, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -136, -136, -136, -136, -136, -340, -340, -136, -136, -204, -204, -136, -340, -136, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, -102, -102, -102, -102, -102, 204, 204, 204, 204, 204, -408, -408, -204, -204, 204, 204, -102, -102, 204, 204, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 204, 204, 204, 204, 204, -102, -102, 204, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -204, -136, -136, -136, -136, -136, -340, -340, -136, -136, -204, -204, -136, -340, -136, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, -102, -102, -102, -102, -102, 204, 204, 204, 204, 204, -102, -102, -102, -102, -102, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, -408, -408, -204, -204, 204, 204, -102, -102, 204, 204, -408, -408, -204, -204, 918, 918, 918, 918, -102, -102, 204, 204, -102, -102, 561, 561, 561, 561, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 680, 680, 680, 680, -102, 204, -102, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 204, 204, 204, 204, 204, -102, -102, 204, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, -102, -102, 204, 204, -102, -102, 561, 561, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 680, 680, 680, 680, -102, 204, -102, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 52, 52, 70, 70, 34, 46, 70, 52, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 104, 104, 104, 104, 104, 92, 92, 104, 104, 100, 100, 104, 92, 104, 100, 100, 100, 100, 100, 104, 104, 92, 104, 100, 100, 104, 92, 104, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 106, 106, 106, 106, 106, 124, 124, 124, 124, 124, 88, 88, 100, 100, 124, 124, 106, 106, 124, 124, 100, 100, 104, 92, 104, 124, 124, 106, 124, 88, 100, 124, 106, 124, 100, 100, 100, 100, 100, 104, 104, 92, 104, 100, 100, 104, 92, 104, 124, 124, 124, 124, 124, 106, 106, 124, 124, 88, 100, 124, 106, 124, 100, 100, 104, 92, 104, 124, 124, 106, 124, 88, 100, 124, 106, 124, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 92, 92, 92, 92, 92, 80, 80, 92, 92, 88, 88, 92, 80, 92, 88, 88, 88, 88, 88, 92, 92, 80, 92, 88, 88, 92, 80, 92, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 200, 200, 200, 200, 200, 188, 188, 200, 200, 196, 196, 200, 188, 200, 196, 196, 196, 196, 196, 200, 200, 188, 200, 196, 196, 200, 188, 200, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 104, 104, 104, 104, 104, 92, 92, 104, 104, 100, 100, 104, 92, 104, 100, 100, 100, 100, 100, 104, 104, 92, 104, 100, 100, 104, 92, 104, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 540, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, -46, -46, -46, -46, -46, 98, 98, 98, 98, 98, -46, -46, -46, -46, -46, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 94, 94, 94, 94, 94, 52, 52, 52, 52, 52, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 238, 238, 238, 238, 238, 406, 406, 406, 406, 406, 238, 238, 238, 238, 238, -118, -118, -118, -118, -118, 188, 188, 188, 188, 188, -118, -118, -118, -118, -118, 545, 545, 545, 545, 545, 545, 545, 545, 545, 545, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 106, 106, 106, 106, 106, 124, 124, 124, 124, 124, 94, 94, 94, 94, 94, 52, 52, 52, 52, 52, 202, 202, 202, 202, 202, 52, 52, 52, 52, 52, 106, 106, 106, 106, 106, 293, 293, 293, 293, 293, 293, 293, 293, 293, 293, 265, 265, 265, 265, 265, 433, 433, 433, 433, 433, 265, 265, 265, 265, 265, 545, 545, 545, 545, 545, 545, 545, 545, 545, 545, 265, 265, 265, 265, 265, 481, 481, 481, 481, 481, 433, 433, 433, 433, 433, 265, 265, 265, 265, 265, 865, 865, 865, 865, 865, 265, 265, 265, 265, 265, 481, 481, 481, 481, 481, -169, -169, -73, -73, 119, 119, -25, -25, 119, 119, -169, -169, -73, -73, 455, 455, 455, 455, -25, -25, 119, 119, -25, -25, 287, 287, 287, 287, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 76, 76, 88, 88, 34, 34, 46, 46, 455, 455, 455, 455, 406, 406, 700, 700, 406, 406, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -376, -376, -172, -172, 236, 236, -70, -70, 236, 236, -376, -376, -172, -172, 950, 950, 950, 950, -70, -70, 236, 236, -70, -70, 593, 593, 593, 593, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 88, 88, 100, 100, 124, 124, 106, 106, 124, 124, 76, 76, 88, 88, 34, 34, 46, 46, 184, 184, 196, 196, 34, 34, 46, 46, 88, 88, 100, 100, 509, 509, 509, 509, 460, 460, 754, 754, 460, 460, 950, 950, 950, 950, 460, 460, 838, 838, 754, 754, 460, 460, 1510, 1510, 460, 460, 838, 838, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -118, -118, 188, 188, -118, -118, 545, 545, 545, 545, 52, 52, 70, 70, 106, 106, 124, 124, 94, 94, 52, 52, 202, 202, 52, 52, 106, 106, 293, 293, 293, 293, 265, 265, 433, 433, 265, 265, 545, 545, 545, 545, 265, 265, 481, 481, 433, 433, 265, 265, 865, 865, 265, 265, 481, 481, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 329, 329, 329, 329, 294, 294, 504, 504, 294, 294, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 680, 680, 680, 680, -102, 204, -102, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 100, 100, 104, 92, 104, 124, 124, 106, 124, 88, 100, 124, 106, 124, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 196, 196, 200, 188, 200, 46, 46, 50, 38, 50, 100, 100, 104, 92, 104, 365, 365, 365, 365, 330, 330, 540, 540, 330, 330, 680, 680, 680, 680, 330, 330, 600, 600, 540, 540, 330, 330, 1080, 1080, 330, 330, 600, 600, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -376, -172, 236, -70, 236, -376, -172, 950, 950, -70, 236, -70, 593, 593, 34, 46, 70, 52, 70, 88, 100, 124, 106, 124, 76, 88, 34, 46, 184, 196, 34, 46, 88, 100, 509, 509, 460, 754, 460, 950, 950, 460, 838, 754, 460, 1510, 460, 838, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, -39, -39, 105, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, -39, -39, 105, 105, -39, -39, 273, 273, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 52, 52, 70, 70, 34, 46, 70, 52, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 88, 88, 88, 92, 92, 80, 92, 88, 88, 92, 80, 92, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 294, 294, 294, 294, 294, 504, 504, 504, 504, 504, 294, 294, 294, 294, 294, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 329, 329, 329, 329, 294, 294, 504, 504, 294, 294, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 204, 204, 204, 204, 204, -102, -102, 204, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -204, -204, -204, -136, -136, -340, -136, -204, -204, -136, -340, -136, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, -102, -102, 204, 204, -102, -102, 561, 561, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 680, 680, 680, 680, -102, 204, -102, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 52, 52, 70, 70, 34, 46, 70, 52, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 100, 100, 100, 100, 100, 104, 104, 92, 104, 100, 100, 104, 92, 104, 124, 124, 124, 124, 124, 106, 106, 124, 124, 88, 100, 124, 106, 124, 100, 100, 104, 92, 104, 124, 124, 106, 124, 88, 100, 124, 106, 124, 88, 88, 88, 88, 88, 92, 92, 80, 92, 88, 88, 92, 80, 92, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 196, 196, 196, 196, 196, 200, 200, 188, 200, 196, 196, 200, 188, 200, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 100, 100, 100, 100, 100, 104, 104, 92, 104, 100, 100, 104, 92, 104, 365, 365, 365, 365, 365, 365, 365, 365, 365, 365, 330, 330, 330, 330, 330, 540, 540, 540, 540, 540, 330, 330, 330, 330, 330, 680, 680, 680, 680, 680, 680, 680, 680, 680, 680, 330, 330, 330, 330, 330, 600, 600, 600, 600, 600, 540, 540, 540, 540, 540, 330, 330, 330, 330, 330, 1080, 1080, 1080, 1080, 1080, 330, 330, 330, 330, 330, 600, 600, 600, 600, 600, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -118, -118, 188, 188, -118, -118, 545, 545, 545, 545, 52, 52, 70, 70, 106, 106, 124, 124, 94, 94, 52, 52, 202, 202, 52, 52, 106, 106, 293, 293, 293, 293, 265, 265, 433, 433, 265, 265, 545, 545, 545, 545, 265, 265, 481, 481, 433, 433, 265, 265, 865, 865, 265, 265, 481, 481, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -376, -172, 236, -70, 236, -376, -172, 950, 950, -70, 236, -70, 593, 593, 34, 46, 70, 52, 70, 88, 100, 124, 106, 124, 76, 88, 34, 46, 184, 196, 34, 46, 88, 100, 509, 509, 460, 754, 460, 950, 950, 460, 838, 754, 460, 1510, 460, 838, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 329, 329, 329, 329, 294, 294, 504, 504, 294, 294, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -204, -204, -136, -340, -136, 204, 204, -102, 204, -408, -204, 204, -102, 204, -204, -204, -136, -340, -136, 680, 680, 680, 680, -102, 204, -102, 561, 561, -408, -204, 204, -102, 204, -408, -204, 918, 918, -102, 204, -102, 561, 561, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 100, 100, 104, 92, 104, 124, 124, 106, 124, 88, 100, 124, 106, 124, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 196, 196, 200, 188, 200, 46, 46, 50, 38, 50, 100, 100, 104, 92, 104, 365, 365, 365, 365, 330, 330, 540, 540, 330, 330, 680, 680, 680, 680, 330, 330, 600, 600, 540, 540, 330, 330, 1080, 1080, 330, 330, 600, 600, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -376, -172, 236, -70, 236, -376, -172, 950, 950, -70, 236, -70, 593, 593, 34, 46, 70, 52, 70, 88, 100, 124, 106, 124, 76, 88, 34, 46, 184, 196, 34, 46, 88, 100, 509, 509, 460, 754, 460, 950, 950, 460, 838, 754, 460, 1510, 460, 838, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481])\n assert answers_match(candidate(expression='100-50*2+25'), [-1250, -25, 1350, 25, 125])\n assert answers_match(candidate(expression='8*7+6-5*4+3'), [-176, -80, 112, -32, 112, -176, -80, 448, 448, -32, 112, -32, 280, 280, 27, 39, 63, 45, 63, 69, 81, 27, 39, 448, 448, 399, 693, 399, -53, 91, -53, 259, 259, 45, 63, 87, 45, 259, 259, 231, 399, 231])\n assert answers_match(candidate(expression='99*99-99+99'), [-9801, 9801, 9603, 99, 9801])\n assert answers_match(candidate(expression='4*3-2+1-5*6+7'), [260, 148, 212, 92, 72, 260, 148, 116, 116, 92, 72, 92, 32, 32, -252, -140, -204, -84, -64, -260, -148, -252, -140, 260, 260, -156, -260, -156, 148, 128, 148, 88, 88, -84, -64, -92, -84, 148, 148, -44, -92, -44, 74, 46, 62, 32, 27, 74, 46, 38, 38, 32, 27, 32, 17, 17, -60, -32, -48, -18, -13, -54, -26, -42, -12, -7, -65, -37, -57, -29, -56, -28, -60, -32, -54, -26, 260, 260, -156, -260, -156, 182, 182, 0, 78, -65, 39, 52, 0, 78, 127, 107, 127, 67, 67, -105, -85, -113, -105, 127, 127, -65, -113, -65, 46, 41, 46, 31, 31, -18, -13, -12, -7, -23, -15, -14, -18, -12, 127, 127, -65, -113, -65, 91, 91, 7, 43, -23, 25, 31, 7, 43])\n assert answers_match(candidate(expression='9*8*7-6*5*4+3*2*1'), [-21096, -21096, -29736, -21096, -29736, -10728, -10728, -29736, -19368, -21096, -29736, -10728, -29736, -19368, -21096, -21096, -29736, -21096, -29736, -8568, -8568, -8568, -8568, -29736, -19368, -29736, -17208, -17208, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, -7704, -7704, -7704, -7704, 1872, 1872, -6192, -6192, 1872, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2196, -2196, -3276, -2196, -3276, -900, -900, -3276, -1980, -2196, -3276, -900, -3276, -1980, -2196, -2196, -3276, -2196, -3276, -630, -630, -630, -630, -3276, -1980, -3276, -1710, -1710, -2196, -3276, -900, -3276, -1980, -2196, -3276, -630, -630, -3276, -1980, -3276, -1710, -1710, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, 22500, 22500, 31500, 22500, 31500, 11700, 11700, 31500, 20700, 22500, 31500, 11700, 31500, 20700, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, 2340, 2340, 3276, 2340, 3276, 3600, 3600, 5040, 3600, 5040, 22500, 22500, 31500, 22500, 31500, -8082, -8082, -8082, -8082, 1494, 1494, -6570, -6570, 1494, 1494, -522, -522, -522, -522, 1494, 1494, 9054, 9054, -6570, -6570, 1494, 1494, 990, 990, 1494, 1494, 9054, 9054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2196, -3276, -900, -3276, -1980, -2196, -3276, -630, -630, -3276, -1980, -3276, -1710, -1710, 3600, 5040, 1872, 5040, 3312, 22500, 31500, 11700, 31500, 20700, -16560, -23184, 3600, 5040, 2340, 3276, 3600, 5040, 22500, 31500, -8082, -8082, 1494, -6570, 1494, -522, -522, 1494, 9054, -6570, 1494, 990, 1494, 9054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -21096, -21096, -29736, -21096, -29736, -10728, -10728, -29736, -19368, -21096, -29736, -10728, -29736, -19368, -21096, -21096, -29736, -21096, -29736, -8568, -8568, -8568, -8568, -29736, -19368, -29736, -17208, -17208, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, -7704, -7704, -7704, -7704, 1872, 1872, -6192, -6192, 1872, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 204, 204, 84, 204, 84, 348, 348, 84, 228, 204, 84, 348, 84, 228, 204, 204, 84, 204, 84, 378, 378, 378, 378, 84, 228, 84, 258, 258, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 204, 204, 84, 204, 84, 348, 348, 84, 228, 204, 84, 348, 84, 228, 204, 204, 84, 204, 84, 378, 378, 378, 378, 84, 228, 84, 258, 258, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, 22500, 22500, 31500, 22500, 31500, 11700, 11700, 31500, 20700, 22500, 31500, 11700, 31500, 20700, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, 24900, 24900, 34860, 24900, 34860, 12948, 12948, 34860, 22908, 24900, 34860, 12948, 34860, 22908, 24900, 24900, 34860, 24900, 34860, 12948, 12948, 34860, 22908, 24900, 34860, 12948, 34860, 22908, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, 2340, 2340, 3276, 2340, 3276, 3600, 3600, 5040, 3600, 5040, 22500, 22500, 31500, 22500, 31500, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, 4740, 4740, 6636, 4740, 6636, 4740, 4740, 6636, 4740, 6636, 3600, 3600, 5040, 3600, 5040, 22500, 22500, 31500, 22500, 31500, 3600, 3600, 5040, 3600, 5040, 24900, 24900, 34860, 24900, 34860, 24900, 24900, 34860, 24900, 34860, -8130, -8130, -8130, -8130, 1446, 1446, -6618, -6618, 1446, 1446, -570, -570, -570, -570, 1446, 1446, 9006, 9006, -6618, -6618, 1446, 1446, 942, 942, 1446, 1446, 9006, 9006, -8130, -8130, -8130, -8130, 1446, 1446, -6618, -6618, 1446, 1446, 390, 390, 390, 390, 390, 390, 390, 390, 1446, 1446, 9006, 9006, 1446, 1446, 9966, 9966, 9966, 9966, -6618, -6618, 1446, 1446, 942, 942, 1446, 1446, 9006, 9006, -6618, -6618, 1446, 1446, 1902, 1902, 1902, 1902, 1446, 1446, 9006, 9006, 1446, 1446, 9966, 9966, 9966, 9966, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 588, 732, 588, 762, 762, 588, 732, 588, 762, 762, 5040, 3312, 31500, 20700, 5040, 3312, 34860, 22908, 34860, 22908, -23184, 5040, 3276, 5040, 31500, -23184, 5040, 6636, 6636, 5040, 31500, 5040, 34860, 34860, -16266, -16266, 2886, -13242, 2886, -1146, -1146, 2886, 18006, -13242, 2886, 1878, 2886, 18006, -16266, -16266, 2886, -13242, 2886, 774, 774, 774, 774, 2886, 18006, 2886, 19926, 19926, -13242, 2886, 1878, 2886, 18006, -13242, 2886, 3798, 3798, 2886, 18006, 2886, 19926, 19926, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2196, -3276, -900, -3276, -1980, -2196, -3276, -630, -630, -3276, -1980, -3276, -1710, -1710, 3600, 5040, 1872, 5040, 3312, 22500, 31500, 11700, 31500, 20700, -16560, -23184, 3600, 5040, 2340, 3276, 3600, 5040, 22500, 31500, -8082, -8082, 1494, -6570, 1494, -522, -522, 1494, 9054, -6570, 1494, 990, 1494, 9054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 3600, 5040, 1872, 5040, 3312, 22500, 31500, 11700, 31500, 20700, 3600, 5040, 1872, 5040, 3312, 24900, 34860, 12948, 34860, 22908, 24900, 34860, 12948, 34860, 22908, -16560, -23184, 3600, 5040, 2340, 3276, 3600, 5040, 22500, 31500, -16560, -23184, 3600, 5040, 4740, 6636, 4740, 6636, 3600, 5040, 22500, 31500, 3600, 5040, 24900, 34860, 24900, 34860, -8130, -8130, 1446, -6618, 1446, -570, -570, 1446, 9006, -6618, 1446, 942, 1446, 9006, -8130, -8130, 1446, -6618, 1446, 390, 390, 390, 390, 1446, 9006, 1446, 9966, 9966, -6618, 1446, 942, 1446, 9006, -6618, 1446, 1902, 1902, 1446, 9006, 1446, 9966, 9966, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 588, 732, 588, 762, 762, 588, 732, 588, 762, 762, 5040, 3312, 31500, 20700, 5040, 3312, 34860, 22908, 34860, 22908, -23184, 5040, 3276, 5040, 31500, -23184, 5040, 6636, 6636, 5040, 31500, 5040, 34860, 34860, -16266, -16266, 2886, -13242, 2886, -1146, -1146, 2886, 18006, -13242, 2886, 1878, 2886, 18006, -16266, -16266, 2886, -13242, 2886, 774, 774, 774, 774, 2886, 18006, 2886, 19926, 19926, -13242, 2886, 1878, 2886, 18006, -13242, 2886, 3798, 3798, 2886, 18006, 2886, 19926, 19926])\n assert answers_match(candidate(expression='7+8*3-2*5+6'), [-145, -97, 95, -1, 95, 9, 15, 95, 249, -43, 53, 27, 53, 123, -285, -195, 165, -15, 165, 9, 15, 23, 29, 165, 319, 165, 319, 473, -43, 53, 27, 53, 123, -99, 81, 27, 41, 81, 151, 81, 151, 221])\n assert answers_match(candidate(expression='1+2-3*4+5-6*7+8'), [246, 126, 36, 78, -12, 246, 126, -132, -132, 78, -12, 78, -84, -84, 76, 36, 6, 20, -10, 66, 26, 76, 36, -132, -132, -162, -312, -162, 94, 4, 94, -68, -68, 20, -10, 10, 20, -68, -68, -82, -152, -82, 82, 42, 12, 26, -4, 82, 42, -44, -44, 26, -4, 26, -28, -28, -94, -54, -24, -38, -8, -88, -48, -18, -32, -2, -114, -74, -104, -64, -98, -58, -94, -54, -88, -48, -104, -104, -134, -284, -134, -44, -44, -164, -74, -464, -314, -224, -164, -74, 110, 20, 110, -52, -52, 36, 6, 26, 36, -52, -52, -66, -136, -66, 42, 12, 42, -12, -12, -38, -8, -32, -2, -58, -48, -42, -38, -32, -40, -40, -54, -124, -54, -12, -12, -68, -26, -208, -138, -96, -68, -26, 246, 126, 36, 78, -12, 246, 126, -132, -132, 78, -12, 78, -84, -84, 76, 36, 6, 20, -10, 66, 26, 76, 36, -132, -132, -162, -312, -162, 94, 4, 94, -68, -68, 20, -10, 10, 20, -68, -68, -82, -152, -82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, -54, -24, -38, -8, -88, -48, -18, -32, -2, -94, -54, -24, -38, -8, -85, -45, -15, -29, 1, -85, -45, -15, -29, 1, -114, -74, -104, -64, -98, -58, -94, -54, -88, -48, -114, -74, -104, -64, -90, -50, -90, -50, -94, -54, -88, -48, -94, -54, -85, -45, -85, -45, -90, -90, -120, -270, -120, -30, -30, -150, -60, -450, -300, -210, -150, -60, -90, -90, -120, -270, -120, 0, 0, 0, 0, -150, -60, -150, -15, -15, -450, -300, -210, -150, -60, -450, -300, -90, -90, -150, -60, -150, -15, -15, 110, 20, 110, -52, -52, 36, 6, 26, 36, -52, -52, -66, -136, -66, 42, 12, 42, -12, -12, -38, -8, -32, -2, -58, -48, -42, -38, -32, -40, -40, -54, -124, -54, -12, -12, -68, -26, -208, -138, -96, -68, -26, 110, 20, 110, -52, -52, 36, 6, 26, 36, -52, -52, -66, -136, -66, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -38, -8, -32, -2, -38, -8, -29, 1, -29, 1, -58, -48, -42, -38, -32, -58, -48, -34, -34, -38, -32, -38, -29, -29, -34, -34, -48, -118, -48, -6, -6, -62, -20, -202, -132, -90, -62, -20, -34, -34, -48, -118, -48, 8, 8, 8, 8, -62, -20, -62, 1, 1, -202, -132, -90, -62, -20, -202, -132, -34, -34, -62, -20, -62, 1, 1])\n assert answers_match(candidate(expression='1+2+3+4+5+6+7+8+9'), [45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45])\n assert answers_match(candidate(expression='2*3+4*5-6*7+8'), [-674, -354, -114, -226, 14, -134, -54, -114, 426, -274, -34, -22, -34, 218, -1190, -630, -210, -406, 14, -134, -54, -110, -30, -30, 510, -210, 510, 870, -274, -34, -22, -34, 218, -502, -82, -22, 2, 2, 254, -82, 254, 422, -334, -174, -54, -110, 10, -64, -24, -54, 216, -134, -14, -8, -14, 112, -1190, -630, -210, -406, 14, -850, -450, -150, -290, 10, -44, -4, -20, 20, -64, -24, -20, 20, -40, 0, -30, 510, -210, 510, 870, 30, 300, -210, -150, 600, 960, 300, 960, 660, -282, -42, -30, -42, 210, -510, -90, -30, -6, -6, 246, -90, 246, 414, -134, -14, -8, -14, 112, -510, -90, -362, -62, 12, 36, -8, 36, 16, -6, 246, -90, 246, 414, 22, 148, -90, -62, 288, 456, 148, 456, 316])\n assert answers_match(candidate(expression='9-8+7*6-5+4*3-2+1'), [-6, 50, 57, 29, 71, -41, 85, 57, 127, 29, 71, 29, 71, 141, -6, -62, -69, -41, -83, 1, 43, 1, -69, 99, 169, -69, 85, -83, 15, 57, 15, 57, 127, -41, -83, 15, -41, 85, 155, -83, 71, -97, -36, -28, -27, -31, -25, -41, -23, -27, -17, -31, -25, -31, -25, -15, -6, -14, -15, -11, -17, -36, -44, -45, -41, -47, 1, 43, 1, -69, 1, -65, 1, -21, 1, -81, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 21, 63, 21, 63, 133, -35, -77, 21, -35, 91, 161, -77, 77, -91, -33, -27, -33, -27, -17, -11, -17, -41, -47, 21, -35, -33, -11, -41, 79, 149, -89, 65, -103, -23, -13, -17, -47, 65, -103, -97, -31, -121, -6, 114, 129, 69, 159, -81, 189, 129, 279, 69, 159, 69, 159, 309, -6, -126, -141, -81, -171, 9, 99, 9, -141, 219, 369, -141, 189, -171, 39, 129, 39, 129, 279, -81, -171, 39, -81, 189, 339, -171, 159, -201, -36, -28, -27, -31, -25, -41, -23, -27, -17, -31, -25, -31, -25, -15, -76, -68, -67, -71, -65, -81, -63, -67, -57, -71, -65, -71, -65, -55, -6, -14, -15, -11, -17, -36, -44, -45, -41, -47, -6, -14, -15, -11, -17, -36, -44, -45, -41, -47, -76, -84, -85, -81, -87, 9, 35, 9, -77, 9, -73, 9, -29, 9, -89, 9, 99, 9, -141, 9, -73, 9, -153, 9, -29, 9, -89, 9, -29, 9, -89, 9, -169, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 177, 327, -183, 147, -213, -21, -11, -61, -51, -15, -45, -15, -45, -85, 51, -117, -111, -45, -135, 147, -213, -111, -231, -45, -135, -45, -135, -255, 21, 63, 21, 63, 133, -35, -77, 21, -35, 91, 161, -77, 77, -91, -33, -27, -33, -27, -17, -11, -17, -41, -47, 21, -35, -33, -11, -41, 79, 149, -89, 65, -103, -23, -13, -17, -47, 65, -103, -97, -31, -121, 53, 143, 53, 143, 293, -67, -157, 53, -67, 203, 353, -157, 173, -187, -33, -27, -33, -27, -17, -73, -67, -73, -67, -57, -11, -17, -41, -47, -11, -17, -41, -47, -81, -87, 21, -35, -33, -11, -41, 53, -67, -33, -73, -11, -41, -11, -41, -81, 79, 149, -89, 65, -103, -23, -13, -17, -47, 65, -103, -97, -31, -121, 175, 325, -185, 145, -215, -23, -13, -63, -53, -17, -47, -17, -47, -87, 49, -119, -113, -47, -137, 145, -215, -113, -233, -47, -137, -47, -137, -257, 8, -48, -55, -27, -69, 43, -83, -55, -125, -27, -69, -27, -69, -139, 8, 64, 71, 43, 85, 1, -41, 1, 71, -97, -167, 71, -83, 85, -13, -55, -13, -55, -125, 43, 85, -13, 43, -83, -153, 85, -69, 99, 38, 30, 29, 33, 27, 43, 25, 29, 19, 33, 27, 33, 27, 17, 8, 16, 17, 13, 19, 38, 46, 47, 43, 49, 1, -41, 1, 71, 1, 67, 1, 23, 1, 83, -79, -149, 89, -65, 103, 23, 13, 17, 47, -65, 103, 97, 31, 121, -19, -61, -19, -61, -131, 37, 79, -19, 37, -89, -159, 79, -75, 93, 35, 29, 35, 29, 19, 13, 19, 43, 49, -19, 37, 35, 13, 43, -77, -147, 91, -63, 105, 25, 15, 19, 49, -63, 105, 99, 33, 123, -6, 42, 48, 24, 60, -36, 72, 48, 108, 24, 60, 24, 60, 120, -6, -54, -60, -36, -72, 0, 36, 0, -60, 84, 144, -60, 72, -72, 12, 48, 12, 48, 108, -36, -72, 12, -36, 72, 132, -72, 60, -84, 8, -56, -64, -32, -80, 48, -96, -64, -144, -32, -80, -32, -80, -160, 8, 72, 80, 48, 96, 0, -48, 0, 80, -112, -192, 80, -96, 96, -16, -64, -16, -64, -144, 48, 96, -16, 48, -96, -176, 96, -80, 112, -46, -54, -55, -51, -57, -41, -59, -55, -65, -51, -57, -51, -57, -67, -86, -94, -95, -91, -97, -81, -99, -95, -105, -91, -97, -91, -97, -107, 38, 30, 29, 33, 27, 43, 25, 29, 19, 33, 27, 33, 27, 17, -41, -49, -50, -46, -52, -36, -54, -50, -60, -46, -52, -46, -52, -62, 43, 35, 34, 38, 32, 48, 30, 34, 24, 38, 32, 38, 32, 22, -6, 2, 3, -1, 5, -36, -28, -27, -31, -25, -6, 2, 3, -1, 5, -36, -28, -27, -31, -25, -76, -68, -67, -71, -65, 8, 16, 17, 13, 19, 38, 46, 47, 43, 49, -6, 2, 3, -1, 5, 8, 16, 17, 13, 19, -46, -38, -37, -41, -35, -86, -78, -77, -81, -75, 38, 46, 47, 43, 49, -41, -33, -32, -36, -30, 43, 51, 52, 48, 54, 0, 44, 0, -68, 0, -64, 0, -20, 0, -80, 0, 108, 0, -132, 0, -64, 0, -144, 0, -20, 0, -80, 0, -20, 0, -80, 0, -160, 0, -40, 0, 72, 0, 68, 0, 24, 0, 84, 0, 36, 0, -60, 0, -48, 0, 80, 0, -100, 0, -180, 0, 68, 0, -90, 0, 78, 0, -4, 0, -64, 0, -4, 0, -64, 0, -144, 0, 24, 0, 84, 0, -4, 0, 24, 0, -84, 0, -164, 0, 84, 0, -74, 0, 94, 75, 145, -93, 61, -107, -27, -17, -21, -51, 61, -107, -101, -35, -125, 171, 321, -189, 141, -219, -27, -17, -67, -57, -21, -51, -21, -51, -91, 45, -123, -117, -51, -141, 141, -219, -117, -237, -51, -141, -51, -141, -261, -79, -149, 89, -65, 103, 23, 13, 17, 47, -65, 103, 97, 31, 121, 63, 123, -81, 51, -93, -91, -171, 101, -75, 117, -61, -71, -101, -111, 23, 13, -56, -66, 28, 18, 3, -27, 3, -27, -67, 17, 47, 3, 17, -37, -77, 47, -32, 52, 63, -105, -99, -33, -123, 159, -201, -99, -219, -33, -123, -33, -123, -243, -63, 105, 99, 33, 123, 51, -93, -75, 117, -153, -273, 99, -138, 114, -9, -99, -9, -99, -219, 33, 123, -9, 33, -129, -249, 123, -114, 138, 23, 65, 23, 65, 135, -33, -75, 23, -33, 93, 163, -75, 79, -89, -31, -25, -31, -25, -15, -9, -15, -39, -45, 23, -33, -31, -9, -39, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 55, 145, 55, 145, 295, -65, -155, 55, -65, 205, 355, -155, 175, -185, -31, -25, -31, -25, -15, -71, -65, -71, -65, -55, -9, -15, -39, -45, -9, -15, -39, -45, -79, -85, 23, -33, -31, -9, -39, 55, -65, -31, -71, -9, -39, -9, -39, -79, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 177, 327, -183, 147, -213, -21, -11, -61, -51, -15, -45, -15, -45, -85, 51, -117, -111, -45, -135, 147, -213, -111, -231, -45, -135, -45, -135, -255, -19, -61, -19, -61, -131, 37, 79, -19, 37, -89, -159, 79, -75, 93, 35, 29, 35, 29, 19, 13, 19, 43, 49, -19, 37, 35, 13, 43, -77, -147, 91, -63, 105, 25, 15, 19, 49, -63, 105, 99, 33, 123, 19, 55, 19, 55, 115, -29, -65, 19, -29, 79, 139, -65, 67, -77, -23, -71, -23, -71, -151, 41, 89, -23, 41, -103, -183, 89, -87, 105, -49, -55, -49, -55, -65, -89, -95, -89, -95, -105, 35, 29, 35, 29, 19, -44, -50, -44, -50, -60, 40, 34, 40, 34, 24, -1, 5, -31, -25, -1, 5, -31, -25, -71, -65, 13, 19, 43, 49, -1, 5, 13, 19, -41, -35, -81, -75, 43, 49, -36, -30, 48, 54, 23, -33, -31, -9, -39, 55, -65, -31, -71, -9, -39, -9, -39, -79, -19, 37, 35, 13, 43, 19, -29, -23, 41, -49, -89, 35, -44, 40, -1, -31, -1, -31, -71, 13, 43, -1, 13, -41, -81, 43, -36, 48, 77, 147, -91, 63, -105, -25, -15, -19, -49, 63, -105, -99, -33, -123, 173, 323, -187, 143, -217, -25, -15, -65, -55, -19, -49, -19, -49, -89, 47, -121, -115, -49, -139, 143, -217, -115, -235, -49, -139, -49, -139, -259, -77, -147, 91, -63, 105, 25, 15, 19, 49, -63, 105, 99, 33, 123, 65, 125, -79, 53, -91, -89, -169, 103, -73, 119, -59, -69, -99, -109, 25, 15, -54, -64, 30, 20, 5, -25, 5, -25, -65, 19, 49, 5, 19, -35, -75, 49, -30, 54, 65, -103, -97, -31, -121, 161, -199, -97, -217, -31, -121, -31, -121, -241, -61, 107, 101, 35, 125, 53, -91, -73, 119, -151, -271, 101, -136, 116, -7, -97, -7, -97, -217, 35, 125, -7, 35, -127, -247, 125, -112, 140])\n assert answers_match(candidate(expression='6*5-4*3+2*1'), [-90, -90, -54, -90, -54, 30, 30, -30, 30, -90, -54, 30, -30, 30, 10, 10, 16, 10, 16, 30, 30, 130, 130, -40, 20, 20, 20, 80, -90, -54, 30, -30, 30, 10, 16, 30, 130, -40, 20, 20, 20, 80])\n assert answers_match(candidate(expression='3-5+8*2-1+4*6'), [182, 222, -202, 142, -242, 7, 12, -34, -41, 142, -242, -68, -74, -116, 302, 367, -322, 237, -387, 7, 12, 2, 7, -34, -41, -34, -41, -46, 117, -267, -93, -99, -141, 237, -387, -93, -123, -99, -141, -99, -141, -171, -186, -226, 198, -146, 238, -11, -16, 30, 37, -146, 238, 64, 70, 112, 230, 280, -250, 180, -300, -138, -168, 150, -108, 180, -43, -48, -48, -53, -11, -16, -45, -50, -13, -18, 14, 7, 14, 7, 2, 30, 37, 14, 30, 5, 0, 37, 3, 35, 132, -252, -78, -84, -126, 252, -372, -78, -108, -84, -126, -84, -126, -156, -156, 228, 54, 60, 102, 180, -300, -108, 180, -138, -168, 54, -150, 42, -36, -78, -36, -78, -108, 60, 102, -36, 60, -90, -120, 102, -102, 90])\n assert answers_match(candidate(expression='100-99+98-97+96'), [96, -96, 96, -96, -96, -94, 98, -290, -94, 96, 96, 98, -98, 98])\n assert answers_match(candidate(expression='9-3+4-2*3'), [8, 0, 8, -6, -6, 4, 12, -4, 4, 12, 12, 24, 0, 24])\n assert answers_match(candidate(expression='1+1*1+1*1*1+1-1*1'), [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 7, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 7, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3])\n assert answers_match(candidate(expression='1*2+3*4-5*6+7'), [-181, -97, -37, -55, 5, -51, -23, -37, 93, -69, -9, -9, -9, 51, -305, -165, -65, -95, 5, -51, -23, -45, -17, -13, 117, -65, 117, 195, -69, -9, -9, -9, 51, -123, -23, -9, -3, 1, 61, -23, 61, 97, -181, -97, -37, -55, 5, -51, -23, -37, 93, -69, -9, -9, -9, 51, -305, -165, -65, -95, 5, -305, -165, -65, -95, 5, -51, -23, -45, -17, -51, -23, -45, -17, -45, -17, -13, 117, -65, 117, 195, -13, 117, -65, -65, 117, 195, 117, 195, 195, -69, -9, -9, -9, 51, -123, -23, -9, -3, 1, 61, -23, 61, 97, -69, -9, -9, -9, 51, -123, -23, -123, -23, -9, -3, -9, -3, -3, 1, 61, -23, 61, 97, 1, 61, -23, -23, 61, 97, 61, 97, 97])\n", "comparison": "unordered"}, "public_tests": ["\"2-1-1\"", "\"2*3-4*5\""], "hints": [], "metadata": {"canonical_parameter_names": ["expression"], "leetcode_dataset_entry_point": "Solution().diffWaysToCompute", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:43:11+00:00", "tests_total": 189, "tests_dropped": 75, "flags": ["any_order"], "topic_tags": ["math", "string", "dynamic-programming", "recursion", "memoization", "bracket-sequences"]}, "language": "cpp", "interface": {"raw_signature": "vector diffWaysToCompute(string expression) {", "container": "Solution", "callable": "diffWaysToCompute", "parameters": [{"name": "expression", "type": "string"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} @@ -193,7 +193,7 @@ {"question_id": 387, "task_id": "first-unique-character-in-a-string", "difficulty": "Easy", "problem_description": "Given a string s, find the first non-repeating character in it and return its index. If it does not exist, return -1.\n\nExample 1:\n\nInput: s = \"leetcode\"\nOutput: 0\nExplanation:\nThe character 'l' at index 0 is the first character that does not occur at any other index.\n\nExample 2:\n\nInput: s = \"loveleetcode\"\nOutput: 2\n\nExample 3:\n\nInput: s = \"aabb\"\nOutput: -1\n\nConstraints:\n\n- 1 <= s.length <= 10^5\n- s consists of only lowercase English letters.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aabbbccccddeeeeeffffffgggggghhhhhhiiiiiiiijjjjjjjjjkkkkkkkkkkklllllllllllllmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnooooooooollllllllllllllllmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnp\") == 165\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 0\n assert candidate(s = \"abcdef\") == 0\n assert candidate(s = \"aabbccddee\") == -1\n assert candidate(s = \"a\") == 0\n assert candidate(s = \"abacabadabacaba\") == 7\n assert candidate(s = \"abcdabcde\") == 8\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == -1\n assert candidate(s = \"swiss\") == 1\n assert candidate(s = \"abacabadabc\") == 7\n assert candidate(s = \"repetition\") == 0\n assert candidate(s = \"zzz\") == -1\n assert candidate(s = \"aabbccddeeffg\") == 12\n assert candidate(s = \"leetcode\") == 0\n assert candidate(s = \"aabb\") == -1\n assert candidate(s = \"loveleetcode\") == 2\n assert candidate(s = \"abcdabcdf\") == 8\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\") == -1\n assert candidate(s = \"development\") == 0\n assert candidate(s = \"aabbcceeff\") == -1\n assert candidate(s = \"zzyyxxwwvvuuttrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == -1\n assert candidate(s = \"algorithm\") == 0\n assert candidate(s = \"unique\") == 1\n assert candidate(s = \"z\") == 0\n assert candidate(s = \"abbacd\") == 4\n assert candidate(s = \"aabbcceeffgghhiijjklmnopqrstuvwxyz\") == 18\n assert candidate(s = \"character\") == 1\n assert candidate(s = \"bba\") == 2\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 0\n assert candidate(s = \"abcdefg\") == 0\n assert candidate(s = \"thisisjustafancysentence\") == 1\n assert candidate(s = \"almostunique\") == 0\n assert candidate(s = \"repetitionsofletters\") == 2\n assert candidate(s = \"abacabadabacabadabacabad\") == -1\n assert candidate(s = \"xyzzyzxyz\") == -1\n assert candidate(s = \"almosteverycharacterisunique\") == 1\n assert candidate(s = \"uniquecharactersarecool\") == 1\n assert candidate(s = \"abcdedcba\") == 4\n assert candidate(s = \"verylongstringwithmanyanonymouscharacterssssssssssssssssssssssss\") == 0\n assert candidate(s = \"uniqueidentifier\") == 3\n assert candidate(s = \"abracadabra\") == 4\n assert candidate(s = \"allcharactersrepeatmorethanonce\") == 12\n assert candidate(s = \"abacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabad\") == -1\n assert candidate(s = \"xylophone\") == 0\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == -1\n assert candidate(s = \"unrepeatedcharacterstring\") == 0\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzyxwvutsrqponmlkjihgfedcba\") == -1\n assert candidate(s = \"bbaaccddeeffgghhiijjkkllmmnnoopqrrssttuuvvwwxxyyzz\") == 30\n assert candidate(s = \"zzzzzyyyyxxxxwwvvvttrrssqqppoonnmmlkkjjiihhggffeedcba\") == 34\n assert candidate(s = \"thisisaverylongstringwithnomanynonrepeatingcharacters\") == 7\n assert candidate(s = \"xyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 0\n assert candidate(s = \"firstuniquicharacter\") == 0\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyz\") == 50\n assert candidate(s = \"nocharactersrepeat\") == 0\n assert candidate(s = \"wovwovwov\") == -1\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == -1\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == -1\n assert candidate(s = \"abcdefghijabcdefghijabcdefghij\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz\") == -1\n assert candidate(s = \"aabbaaccddeeffaabbccddeeffaabbccddeeff\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwooxxyyzz\") == -1\n assert candidate(s = \"banana\") == 0\n assert candidate(s = \"thisisaverylongstringwithseveralcharacters\") == 10\n assert candidate(s = \"aaaaabbbbbcccccdddddeeeeefffffggggghhhhiiiiijjjjkkkkklllllmmmmmnnnnnooooo\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwxyzz\") == 44\n assert candidate(s = \"s\") == 0\n assert candidate(s = \"swissknife\") == 1\n assert candidate(s = \"abacaxabacayabacaza\") == 5\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwxyz\") == 44\n assert candidate(s = \"thisproblemhasaveryunusalcharacterdistribution\") == 4\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzz\") == -1\n assert candidate(s = \"aabbcdeef\") == 4\n assert candidate(s = \"aabbcdeeffgg\") == 4\n assert candidate(s = \"abcdefghijhgfedcba\") == 8\n assert candidate(s = \"single\") == 0\n assert candidate(s = \"uniquecharacter\") == 1\n assert candidate(s = \"mississippi\") == 0\n assert candidate(s = \"hashmapimplementation\") == 2\n assert candidate(s = \"abcdabcdbacd\") == -1\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == -1\n assert candidate(s = \"supercalifragilisticexpialidocious\") == 9\n assert candidate(s = \"firstnonrepeatingcharacter\") == 0\n assert candidate(s = \"zzzzyyyyyxxxxxwwwwvvvvuuuuttttssssrrrrqqqqpppooooonnnnmmmmllllkkkkjjjjiiiihhhhggggffffeeeeddddccccbbbbaaaa\") == -1\n assert candidate(s = \"onlyonecharacterrepeats\") == 2\n assert candidate(s = \"ababababababababababababababababababab\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwooxxyyzzzz\") == -1\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\") == 3\n assert candidate(s = \"bbaaccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzza\") == -1\n assert candidate(s = \"almostuniquecharacter\") == 1\n", "comparison": "exact"}, "public_tests": ["\"leetcode\"", "\"loveleetcode\"", "\"aabb\""], "hints": [], "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().firstUniqChar", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:33+00:00", "tests_total": 91, "tests_dropped": 1, "flags": [], "topic_tags": ["hash-table", "string", "queue", "counting"]}, "language": "cpp", "interface": {"raw_signature": "int firstUniqChar(string s) {", "container": "Solution", "callable": "firstUniqChar", "parameters": [{"name": "s", "type": "string"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 389, "task_id": "find-the-difference", "difficulty": "Easy", "problem_description": "You are given two strings s and t.\n\nString t is generated by random shuffling string s and then add one more letter at a random position.\n\nReturn the letter that was added to t.\n\nExample 1:\n\nInput: s = \"abcd\", t = \"abcde\"\nOutput: \"e\"\nExplanation: 'e' is the letter that was added.\n\nExample 2:\n\nInput: s = \"\", t = \"y\"\nOutput: \"y\"\n\nConstraints:\n\n- 0 <= s.length <= 1000\n- t.length == s.length + 1\n- s and t consist of lowercase English letters.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcd\",t = \"abcde\") == \"e\"\n assert candidate(s = \"aeiou\",t = \"aeiouf\") == \"f\"\n assert candidate(s = \"abcdxyz\",t = \"abcdzyxw\") == \"w\"\n assert candidate(s = \"a\",t = \"ab\") == \"b\"\n assert candidate(s = \"xyz\",t = \"zyxw\") == \"w\"\n assert candidate(s = \"\",t = \"y\") == \"y\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyza\") == \"a\"\n assert candidate(s = \"hello\",t = \"helloa\") == \"a\"\n assert candidate(s = \"hello\",t = \"hleloa\") == \"a\"\n assert candidate(s = \"aeiou\",t = \"aeiozu\") == \"z\"\n assert candidate(s = \"ae\",t = \"aea\") == \"a\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzp\") == \"p\"\n assert candidate(s = \"thisisaverylongstringfortesting\",t = \"thisisaverylongstringfortestingz\") == \"z\"\n assert candidate(s = \"thisisaverylongstringwithalotofcharacters\",t = \"thisisaverylongstringwithalotofcharactersz\") == \"z\"\n assert candidate(s = \"almostsame\",t = \"almostsamee\") == \"e\"\n assert candidate(s = \"abcdabcdabcdabcdabcdabcd\",t = \"abcdabcdabcdabcdabcdabcde\") == \"e\"\n assert candidate(s = \"sameletters\",t = \"samesletters\") == \"s\"\n assert candidate(s = \"mississippi\",t = \"mississippix\") == \"x\"\n assert candidate(s = \"thisisaverylongstringthatcontainsavarietyofcharacters\",t = \"thisisaverylongstringthatcontainsavarietyofcharactorst\") == \"o\"\n assert candidate(s = \"mississippi\",t = \"mississippiw\") == \"w\"\n assert candidate(s = \"samechar\",t = \"samechars\") == \"s\"\n assert candidate(s = \"quickbrownfoxjumps\",t = \"quickbrownfoxjumpsl\") == \"l\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammingz\") == \"z\"\n assert candidate(s = \"singlecharacter\",t = \"singlecharacterr\") == \"r\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzj\") == \"j\"\n assert candidate(s = \"abcdabcdabcd\",t = \"abcdabcdabcdd\") == \"d\"\n assert candidate(s = \"uniqueletters\",t = \"uniquelettersx\") == \"x\"\n assert candidate(s = \"xyzzzxyzzz\",t = \"xyzzzxyzzzx\") == \"x\"\n assert candidate(s = \"alibabacloud\",t = \"alibabacloudu\") == \"u\"\n assert candidate(s = \"xyxzyzy\",t = \"xyxzyzyz\") == \"z\"\n assert candidate(s = \"abcdabcdabcd\",t = \"abcdabcdabcdx\") == \"x\"\n assert candidate(s = \"different\",t = \"differenti\") == \"i\"\n assert candidate(s = \"finding\",t = \"findinwg\") == \"w\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzx\") == \"x\"\n assert candidate(s = \"onemore\",t = \"onemroem\") == \"m\"\n assert candidate(s = \"hellothereeveryone\",t = \"hellothereeveryonex\") == \"x\"\n assert candidate(s = \"mississippi\",t = \"mississippip\") == \"p\"\n assert candidate(s = \"pneumonoultramicroscopicsilicovolcanoconiosis\",t = \"pneumonoultramicroscopicsilicovolcanoconiosisp\") == \"p\"\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydogg\") == \"g\"\n assert candidate(s = \"hellothisisanexample\",t = \"thisisanexamplehelloo\") == \"o\"\n assert candidate(s = \"abracadabra\",t = \"abracadabrak\") == \"k\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammings\") == \"s\"\n assert candidate(s = \"mamamamamamama\",t = \"mmamamamamamama\") == \"m\"\n assert candidate(s = \"repeatedcharactershhhhh\",t = \"repeatedcharactershhhhha\") == \"a\"\n assert candidate(s = \"abcdabcdabcd\",t = \"abcdabcdabcde\") == \"e\"\n assert candidate(s = \"abcdabcd\",t = \"abcdabcde\") == \"e\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzaaa\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzaaab\") == \"b\"\n assert candidate(s = \"uniquecharacters\",t = \"uniquecharactersn\") == \"n\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"qwertypoiuytrewq\",t = \"qwertypoiuytrewqa\") == \"a\"\n assert candidate(s = \"abcdefghijklnmopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcbaq\") == \"q\"\n assert candidate(s = \"samecharacters\",t = \"samecharactersc\") == \"c\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzz\") == \"z\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzq\") == \"q\"\n assert candidate(s = \"short\",t = \"shorrt\") == \"r\"\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydogq\") == \"q\"\n assert candidate(s = \"onetwothree\",t = \"onetwothreef\") == \"f\"\n assert candidate(s = \"hellothere\",t = \"hellotherex\") == \"x\"\n assert candidate(s = \"uniqueletter\",t = \"uniqueletteru\") == \"u\"\n assert candidate(s = \"uniqueletters\",t = \"enuiqueletters\") == \"e\"\n assert candidate(s = \"thisisalongstring\",t = \"thisisalongstringx\") == \"x\"\n assert candidate(s = \"nogapsbetweenletters\",t = \"nogapsbetweenlettersn\") == \"n\"\n assert candidate(s = \"abcdefg\",t = \"gfedcbaa\") == \"a\"\n assert candidate(s = \"repeated\",t = \"repeatedr\") == \"r\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammingg\") == \"g\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzb\") == \"b\"\n assert candidate(s = \"balloon\",t = \"ooblaanl\") == \"a\"\n assert candidate(s = \"randomstring\",t = \"randomstrings\") == \"s\"\n assert candidate(s = \"uniqueletters\",t = \"uniqueletterst\") == \"t\"\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",t = \"thequickbrownfoxjumpsoverthelazydoga\") == \"a\"\n assert candidate(s = \"xyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxz\",t = \"xyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzj\") == \"j\"\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydogm\") == \"m\"\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",t = \"thequickbrownfoxjumpsoverthelazydogp\") == \"p\"\n assert candidate(s = \"xyzz\",t = \"xyzzz\") == \"z\"\n assert candidate(s = \"repeatedlettersinthisstring\",t = \"repeatedlettersinthisstringi\") == \"i\"\n assert candidate(s = \"aaaabbbbccccddddeee\",t = \"aaaabbbbccccddddeeef\") == \"f\"\n assert candidate(s = \"zzzzzzzzzz\",t = \"zzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzz\") == \"z\"\n assert candidate(s = \"thesameletterrepeatedseveraltime\",t = \"thesameletterrepeatedseveraltimee\") == \"e\"\n assert candidate(s = \"duplicatecharacters\",t = \"duplicatecharacterst\") == \"t\"\n assert candidate(s = \"complexinputwithdifferentcharacters\",t = \"complexinputwithdifferentcharactersg\") == \"g\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzx\") == \"x\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammingo\") == \"o\"\n assert candidate(s = \"xyzz\",t = \"xyzzy\") == \"y\"\n", "comparison": "exact"}, "public_tests": ["\"abcd\"\n\"abcde\"", "\"\"\n\"y\""], "hints": [], "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().findTheDifference", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:38+00:00", "tests_total": 96, "tests_dropped": 11, "flags": [], "topic_tags": ["hash-table", "string", "bit-manipulation", "sorting"]}, "language": "cpp", "interface": {"raw_signature": "char findTheDifference(string s, string t) {", "container": "Solution", "callable": "findTheDifference", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "char", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 390, "task_id": "elimination-game", "difficulty": "Medium", "problem_description": "You have a list arr of all integers in the range [1, n] sorted in a strictly increasing order. Apply the following algorithm on arr:\n\n- Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.\n- Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.\n- Keep repeating the steps again, alternating left to right and right to left, until a single number remains.\n\nGiven the integer n, return the last number that remains in arr.\n\nExample 1:\n\nInput: n = 9\nOutput: 6\nExplanation:\narr = [1, 2, 3, 4, 5, 6, 7, 8, 9]\narr = [2, 4, 6, 8]\narr = [2, 6]\narr = [6]\n\nExample 2:\n\nInput: n = 1\nOutput: 1\n\nConstraints:\n\n- 1 <= n <= 10^9\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 11) == 8\n assert candidate(n = 100) == 54\n assert candidate(n = 9) == 6\n assert candidate(n = 1000000) == 481110\n assert candidate(n = 2) == 2\n assert candidate(n = 20) == 6\n assert candidate(n = 1) == 1\n assert candidate(n = 1000000000) == 534765398\n assert candidate(n = 1000) == 510\n assert candidate(n = 10) == 8\n assert candidate(n = 25) == 14\n assert candidate(n = 244140) == 130558\n assert candidate(n = 15258) == 8160\n assert candidate(n = 3) == 2\n assert candidate(n = 3814) == 2040\n assert candidate(n = 119) == 56\n assert candidate(n = 29) == 14\n assert candidate(n = 999999999) == 534765056\n assert candidate(n = 12345) == 5502\n assert candidate(n = 4096) == 1366\n assert candidate(n = 976562) == 522232\n assert candidate(n = 1953125) == 908662\n assert candidate(n = 50) == 24\n assert candidate(n = 2047) == 1024\n assert candidate(n = 16383) == 8192\n assert candidate(n = 5) == 2\n assert candidate(n = 10001) == 5974\n assert candidate(n = 16384) == 5462\n assert candidate(n = 59) == 32\n assert candidate(n = 250000000) == 133691350\n assert candidate(n = 238) == 128\n assert candidate(n = 4) == 2\n assert candidate(n = 125000000) == 58154326\n assert candidate(n = 10000) == 5974\n assert candidate(n = 1001) == 510\n assert candidate(n = 15625000) == 8355710\n assert candidate(n = 7812500) == 3634646\n assert candidate(n = 62500000) == 33422838\n assert candidate(n = 122070) == 56792\n assert candidate(n = 50000000) == 33551830\n assert candidate(n = 128) == 86\n assert candidate(n = 1024) == 342\n assert candidate(n = 101) == 54\n assert candidate(n = 10000000) == 6150102\n assert candidate(n = 61035) == 32640\n assert candidate(n = 100000) == 55286\n assert candidate(n = 2048) == 1366\n assert candidate(n = 1048576) == 349526\n assert candidate(n = 999) == 504\n assert candidate(n = 953) == 510\n assert candidate(n = 3906250) == 2088928\n assert candidate(n = 8192) == 5462\n assert candidate(n = 30517) == 14198\n assert candidate(n = 65536) == 21846\n assert candidate(n = 5000) == 2014\n assert candidate(n = 7629) == 3550\n assert candidate(n = 256) == 86\n assert candidate(n = 1023) == 512\n assert candidate(n = 9999) == 5984\n assert candidate(n = 31250000) == 14538582\n assert candidate(n = 476) == 222\n assert candidate(n = 127) == 64\n assert candidate(n = 987654321) == 534740470\n assert candidate(n = 5000000) == 1924950\n assert candidate(n = 500000) == 259446\n assert candidate(n = 488281) == 227166\n assert candidate(n = 98765) == 54750\n assert candidate(n = 500000000) == 232617302\n assert candidate(n = 31) == 16\n assert candidate(n = 1000001) == 481110\n assert candidate(n = 14) == 8\n assert candidate(n = 512) == 342\n assert candidate(n = 999999) == 481152\n assert candidate(n = 123456) == 63318\n assert candidate(n = 500) == 246\n assert candidate(n = 1907) == 888\n assert candidate(n = 7) == 4\n", "comparison": "exact"}, "public_tests": ["9", "1"], "hints": [], "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().lastRemaining", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:41+00:00", "tests_total": 78, "tests_dropped": 1, "flags": [], "topic_tags": ["math", "recursion"]}, "language": "cpp", "interface": {"raw_signature": "int lastRemaining(int n) {", "container": "Solution", "callable": "lastRemaining", "parameters": [{"name": "n", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} -{"question_id": 391, "task_id": "perfect-rectangle", "difficulty": "Hard", "problem_description": "Given an array rectangles where rectangles[i] = [x_i, y_i, a_i, b_i] represents an axis-aligned rectangle. The bottom-left point of the rectangle is (x_i, y_i) and the top-right point of it is (a_i, b_i).\n\nReturn true if all the rectangles together form an exact cover of a rectangular region.\n\nExample 1:\n\nInput: rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]\nOutput: true\nExplanation: All 5 rectangles together form an exact cover of a rectangular region.\n\nExample 2:\n\nInput: rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]\nOutput: false\nExplanation: Because there is a gap between the two rectangular regions.\n\nExample 3:\n\nInput: rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]\nOutput: false\nExplanation: Because two of the rectangles overlap with each other.\n\nConstraints:\n\n- 1 <= rectangles.length <= 2 * 10^4\n- rectangles[i].length == 4\n- -10^5 <= x_i < a_i <= 10^5\n- -10^5 <= y_i < b_i <= 10^5\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 3, 2], [1, 0, 2, 2]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 4, 2], [3, 2, 4, 4], [1, 3, 2, 4], [2, 3, 3, 4]]) == True\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 2, 4, 4], [2, 0, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 0, 4, 2], [0, 2, 2, 4], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 4], [3, 1, 4, 2], [3, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2]]) == True\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 4, 2], [1, 3, 2, 4], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [2, 2, 4, 4], [3, 3, 5, 5], [4, 4, 6, 6], [5, 5, 7, 7], [6, 6, 8, 8], [7, 7, 9, 9], [8, 8, 10, 10]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [5, 0, 10, 5], [0, 5, 5, 10], [5, 5, 10, 10], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [2, 2, 3, 3], [3, 2, 4, 3], [2, 3, 3, 4], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 3], [0, 3, 1, 4], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [0, 4, 3, 5]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 4, 4], [2, 2, 5, 5], [3, 3, 6, 6], [4, 4, 7, 7], [5, 5, 8, 8], [6, 6, 9, 9], [7, 7, 10, 10]]) == False\n assert candidate(rectangles = [[1, 1, 11, 11], [2, 2, 10, 10], [3, 3, 9, 9], [4, 4, 8, 8], [5, 5, 7, 7], [6, 6, 7, 7], [6, 6, 7, 7], [7, 7, 8, 8]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [0, -1, 1, 0]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [2, 1, 3, 2]]) == False\n assert candidate(rectangles = [[-10, -10, 10, 10], [0, 0, 5, 5], [5, 5, 10, 10], [-10, 0, -5, 5], [-5, 0, 0, 5]]) == False\n assert candidate(rectangles = [[1, 1, 10, 10], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [1, 5, 5, 10], [5, 1, 10, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [2, 0, 3, 2], [3, 0, 4, 2], [0, 2, 4, 3]]) == True\n assert candidate(rectangles = [[1, 1, 4, 4], [2, 2, 3, 3], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [2, 1, 3, 2], [0, 2, 1, 3], [1, 2, 2, 3], [2, 2, 3, 3]]) == True\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 3, 3], [3, 1, 5, 3], [5, 1, 7, 3], [7, 1, 9, 3], [1, 3, 3, 5], [3, 3, 5, 5], [5, 3, 7, 5], [7, 3, 9, 5], [1, 5, 3, 7], [3, 5, 5, 7], [5, 5, 7, 7], [7, 5, 9, 7], [1, 7, 3, 9], [3, 7, 5, 9], [5, 7, 7, 9], [7, 7, 9, 9]]) == False\n assert candidate(rectangles = [[-10, -10, -5, -5], [-5, -5, 0, 0], [0, 0, 5, 5], [5, 5, 10, 10], [-10, 0, -5, 5], [-5, 0, 0, 5], [0, 0, 5, 10], [5, 0, 10, 10], [-10, 5, -5, 10], [-5, 5, 0, 10], [0, 5, 5, 15], [5, 5, 10, 15]]) == False\n assert candidate(rectangles = [[0, 0, 6, 6], [1, 1, 5, 5], [2, 2, 4, 4], [3, 3, 5, 5], [1, 2, 5, 3], [2, 1, 4, 5], [2, 3, 5, 4]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 5, 3], [1, 3, 5, 5], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [0, 4, 2, 6], [2, 0, 4, 2], [2, 2, 4, 4], [2, 4, 4, 6]]) == True\n assert candidate(rectangles = [[-2, -2, 0, 0], [0, 0, 2, 2], [2, 2, 4, 4], [-2, 2, 0, 4], [0, -2, 2, 0], [2, -2, 4, 0]]) == False\n assert candidate(rectangles = [[-100000, -100000, 100000, 100000]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 2, 2], [0, 0, 4, 4], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [1, 3, 3, 5], [3, 1, 5, 3], [3, 3, 5, 5], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[-2, -2, 3, 3], [1, 1, 4, 4], [0, 0, 1, 1], [3, 3, 4, 4], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 5, 3], [1, 3, 3, 5], [3, 3, 5, 5], [1, 1, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 4, 4], [2, 2, 3, 3], [5, 5, 8, 8], [6, 6, 7, 7], [1, 5, 4, 8], [5, 1, 8, 4], [2, 6, 3, 7], [6, 2, 7, 3]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 2, 2], [0, 0, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4], [0, 4, 2, 6], [2, 4, 4, 6], [0, 6, 4, 8]]) == True\n assert candidate(rectangles = [[-100000, -100000, 100000, 100000], [0, 0, 1, 1]]) == False\n assert candidate(rectangles = [[-1, -1, 1, 1], [-1, 1, 1, 3], [1, -1, 3, 1], [1, 1, 3, 3]]) == True\n assert candidate(rectangles = [[0, 0, 5, 5], [1, 1, 2, 2], [3, 3, 4, 4], [2, 2, 3, 3], [0, 4, 5, 5], [4, 0, 5, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [2, 1, 3, 2], [0, 2, 1, 3], [1, 2, 2, 3], [2, 2, 3, 3], [0, 0, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [1, 1, 4, 4], [2, 2, 3, 3], [0, 5, 5, 6], [5, 0, 6, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4]]) == True\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [-1, -1, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [1, 1, 3, 3], [2, 2, 4, 4], [3, 3, 5, 5], [4, 4, 6, 6], [5, 5, 7, 7], [6, 6, 8, 8], [7, 7, 9, 9]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 2], [0, 2, 2, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 1], [2, 0, 4, 1], [0, 1, 1, 2], [1, 1, 3, 2], [3, 1, 4, 2], [0, 2, 1, 3], [1, 2, 3, 3], [3, 2, 4, 3]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 0, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 0, 4, 2], [0, 2, 2, 4], [2, 2, 4, 4], [1, 1, 3, 3], [1, 3, 3, 4], [3, 1, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 1000, 1000], [250, 250, 750, 750], [500, 500, 501, 501], [501, 501, 502, 502], [502, 502, 503, 503]]) == False\n assert candidate(rectangles = [[1, 1, 2, 2], [2, 2, 3, 3], [1, 2, 2, 3], [2, 1, 3, 2], [1, 3, 2, 4], [3, 1, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 6, 6], [1, 1, 5, 5], [2, 2, 4, 4], [1, 2, 2, 3], [2, 1, 3, 2], [3, 3, 4, 4], [4, 4, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [0, 0, 5, 5]]) == False\n assert candidate(rectangles = [[-2, -2, 2, 2], [-2, 2, 2, 4], [2, -2, 4, 2], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 2, 2], [2, 2, 3, 3], [1, 2, 2, 3], [2, 1, 3, 2]]) == False\n assert candidate(rectangles = [[0, 0, 1, 3], [1, 0, 2, 3], [2, 0, 3, 3], [0, 3, 1, 6], [1, 3, 2, 6], [2, 3, 3, 6], [0, 6, 1, 9], [1, 6, 2, 9], [2, 6, 3, 9]]) == True\n assert candidate(rectangles = [[1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [1, 5, 2, 6], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [2, 4, 3, 5], [2, 5, 3, 6]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 0, 2, 3]]) == False\n assert candidate(rectangles = [[0, 0, 3, 3], [3, 0, 6, 3], [6, 0, 9, 3], [0, 3, 3, 6], [3, 3, 6, 6], [6, 3, 9, 6]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [0, 5, 5, 6]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3]]) == True\n assert candidate(rectangles = [[1, 1, 5, 5], [5, 5, 9, 9], [1, 5, 5, 9], [5, 1, 9, 5], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [1, 5, 3, 7], [3, 5, 5, 7], [1, 7, 3, 9], [3, 7, 5, 9]]) == True\n assert candidate(rectangles = [[0, 0, 10, 5], [0, 5, 10, 10], [0, 0, 5, 10], [5, 0, 10, 5], [5, 5, 10, 10]]) == False\n assert candidate(rectangles = [[-2, -2, 0, 0], [0, 0, 2, 2], [2, 2, 4, 4], [-2, 2, 0, 4], [-2, 4, 0, 6]]) == False\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 5], [2, 1, 3, 3], [2, 3, 3, 5], [3, 1, 4, 3], [3, 3, 4, 5], [4, 1, 5, 3], [4, 3, 5, 5]]) == True\n assert candidate(rectangles = [[0, 0, 4, 4], [1, 1, 3, 3], [2, 2, 4, 4], [0, 1, 1, 2], [1, 0, 2, 1]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 3, 2], [0, 2, 3, 3], [0, 3, 3, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 3], [0, 3, 1, 4], [0, 4, 1, 5], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [2, 4, 3, 5]]) == True\n assert candidate(rectangles = [[1, 1, 2, 2], [1, 2, 2, 3], [2, 1, 3, 2], [2, 2, 3, 3], [1.5, 1.5, 2.5, 2.5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 1], [2, 0, 3, 2], [0, 2, 3, 3], [0, 1, 3, 2]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [0, 0, 5, 5], [5, 0, 10, 5], [0, 5, 5, 10], [5, 5, 10, 10], [1, 1, 4, 4]]) == False\n assert candidate(rectangles = [[-100, -100, 100, 100], [0, 0, 200, 200], [50, 50, 150, 150], [100, 100, 200, 200]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 5, 5], [5, 5, 9, 9], [0, 5, 5, 10], [5, 0, 10, 5]]) == False\n assert candidate(rectangles = [[-2, -2, 2, 2], [-1, -1, 1, 1], [0, 0, 2, 2], [1, 1, 3, 3], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[-5, -5, 5, 5], [0, 0, 3, 3], [3, 3, 6, 6], [-6, -6, -3, -3], [-3, -3, 0, 0]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [5, 5, 6, 6]]) == False\n assert candidate(rectangles = [[0, 0, 2, 1], [0, 1, 2, 2], [0, 2, 2, 3], [0, 3, 2, 4], [1, 0, 3, 1], [1, 1, 3, 2], [1, 2, 3, 3], [1, 3, 3, 4]]) == False\n assert candidate(rectangles = [[-5, -5, -3, -3], [-3, -3, 0, 0], [0, 0, 3, 3], [3, 3, 5, 5], [1, 1, 2, 2], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4], [1, 1, 3, 3], [3, 1, 5, 3], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[-10000, -10000, 10000, 10000], [-10000, -10000, 0, 0], [0, 0, 10000, 10000]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [5, 5, 6, 6], [6, 6, 7, 7], [7, 7, 8, 8], [8, 8, 9, 9], [9, 9, 10, 10]]) == False\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [1, 5, 2, 6], [1, 6, 2, 7], [1, 7, 2, 8], [1, 8, 2, 9]]) == True\n assert candidate(rectangles = [[0, 0, 100000, 1], [0, 1, 100000, 2], [0, 2, 100000, 3], [0, 3, 100000, 4], [0, 4, 100000, 5]]) == True\n assert candidate(rectangles = [[0, 0, 5, 5], [0, 5, 5, 10], [5, 0, 10, 5], [5, 5, 10, 10], [2, 2, 3, 3], [7, 7, 8, 8]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3]]) == False\n assert candidate(rectangles = [[0, 0, 4, 4], [1, 1, 3, 3], [2, 2, 4, 4], [0, 1, 2, 3], [1, 0, 3, 2], [1, 2, 3, 4], [2, 1, 4, 3]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3]]) == False\n", "comparison": "exact"}, "public_tests": ["[[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]", "[[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]", "[[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]"], "hints": [], "metadata": {"canonical_parameter_names": ["rectangles"], "leetcode_dataset_entry_point": "Solution().isRectangleCover", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:43+00:00", "tests_total": 98, "tests_dropped": 9, "flags": ["has_images"], "topic_tags": ["array", "hash-table", "math", "geometry", "sweep-line"]}, "language": "cpp", "interface": {"raw_signature": "bool isRectangleCover(vector>& rectangles) {", "container": "Solution", "callable": "isRectangleCover", "parameters": [{"name": "rectangles", "type": "vector>&"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 391, "task_id": "perfect-rectangle", "difficulty": "Hard", "problem_description": "Given an array rectangles where rectangles[i] = [x_i, y_i, a_i, b_i] represents an axis-aligned rectangle. The bottom-left point of the rectangle is (x_i, y_i) and the top-right point of it is (a_i, b_i).\n\nReturn true if all the rectangles together form an exact cover of a rectangular region.\n\nExample 1:\n\nInput: rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]\nOutput: true\nExplanation: All 5 rectangles together form an exact cover of a rectangular region.\n\nExample 2:\n\nInput: rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]\nOutput: false\nExplanation: Because there is a gap between the two rectangular regions.\n\nExample 3:\n\nInput: rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]\nOutput: false\nExplanation: Because two of the rectangles overlap with each other.\n\nConstraints:\n\n- 1 <= rectangles.length <= 2 * 10^4\n- rectangles[i].length == 4\n- -10^5 <= x_i < a_i <= 10^5\n- -10^5 <= y_i < b_i <= 10^5\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 3, 2], [1, 0, 2, 2]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 4, 2], [3, 2, 4, 4], [1, 3, 2, 4], [2, 3, 3, 4]]) == True\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 2, 4, 4], [2, 0, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 0, 4, 2], [0, 2, 2, 4], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 4], [3, 1, 4, 2], [3, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2]]) == True\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 4, 2], [1, 3, 2, 4], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [2, 2, 4, 4], [3, 3, 5, 5], [4, 4, 6, 6], [5, 5, 7, 7], [6, 6, 8, 8], [7, 7, 9, 9], [8, 8, 10, 10]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [5, 0, 10, 5], [0, 5, 5, 10], [5, 5, 10, 10], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [2, 2, 3, 3], [3, 2, 4, 3], [2, 3, 3, 4], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 3], [0, 3, 1, 4], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [0, 4, 3, 5]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 4, 4], [2, 2, 5, 5], [3, 3, 6, 6], [4, 4, 7, 7], [5, 5, 8, 8], [6, 6, 9, 9], [7, 7, 10, 10]]) == False\n assert candidate(rectangles = [[1, 1, 11, 11], [2, 2, 10, 10], [3, 3, 9, 9], [4, 4, 8, 8], [5, 5, 7, 7], [6, 6, 7, 7], [6, 6, 7, 7], [7, 7, 8, 8]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [0, -1, 1, 0]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [2, 1, 3, 2]]) == False\n assert candidate(rectangles = [[-10, -10, 10, 10], [0, 0, 5, 5], [5, 5, 10, 10], [-10, 0, -5, 5], [-5, 0, 0, 5]]) == False\n assert candidate(rectangles = [[1, 1, 10, 10], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [1, 5, 5, 10], [5, 1, 10, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [2, 0, 3, 2], [3, 0, 4, 2], [0, 2, 4, 3]]) == True\n assert candidate(rectangles = [[1, 1, 4, 4], [2, 2, 3, 3], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [2, 1, 3, 2], [0, 2, 1, 3], [1, 2, 2, 3], [2, 2, 3, 3]]) == True\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 3, 3], [3, 1, 5, 3], [5, 1, 7, 3], [7, 1, 9, 3], [1, 3, 3, 5], [3, 3, 5, 5], [5, 3, 7, 5], [7, 3, 9, 5], [1, 5, 3, 7], [3, 5, 5, 7], [5, 5, 7, 7], [7, 5, 9, 7], [1, 7, 3, 9], [3, 7, 5, 9], [5, 7, 7, 9], [7, 7, 9, 9]]) == False\n assert candidate(rectangles = [[-10, -10, -5, -5], [-5, -5, 0, 0], [0, 0, 5, 5], [5, 5, 10, 10], [-10, 0, -5, 5], [-5, 0, 0, 5], [0, 0, 5, 10], [5, 0, 10, 10], [-10, 5, -5, 10], [-5, 5, 0, 10], [0, 5, 5, 15], [5, 5, 10, 15]]) == False\n assert candidate(rectangles = [[0, 0, 6, 6], [1, 1, 5, 5], [2, 2, 4, 4], [3, 3, 5, 5], [1, 2, 5, 3], [2, 1, 4, 5], [2, 3, 5, 4]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 5, 3], [1, 3, 5, 5], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [0, 4, 2, 6], [2, 0, 4, 2], [2, 2, 4, 4], [2, 4, 4, 6]]) == True\n assert candidate(rectangles = [[-2, -2, 0, 0], [0, 0, 2, 2], [2, 2, 4, 4], [-2, 2, 0, 4], [0, -2, 2, 0], [2, -2, 4, 0]]) == False\n assert candidate(rectangles = [[-100000, -100000, 100000, 100000]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 2, 2], [0, 0, 4, 4], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [1, 3, 3, 5], [3, 1, 5, 3], [3, 3, 5, 5], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[-2, -2, 3, 3], [1, 1, 4, 4], [0, 0, 1, 1], [3, 3, 4, 4], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 5, 3], [1, 3, 3, 5], [3, 3, 5, 5], [1, 1, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 4, 4], [2, 2, 3, 3], [5, 5, 8, 8], [6, 6, 7, 7], [1, 5, 4, 8], [5, 1, 8, 4], [2, 6, 3, 7], [6, 2, 7, 3]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 2, 2], [0, 0, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4], [0, 4, 2, 6], [2, 4, 4, 6], [0, 6, 4, 8]]) == True\n assert candidate(rectangles = [[-100000, -100000, 100000, 100000], [0, 0, 1, 1]]) == False\n assert candidate(rectangles = [[-1, -1, 1, 1], [-1, 1, 1, 3], [1, -1, 3, 1], [1, 1, 3, 3]]) == True\n assert candidate(rectangles = [[0, 0, 5, 5], [1, 1, 2, 2], [3, 3, 4, 4], [2, 2, 3, 3], [0, 4, 5, 5], [4, 0, 5, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [2, 1, 3, 2], [0, 2, 1, 3], [1, 2, 2, 3], [2, 2, 3, 3], [0, 0, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [1, 1, 4, 4], [2, 2, 3, 3], [0, 5, 5, 6], [5, 0, 6, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4]]) == True\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [-1, -1, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [1, 1, 3, 3], [2, 2, 4, 4], [3, 3, 5, 5], [4, 4, 6, 6], [5, 5, 7, 7], [6, 6, 8, 8], [7, 7, 9, 9]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 2], [0, 2, 2, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 1], [2, 0, 4, 1], [0, 1, 1, 2], [1, 1, 3, 2], [3, 1, 4, 2], [0, 2, 1, 3], [1, 2, 3, 3], [3, 2, 4, 3]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 0, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 0, 4, 2], [0, 2, 2, 4], [2, 2, 4, 4], [1, 1, 3, 3], [1, 3, 3, 4], [3, 1, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 1000, 1000], [250, 250, 750, 750], [500, 500, 501, 501], [501, 501, 502, 502], [502, 502, 503, 503]]) == False\n assert candidate(rectangles = [[1, 1, 2, 2], [2, 2, 3, 3], [1, 2, 2, 3], [2, 1, 3, 2], [1, 3, 2, 4], [3, 1, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 6, 6], [1, 1, 5, 5], [2, 2, 4, 4], [1, 2, 2, 3], [2, 1, 3, 2], [3, 3, 4, 4], [4, 4, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [0, 0, 5, 5]]) == False\n assert candidate(rectangles = [[-2, -2, 2, 2], [-2, 2, 2, 4], [2, -2, 4, 2], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 2, 2], [2, 2, 3, 3], [1, 2, 2, 3], [2, 1, 3, 2]]) == False\n assert candidate(rectangles = [[0, 0, 1, 3], [1, 0, 2, 3], [2, 0, 3, 3], [0, 3, 1, 6], [1, 3, 2, 6], [2, 3, 3, 6], [0, 6, 1, 9], [1, 6, 2, 9], [2, 6, 3, 9]]) == True\n assert candidate(rectangles = [[1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [1, 5, 2, 6], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [2, 4, 3, 5], [2, 5, 3, 6]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 0, 2, 3]]) == False\n assert candidate(rectangles = [[0, 0, 3, 3], [3, 0, 6, 3], [6, 0, 9, 3], [0, 3, 3, 6], [3, 3, 6, 6], [6, 3, 9, 6]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [0, 5, 5, 6]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3]]) == True\n assert candidate(rectangles = [[1, 1, 5, 5], [5, 5, 9, 9], [1, 5, 5, 9], [5, 1, 9, 5], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [1, 5, 3, 7], [3, 5, 5, 7], [1, 7, 3, 9], [3, 7, 5, 9]]) == True\n assert candidate(rectangles = [[0, 0, 10, 5], [0, 5, 10, 10], [0, 0, 5, 10], [5, 0, 10, 5], [5, 5, 10, 10]]) == False\n assert candidate(rectangles = [[-2, -2, 0, 0], [0, 0, 2, 2], [2, 2, 4, 4], [-2, 2, 0, 4], [-2, 4, 0, 6]]) == False\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 5], [2, 1, 3, 3], [2, 3, 3, 5], [3, 1, 4, 3], [3, 3, 4, 5], [4, 1, 5, 3], [4, 3, 5, 5]]) == True\n assert candidate(rectangles = [[0, 0, 4, 4], [1, 1, 3, 3], [2, 2, 4, 4], [0, 1, 1, 2], [1, 0, 2, 1]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 3, 2], [0, 2, 3, 3], [0, 3, 3, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 3], [0, 3, 1, 4], [0, 4, 1, 5], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [2, 4, 3, 5]]) == True\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 1], [2, 0, 3, 2], [0, 2, 3, 3], [0, 1, 3, 2]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [0, 0, 5, 5], [5, 0, 10, 5], [0, 5, 5, 10], [5, 5, 10, 10], [1, 1, 4, 4]]) == False\n assert candidate(rectangles = [[-100, -100, 100, 100], [0, 0, 200, 200], [50, 50, 150, 150], [100, 100, 200, 200]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 5, 5], [5, 5, 9, 9], [0, 5, 5, 10], [5, 0, 10, 5]]) == False\n assert candidate(rectangles = [[-2, -2, 2, 2], [-1, -1, 1, 1], [0, 0, 2, 2], [1, 1, 3, 3], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[-5, -5, 5, 5], [0, 0, 3, 3], [3, 3, 6, 6], [-6, -6, -3, -3], [-3, -3, 0, 0]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [5, 5, 6, 6]]) == False\n assert candidate(rectangles = [[0, 0, 2, 1], [0, 1, 2, 2], [0, 2, 2, 3], [0, 3, 2, 4], [1, 0, 3, 1], [1, 1, 3, 2], [1, 2, 3, 3], [1, 3, 3, 4]]) == False\n assert candidate(rectangles = [[-5, -5, -3, -3], [-3, -3, 0, 0], [0, 0, 3, 3], [3, 3, 5, 5], [1, 1, 2, 2], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4], [1, 1, 3, 3], [3, 1, 5, 3], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[-10000, -10000, 10000, 10000], [-10000, -10000, 0, 0], [0, 0, 10000, 10000]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [5, 5, 6, 6], [6, 6, 7, 7], [7, 7, 8, 8], [8, 8, 9, 9], [9, 9, 10, 10]]) == False\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [1, 5, 2, 6], [1, 6, 2, 7], [1, 7, 2, 8], [1, 8, 2, 9]]) == True\n assert candidate(rectangles = [[0, 0, 100000, 1], [0, 1, 100000, 2], [0, 2, 100000, 3], [0, 3, 100000, 4], [0, 4, 100000, 5]]) == True\n assert candidate(rectangles = [[0, 0, 5, 5], [0, 5, 5, 10], [5, 0, 10, 5], [5, 5, 10, 10], [2, 2, 3, 3], [7, 7, 8, 8]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3]]) == False\n assert candidate(rectangles = [[0, 0, 4, 4], [1, 1, 3, 3], [2, 2, 4, 4], [0, 1, 2, 3], [1, 0, 3, 2], [1, 2, 3, 4], [2, 1, 4, 3]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3]]) == False\n", "comparison": "exact"}, "public_tests": ["[[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]", "[[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]", "[[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]"], "hints": [], "metadata": {"canonical_parameter_names": ["rectangles"], "leetcode_dataset_entry_point": "Solution().isRectangleCover", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:43+00:00", "tests_total": 98, "tests_dropped": 10, "flags": ["has_images"], "topic_tags": ["array", "hash-table", "math", "geometry", "sweep-line"]}, "language": "cpp", "interface": {"raw_signature": "bool isRectangleCover(vector>& rectangles) {", "container": "Solution", "callable": "isRectangleCover", "parameters": [{"name": "rectangles", "type": "vector>&"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 392, "task_id": "is-subsequence", "difficulty": "Easy", "problem_description": "Given two strings s and t, return true if s is a subsequence of t, or false otherwise.\n\nA subsequence of a string is a new string that is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., \"ace\" is a subsequence of \"abcde\" while \"aec\" is not).\n\nExample 1:\n\nInput: s = \"abc\", t = \"ahbgdc\"\nOutput: true\n\nExample 2:\n\nInput: s = \"axc\", t = \"ahbgdc\"\nOutput: false\n\nConstraints:\n\n- 0 <= s.length <= 100\n- 0 <= t.length <= 10^4\n- s and t consist only of lowercase English letters.\n\nFollow up: Suppose there are lots of incoming s, say s_1, s_2, ..., s_k where k >= 10^9, and you want to check one by one to see if t has its subsequence. In this scenario, how would you change your code?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abc\",t = \"abdc\") == True\n assert candidate(s = \"xyz\",t = \"abcdefghijklmnopqrstuvwxyz\") == True\n assert candidate(s = \"aec\",t = \"abcde\") == False\n assert candidate(s = \"\",t = \"ahbgdc\") == True\n assert candidate(s = \"\",t = \"\") == True\n assert candidate(s = \"zyx\",t = \"abcdefghijklmnopqrstuvwxyz\") == False\n assert candidate(s = \"abcd\",t = \"abcde\") == True\n assert candidate(s = \"abc\",t = \"abcbc\") == True\n assert candidate(s = \"bb\",t = \"aabbb\") == True\n assert candidate(s = \"aaaaaa\",t = \"bbaaaa\") == False\n assert candidate(s = \"abc\",t = \"bahbgdca\") == True\n assert candidate(s = \"ab\",t = \"baab\") == True\n assert candidate(s = \"bd\",t = \"abcde\") == True\n assert candidate(s = \"bd\",t = \"abcd\") == True\n assert candidate(s = \"axc\",t = \"ahbgdc\") == False\n assert candidate(s = \"a\",t = \"ahbgdc\") == True\n assert candidate(s = \"a\",t = \"a\") == True\n assert candidate(s = \"abc\",t = \"ahbgdc\") == True\n assert candidate(s = \"acb\",t = \"ahbgdc\") == False\n assert candidate(s = \"bcd\",t = \"ahbgdc\") == False\n assert candidate(s = \"abc\",t = \"\") == False\n assert candidate(s = \"ahbgdc\",t = \"ahbgdc\") == True\n assert candidate(s = \"abcd\",t = \"abbbcd\") == True\n assert candidate(s = \"b\",t = \"abcde\") == True\n assert candidate(s = \"abc\",t = \"abc\") == True\n assert candidate(s = \"abc\",t = \"abcde\") == True\n assert candidate(s = \"test\",t = \"ttttteeeesstttt\") == True\n assert candidate(s = \"challenge\",t = \"chllenge\") == False\n assert candidate(s = \"leetcode\",t = \"lleettccooddee\") == True\n assert candidate(s = \"consecutive\",t = \"consecutivve\") == True\n assert candidate(s = \"example\",t = \"exxample\") == True\n assert candidate(s = \"interview\",t = \"intrvw\") == False\n assert candidate(s = \"substring\",t = \"subtrring\") == False\n assert candidate(s = \"hello\",t = \"ohellomyworld\") == True\n assert candidate(s = \"characters\",t = \"characttrrs\") == False\n assert candidate(s = \"python\",t = \"pyyyynntthhoonn\") == True\n assert candidate(s = \"challenge\",t = \"cchhaalllleennnggggeee\") == True\n assert candidate(s = \"algorithm\",t = \"aggglllllllllooooooorrrrrriiiiiiiiiimmmmmm\") == False\n assert candidate(s = \"a\",t = \"\") == False\n assert candidate(s = \"complexity\",t = \"ccllllcooooooommmppppppllllleeeeeexxxxxxyyyyyyytttttttt\") == False\n assert candidate(s = \"\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == True\n assert candidate(s = \"word\",t = \"wwwooorrrrdddd\") == True\n assert candidate(s = \"algorithm\",t = \"algotihm\") == False\n assert candidate(s = \"repeated\",t = \"reppeted\") == False\n assert candidate(s = \"dynamic\",t = \"dyyyyynnaaaaaammmmcccciiiiiiiiinnnnnnnnggggggg\") == False\n assert candidate(s = \"abcd\",t = \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\") == True\n assert candidate(s = \"abcdabcd\",t = \"abxycdxeyzabcd\") == True\n assert candidate(s = \"complex\",t = \"complxc\") == False\n assert candidate(s = \"interview\",t = \"iiiiinnnnnttttttterrrrrrrrreevvvvvvvvvw\") == False\n assert candidate(s = \"mississippi\",t = \"mmissiissippiissippississippi\") == True\n assert candidate(s = \"substrings\",t = \"sssssuuuuubbstrrrrrriiiiinnnggggggsss\") == True\n assert candidate(s = \"substring\",t = \"ssssuusssubbssssttrrrriiiinnngggggg\") == True\n assert candidate(s = \"sequence\",t = \"seqqqqquuuuueeeennnnccceeeeee\") == True\n assert candidate(s = \"programming\",t = \"ppppprrogggggggrrrrrroooooogggggggaaaaammmmiiiiinnnnnggggggg\") == True\n assert candidate(s = \"repeated\",t = \"reeeepppeeeaaaatteeedd\") == True\n assert candidate(s = \"abcabcabc\",t = \"aabbccabcabcabc\") == True\n assert candidate(s = \"z\",t = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(s = \"consecutive\",t = \"ccoonnnsseecccccoooooonnnsssccceeeeeevvvvvvvveeeennnnnnncccccccceeeeeee\") == False\n assert candidate(s = \"\",t = \"a\") == True\n assert candidate(s = \"hello\",t = \"hhelllllooooworld\") == True\n assert candidate(s = \"example\",t = \"eeeexxaample\") == True\n assert candidate(s = \"subsequence\",t = \"ssubsuuubbbbsssseeeeeqqqqqqqqqqccceeeennnnneeeeee\") == False\n assert candidate(s = \"characters\",t = \"ccccchhhhaaaaaarrrrrrrtttteeeeeeccchhhhaaaaaarrrrrrrtttteeeeee\") == False\n assert candidate(s = \"abcdef\",t = \"fedcbazyxwvutsrqponmlkjihgfedcba\") == False\n assert candidate(s = \"subsequence\",t = \"substringsequence\") == True\n assert candidate(s = \"abcdefg\",t = \"axbxcxdxexfxgx\") == True\n assert candidate(s = \"abcdefg\",t = \"azbycxdwevfug\") == True\n assert candidate(s = \"sequence\",t = \"sqeuences\") == False\n", "comparison": "exact"}, "public_tests": ["\"abc\"\n\"ahbgdc\"", "\"axc\"\n\"ahbgdc\""], "hints": [], "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().isSubsequence", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:45+00:00", "tests_total": 69, "tests_dropped": 1, "flags": [], "topic_tags": ["two-pointers", "string", "dynamic-programming"]}, "language": "cpp", "interface": {"raw_signature": "bool isSubsequence(string s, string t) {", "container": "Solution", "callable": "isSubsequence", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 393, "task_id": "utf-8-validation", "difficulty": "Medium", "problem_description": "Given an integer array data representing the data, return whether it is a valid UTF-8 encoding (i.e. it translates to a sequence of valid UTF-8 encoded characters).\n\nA character in UTF8 can be from 1 to 4 bytes long, subjected to the following rules:\n\n1. For a 1-byte character, the first bit is a 0, followed by its Unicode code.\n2. For an n-bytes character, the first n bits are all one's, the n + 1 bit is 0, followed by n - 1 bytes with the most significant 2 bits being 10.\n\nThis is how the UTF-8 encoding would work:\n\n Number of Bytes | UTF-8 Octet Sequence\n | (binary)\n --------------------+-----------------------------------------\n 1 | 0xxxxxxx\n 2 | 110xxxxx 10xxxxxx\n 3 | 1110xxxx 10xxxxxx 10xxxxxx\n 4 | 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx\n\nx denotes a bit in the binary form of a byte that may be either 0 or 1.\n\nNote: The input is an array of integers. Only the least significant 8 bits of each integer is used to store the data. This means each integer represents only 1 byte of data.\n\nExample 1:\n\nInput: data = [197,130,1]\nOutput: true\nExplanation: data represents the octet sequence: 11000101 10000010 00000001.\nIt is a valid utf-8 encoding for a 2-bytes character followed by a 1-byte character.\n\nExample 2:\n\nInput: data = [235,140,4]\nOutput: false\nExplanation: data represented the octet sequence: 11101011 10001100 00000100.\nThe first 3 bits are all one's and the 4th bit is 0 means it is a 3-bytes character.\nThe next byte is a continuation byte which starts with 10 and that's correct.\nBut the second continuation byte does not start with 10, so it is invalid.\n\nConstraints:\n\n- 1 <= data.length <= 2 * 10^4\n- 0 <= data[i] <= 255\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(data = [237, 130, 130, 130]) == False\n assert candidate(data = [237, 128, 128, 130, 128, 128]) == False\n assert candidate(data = [238, 130, 130]) == True\n assert candidate(data = [31, 130, 130, 130]) == False\n assert candidate(data = [237, 130, 130, 130, 130]) == False\n assert candidate(data = [228, 189, 160]) == True\n assert candidate(data = [235, 140, 4]) == False\n assert candidate(data = [240, 162, 134, 142]) == True\n assert candidate(data = [237, 130, 130, 130, 130, 130, 130]) == False\n assert candidate(data = [251, 117, 104, 101, 108, 108, 111]) == False\n assert candidate(data = [240, 162, 134, 161]) == True\n assert candidate(data = [145]) == False\n assert candidate(data = [238, 130, 69]) == False\n assert candidate(data = [228, 189, 160, 229, 165, 189]) == True\n assert candidate(data = [197, 130, 1]) == True\n assert candidate(data = [235, 140, 4]) == False\n assert candidate(data = [197, 130, 1]) == True\n assert candidate(data = [192, 128, 191, 127]) == False\n assert candidate(data = [250, 145, 145, 145]) == False\n assert candidate(data = [0]) == True\n assert candidate(data = [240, 162, 134, 140]) == True\n assert candidate(data = [255]) == False\n assert candidate(data = [65, 66, 67, 68]) == True\n assert candidate(data = [224, 184, 148, 163]) == False\n assert candidate(data = [248, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [192, 128]) == True\n assert candidate(data = [240, 162, 138, 147, 145]) == False\n assert candidate(data = [237, 130, 130, 130]) == False\n assert candidate(data = [240, 162, 134, 142, 240, 162, 134, 142, 240, 162, 134, 142]) == True\n assert candidate(data = [252, 128, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139]) == False\n assert candidate(data = [110, 188, 142, 224, 160, 128]) == False\n assert candidate(data = [192, 128, 192, 128, 192, 128, 192, 192]) == False\n assert candidate(data = [225, 184, 165, 225, 184, 170, 225, 184, 185, 225, 184, 190]) == True\n assert candidate(data = [224, 160, 128, 224, 160, 128, 224, 160, 128]) == True\n assert candidate(data = [240, 159, 146, 150, 240, 159, 146, 150, 240, 159, 146, 150]) == True\n assert candidate(data = [240, 184, 152, 168, 224, 164, 174, 240, 157, 151, 166]) == True\n assert candidate(data = [248, 130, 130, 130, 130]) == False\n assert candidate(data = [248, 144, 144, 144, 144, 144]) == False\n assert candidate(data = [192, 128, 192, 128, 192, 128]) == True\n assert candidate(data = [240, 144, 144, 144, 144, 144, 144, 144]) == False\n assert candidate(data = [192, 128, 224, 162, 128, 240, 144, 128]) == False\n assert candidate(data = [248, 130, 129, 128, 128, 128, 128]) == False\n assert candidate(data = [235, 140, 141, 236, 140, 141, 237, 140, 141]) == True\n assert candidate(data = [224, 168, 128, 225, 184, 141, 225, 184, 172, 225, 184, 170, 225, 185, 172, 225, 184, 162]) == True\n assert candidate(data = [192, 128, 224, 160, 128, 225, 184, 160]) == True\n assert candidate(data = [244, 160, 128, 128, 244, 160, 128, 128]) == True\n assert candidate(data = [255, 255, 255, 255]) == False\n assert candidate(data = [225, 184, 160, 225, 184, 161, 225, 184, 162]) == True\n assert candidate(data = [192, 128, 192, 128, 192, 128, 192, 128]) == True\n assert candidate(data = [248, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [250, 145, 145, 145, 145]) == False\n assert candidate(data = [225, 184, 168, 225, 184, 169, 225, 184, 170]) == True\n assert candidate(data = [240, 159, 191, 191, 240, 159, 191, 191]) == True\n assert candidate(data = [224, 162, 130, 192, 128]) == True\n assert candidate(data = [192, 128, 192, 129, 192, 130, 192, 131, 192, 132, 192, 133, 192, 134, 192, 135, 192, 136, 192, 137, 192, 138, 192, 139, 192, 140, 192, 141, 192, 142, 192, 143]) == True\n assert candidate(data = [225, 184, 150, 225, 184, 185, 225, 184, 186, 225, 184, 187, 225, 184, 188]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [230, 138, 142, 230, 138, 143, 230, 138, 144]) == True\n assert candidate(data = [65, 66, 67, 68, 69, 70, 71, 72]) == True\n assert candidate(data = [240, 144, 144, 144, 240, 144, 144, 144, 240, 144, 144, 144, 240, 144, 144, 144]) == True\n assert candidate(data = [239, 188, 140, 239, 188, 141, 239, 188, 142, 239, 188, 143]) == True\n assert candidate(data = [225, 186, 130, 225, 186, 130, 225, 186, 130, 225, 186, 130, 225, 186, 130, 225, 186, 130]) == True\n assert candidate(data = [224, 160, 128, 224, 160, 129, 224, 160, 130]) == True\n assert candidate(data = [240, 159, 146, 140, 224, 164, 162, 194, 161]) == True\n assert candidate(data = [240, 128, 128, 128, 224, 160, 128, 192, 128]) == True\n assert candidate(data = [253, 160, 160, 160, 160, 160, 160, 160]) == False\n assert candidate(data = [244, 141, 132, 132, 244, 141, 132, 132]) == True\n assert candidate(data = [250, 145, 130, 147, 128, 130, 147, 128]) == False\n assert candidate(data = [240, 184, 144, 144, 240, 184, 144, 144]) == True\n assert candidate(data = [239, 187, 191, 239, 187, 191, 239, 187, 191]) == True\n assert candidate(data = [128, 129, 130, 131, 132, 133, 134, 135]) == False\n assert candidate(data = [192, 128, 224, 162, 130, 240, 159, 146, 150]) == True\n assert candidate(data = [255, 192, 128, 145]) == False\n assert candidate(data = [250, 154, 141, 154, 141, 154, 141, 154]) == False\n assert candidate(data = [252, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(data = [6, 239, 191, 191, 224, 160, 128, 239, 191, 191]) == True\n assert candidate(data = [224, 160, 128, 225, 184, 160, 239, 189, 191]) == True\n assert candidate(data = [225, 186, 185, 225, 186, 185, 225, 186, 185]) == True\n assert candidate(data = [224, 160, 128, 225, 184, 128, 237, 128, 128, 240, 144, 128, 128]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [250, 145, 130, 128, 10]) == False\n assert candidate(data = [239, 187, 191, 239, 187, 191, 239, 187, 191, 239, 187, 191]) == True\n assert candidate(data = [240, 128, 128, 128, 240, 129, 129, 129]) == True\n assert candidate(data = [191, 128, 191, 128, 191, 128]) == False\n assert candidate(data = [255, 140, 140, 140]) == False\n assert candidate(data = [192, 128, 224, 162, 138, 240, 159, 146, 150]) == True\n assert candidate(data = [128, 191, 223, 239, 255, 0, 127, 192]) == False\n assert candidate(data = [240, 144, 144, 128, 240, 144, 144, 144]) == True\n assert candidate(data = [240, 159, 146, 150, 240, 159, 146, 150]) == True\n assert candidate(data = [240, 145, 129, 128, 128]) == False\n assert candidate(data = [240, 145, 145, 145, 240, 145, 145, 145]) == True\n assert candidate(data = [234, 162, 134, 235, 140, 4, 236, 128, 132]) == False\n assert candidate(data = [240, 184, 152, 149, 240, 184, 152, 150]) == True\n assert candidate(data = [192, 128, 224, 160, 128, 240, 144, 128, 128]) == True\n assert candidate(data = [192, 128, 192, 128, 192, 128, 192, 128]) == True\n assert candidate(data = [240, 145, 128, 147, 128, 130, 147, 128, 237, 128, 128, 237, 128, 128]) == False\n assert candidate(data = [240, 145, 128, 128, 240, 145, 128, 128, 240, 145, 128, 128]) == True\n assert candidate(data = [224, 160, 128, 128, 224, 160, 128, 128, 224, 160, 128, 128]) == False\n assert candidate(data = [225, 184, 165, 225, 184, 170, 225, 184, 185]) == True\n assert candidate(data = [192, 128, 192, 128, 192, 128, 128, 192]) == False\n assert candidate(data = [224, 160, 128, 224, 160, 128, 192, 128, 128]) == False\n assert candidate(data = [239, 189, 191, 239, 189, 191]) == True\n assert candidate(data = [194, 128, 224, 160, 128, 240, 176, 128, 248, 192, 128, 128]) == False\n assert candidate(data = [192, 128, 224, 162, 138, 147, 240, 144, 144, 144, 0]) == False\n assert candidate(data = [239, 188, 140, 239, 188, 141, 239, 188, 142]) == True\n assert candidate(data = [10, 192, 128, 11, 194, 191, 14, 224, 160, 128, 15, 225, 184, 160]) == True\n assert candidate(data = [194, 128, 224, 160, 128, 240, 144, 128, 128, 250, 144, 128, 128]) == False\n assert candidate(data = [0, 0, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(data = [224, 160, 128, 237, 130, 176, 240, 144, 144, 128]) == True\n assert candidate(data = [255, 160, 130, 145]) == False\n assert candidate(data = [225, 186, 130, 225, 186, 130, 225, 186, 130]) == True\n assert candidate(data = [128, 129, 130, 131, 132, 133, 134, 135, 136, 137]) == False\n assert candidate(data = [240, 145, 129, 128, 240, 145, 129, 128, 240, 145, 129, 128]) == True\n assert candidate(data = [228, 189, 160, 229, 165, 189, 228, 184, 173]) == True\n assert candidate(data = [224, 162, 138, 224, 162, 138]) == True\n assert candidate(data = [194, 128, 226, 128, 128, 239, 184, 141]) == True\n assert candidate(data = [248, 130, 130, 130, 130, 130, 130, 130]) == False\n assert candidate(data = [240, 159, 146, 150, 192, 128, 224, 162, 130]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [240, 144, 144, 144, 144]) == False\n assert candidate(data = [10, 192, 130, 224, 162, 138, 240, 144, 144, 144, 192, 130]) == True\n assert candidate(data = [248, 130, 130, 130, 130, 130, 130]) == False\n assert candidate(data = [240, 145, 130, 128, 225, 186, 130, 192, 128]) == True\n assert candidate(data = [255, 255, 255, 255]) == False\n assert candidate(data = [192, 129, 192, 130, 192, 131, 192, 132]) == True\n assert candidate(data = [240, 144, 144, 144, 240, 144, 144, 144]) == True\n assert candidate(data = [255, 128, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [240, 162, 138, 147, 240, 162, 138, 147]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [248, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [192, 128, 224, 162, 138, 240, 144, 144, 144]) == True\n assert candidate(data = [237, 140, 141, 142, 143, 144, 145]) == False\n", "comparison": "exact"}, "public_tests": ["[197,130,1]", "[235,140,4]"], "hints": ["Read the data integer by integer. When you read it, process the least significant 8 bits of it.", "Assume the next encoding is 1-byte data. If it is not 1-byte data, read the next integer and assume it is 2-bytes data.", "Similarly, if it is not 2-bytes data, try 3-bytes then 4-bytes. If you read four integers and it still does not match any pattern, return false."], "metadata": {"canonical_parameter_names": ["data"], "leetcode_dataset_entry_point": "Solution().validUtf8", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:48+00:00", "tests_total": 135, "tests_dropped": 1, "flags": [], "topic_tags": ["array", "bit-manipulation"]}, "language": "cpp", "interface": {"raw_signature": "bool validUtf8(vector& data) {", "container": "Solution", "callable": "validUtf8", "parameters": [{"name": "data", "type": "vector&"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 394, "task_id": "decode-string", "difficulty": "Medium", "problem_description": "Given an encoded string, return its decoded string.\n\nThe encoding rule is: k[encoded_string], where the encoded_string inside the square brackets is being repeated exactly k times. Note that k is guaranteed to be a positive integer.\n\nYou may assume that the input string is always valid; there are no extra white spaces, square brackets are well-formed, etc. Furthermore, you may assume that the original data does not contain any digits and that digits are only for those repeat numbers, k. For example, there will not be input like 3a or 2[4].\n\nThe test cases are generated so that the length of the output will never exceed 10^5.\n\nExample 1:\n\nInput: s = \"3[a]2[bc]\"\nOutput: \"aaabcbc\"\n\nExample 2:\n\nInput: s = \"3[a2[c]]\"\nOutput: \"accaccacc\"\n\nExample 3:\n\nInput: s = \"2[abc]3[cd]ef\"\nOutput: \"abcabccdcdcdef\"\n\nConstraints:\n\n- 1 <= s.length <= 30\n- s consists of lowercase English letters, digits, and square brackets '[]'.\n- s is guaranteed to be a valid input.\n- All the integers in s are in the range [1, 300].\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"2[ab3[cd]]\") == \"abcdcdcdabcdcdcd\"\n assert candidate(s = \"2[ab3[c]]\") == \"abcccabccc\"\n assert candidate(s = \"1[a1[b1[c]]]\") == \"abc\"\n assert candidate(s = \"2[3[a]]\") == \"aaaaaa\"\n assert candidate(s = \"a1[b]\") == \"ab\"\n assert candidate(s = \"3[a3[b]1[c]]\") == \"abbbcabbbcabbbc\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"10[abc]\") == \"abcabcabcabcabcabcabcabcabcabc\"\n assert candidate(s = \"1[2[3[4[a]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"2[3[a]b]\") == \"aaabaaab\"\n assert candidate(s = \"4[ab]\") == \"abababab\"\n assert candidate(s = \"1[a2[b3[c]]]\") == \"abcccbccc\"\n assert candidate(s = \"10[a]\") == \"aaaaaaaaaa\"\n assert candidate(s = \"a2[b]c\") == \"abbc\"\n assert candidate(s = \"2[abc]3[cd]ef\") == \"abcabccdcdcdef\"\n assert candidate(s = \"1[a]\") == \"a\"\n assert candidate(s = \"3[a2[c]]\") == \"accaccacc\"\n assert candidate(s = \"3[a]2[bc]\") == \"aaabcbc\"\n assert candidate(s = \"abc\") == \"abc\"\n assert candidate(s = \"3[a3[b2[c]]]\") == \"abccbccbccabccbccbccabccbccbcc\"\n assert candidate(s = \"100[ab]\") == \"abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababab\"\n assert candidate(s = \"a[b]\") == \"a\"\n assert candidate(s = \"2[b3[c]]\") == \"bcccbccc\"\n assert candidate(s = \"1[xyz]2[uvw]\") == \"xyzuvwuvw\"\n assert candidate(s = \"a2[b3[c]]\") == \"abcccbccc\"\n assert candidate(s = \"1[a1[b]]\") == \"ab\"\n assert candidate(s = \"4[3[z]2[y]]\") == \"zzzyyzzzyyzzzyyzzzyy\"\n assert candidate(s = \"5[ab3[c2[d]]]\") == \"abcddcddcddabcddcddcddabcddcddcddabcddcddcddabcddcddcdd\"\n assert candidate(s = \"5[a1[b2[c3[d4[e]]]]]\") == \"abcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeee\"\n assert candidate(s = \"a2[b3[c4[d5[e6[f7[g]]]]]]\") == \"abcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggbcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfggggggg\"\n assert candidate(s = \"abc3[d2[e1[f]]]\") == \"abcdefefdefefdefef\"\n assert candidate(s = \"5[a2[b3[c4[d]]]]\") == \"abcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcdddd\"\n assert candidate(s = \"3[2[mn]1[op]2[qr]]\") == \"mnmnopqrqrmnmnopqrqrmnmnopqrqr\"\n assert candidate(s = \"5[c2[d]]\") == \"cddcddcddcddcdd\"\n assert candidate(s = \"a1[b2[c3[d]]]\") == \"abcdddcddd\"\n assert candidate(s = \"7[2[x]3[y]]\") == \"xxyyyxxyyyxxyyyxxyyyxxyyyxxyyyxxyyy\"\n assert candidate(s = \"2[ab3[cd]]4[ef5[gh]]\") == \"abcdcdcdabcdcdcdefghghghghghefghghghghghefghghghghghefghghghghgh\"\n assert candidate(s = \"3[ab2[c]]4[de]\") == \"abccabccabccdededede\"\n assert candidate(s = \"4[ab3[c2[d]]]\") == \"abcddcddcddabcddcddcddabcddcddcddabcddcddcdd\"\n assert candidate(s = \"3[a2[b1[c0[d]]]]\") == \"abcbcabcbcabcbc\"\n assert candidate(s = \"3[a4[b5[c6[d7[e8[f]]]]]]\") == \"abcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffabcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffabcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffff\"\n assert candidate(s = \"3[2[a]1[b]]2[3[c]4[d]]\") == \"aabaabaabcccddddcccdddd\"\n assert candidate(s = \"2[3[a]2[b3[c]2[d]]]\") == \"aaabcccddbcccddaaabcccddbcccdd\"\n assert candidate(s = \"6[ab2[cd3[ef]]]\") == \"abcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefef\"\n assert candidate(s = \"7[fg]2[h3[i]]\") == \"fgfgfgfgfgfgfghiiihiii\"\n assert candidate(s = \"7[x2[y3[z4[w]]]]\") == \"xyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwww\"\n assert candidate(s = \"5[2[x3[y]]4[z]]\") == \"xyyyxyyyzzzzxyyyxyyyzzzzxyyyxyyyzzzzxyyyxyyyzzzzxyyyxyyyzzzz\"\n assert candidate(s = \"6[ab2[cd3[ef4[gh]]]]\") == \"abcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghgh\"\n assert candidate(s = \"2[x2[y3[z]]]1[a]\") == \"xyzzzyzzzxyzzzyzzza\"\n assert candidate(s = \"7[z]6[y5[x4[w3[v2[u1[t]]]]]]\") == \"zzzzzzzyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvutut\"\n assert candidate(s = \"2[a3[b4[c]]]\") == \"abccccbccccbccccabccccbccccbcccc\"\n assert candidate(s = \"10[a9[bc3[de]]]\") == \"abcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdedede\"\n assert candidate(s = \"3[ab]4[cd]5[ef]\") == \"abababcdcdcdcdefefefefef\"\n assert candidate(s = \"10[ab]\") == \"abababababababababab\"\n assert candidate(s = \"5[4[3[2[1[x]]]]]\") == \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n assert candidate(s = \"2[ab3[cd4[ef]]]\") == \"abcdefefefefcdefefefefcdefefefefabcdefefefefcdefefefefcdefefefef\"\n assert candidate(s = \"5[ab]3[cd]2[ef1[gh]]\") == \"abababababcdcdcdefghefgh\"\n assert candidate(s = \"7[2[pq]3[rs]]\") == \"pqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrs\"\n assert candidate(s = \"2[3[a]b]4[c5[d]]\") == \"aaabaaabcdddddcdddddcdddddcddddd\"\n assert candidate(s = \"3[2[3[4[a]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"6[2[a]3[b]]\") == \"aabbbaabbbaabbbaabbbaabbbaabbb\"\n assert candidate(s = \"2[abc3[def4[ghi5[jkl]]]]\") == \"abcdefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklabcdefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkl\"\n assert candidate(s = \"2[a3[b4[c5[d6[e]]]]]\") == \"abcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeeabcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeee\"\n assert candidate(s = \"3[2[1[0[]]]]\") == \"\"\n assert candidate(s = \"10[f9[g]]\") == \"fgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfggggggggg\"\n assert candidate(s = \"15[abc10[de]]\") == \"abcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdededededededededede\"\n assert candidate(s = \"5[k9[l10[m]]]\") == \"klmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmm\"\n assert candidate(s = \"5[xy2[z3[w4[v]]]]\") == \"xyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvv\"\n assert candidate(s = \"1[1[1[1[ab]]]]\") == \"ab\"\n assert candidate(s = \"5[1[2[3[4[5[a]]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"4[ab2[c]]\") == \"abccabccabccabcc\"\n assert candidate(s = \"4[a2[b3[c]]]\") == \"abcccbcccabcccbcccabcccbcccabcccbccc\"\n assert candidate(s = \"2[x3[y4[z]]]\") == \"xyzzzzyzzzzyzzzzxyzzzzyzzzzyzzzz\"\n assert candidate(s = \"3[2[3[4[a]]]5[b]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaabbbbbaaaaaaaaaaaaaaaaaaaaaaaabbbbbaaaaaaaaaaaaaaaaaaaaaaaabbbbb\"\n assert candidate(s = \"10[ab2[cd]ef3[gh]]\") == \"abcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghgh\"\n assert candidate(s = \"5[abc2[def]]\") == \"abcdefdefabcdefdefabcdefdefabcdefdefabcdefdef\"\n assert candidate(s = \"3[2[3[a2[b]]]]\") == \"abbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabb\"\n assert candidate(s = \"2[3[ab]]\") == \"abababababab\"\n assert candidate(s = \"3[xy2[z]]2[ab]\") == \"xyzzxyzzxyzzabab\"\n assert candidate(s = \"10[1[a]2[b]3[c]4[d]5[e]]\") == \"abbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeee\"\n assert candidate(s = \"3[2[3[4[x]]]]\") == \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n assert candidate(s = \"2[3[a]b4[c]]\") == \"aaabccccaaabcccc\"\n assert candidate(s = \"10[x]\") == \"xxxxxxxxxx\"\n assert candidate(s = \"4[2[xy]z]\") == \"xyxyzxyxyzxyxyzxyxyz\"\n assert candidate(s = \"6[a5[b4[c3[d2[e1[f]]]]]]\") == \"abcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefef\"\n assert candidate(s = \"4[x5[yz]w]\") == \"xyzyzyzyzyzwxyzyzyzyzyzwxyzyzyzyzyzwxyzyzyzyzyzw\"\n assert candidate(s = \"4[3[2[b1[c]]]]\") == \"bcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbc\"\n assert candidate(s = \"2[x3[xy4[z]]]\") == \"xxyzzzzxyzzzzxyzzzzxxyzzzzxyzzzzxyzzzz\"\n assert candidate(s = \"2[3[a2[b]]c]\") == \"abbabbabbcabbabbabbc\"\n assert candidate(s = \"9[abc]8[def]7[ghi]\") == \"abcabcabcabcabcabcabcabcabcdefdefdefdefdefdefdefdefghighighighighighighi\"\n assert candidate(s = \"4[ab]5[cd]\") == \"ababababcdcdcdcdcd\"\n assert candidate(s = \"2[3[xy]z]\") == \"xyxyxyzxyxyxyz\"\n assert candidate(s = \"4[x3[y2[z]]]\") == \"xyzzyzzyzzxyzzyzzyzzxyzzyzzyzzxyzzyzzyzz\"\n assert candidate(s = \"3[2[a]b]\") == \"aabaabaab\"\n assert candidate(s = \"abc2[3[de]fg]\") == \"abcdededefgdededefg\"\n assert candidate(s = \"1[abc2[def3[ghi]]]\") == \"abcdefghighighidefghighighi\"\n assert candidate(s = \"2[abc2[def3[ghi]]]\") == \"abcdefghighighidefghighighiabcdefghighighidefghighighi\"\n assert candidate(s = \"1[2[3[4[5[a]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"5[ab3[cd]]\") == \"abcdcdcdabcdcdcdabcdcdcdabcdcdcdabcdcdcd\"\n assert candidate(s = \"2[x3[y4[z]]]1[w]\") == \"xyzzzzyzzzzyzzzzxyzzzzyzzzzyzzzzw\"\n assert candidate(s = \"7[2[a]3[b]]\") == \"aabbbaabbbaabbbaabbbaabbbaabbbaabbb\"\n assert candidate(s = \"4[x5[y]]\") == \"xyyyyyxyyyyyxyyyyyxyyyyy\"\n assert candidate(s = \"2[abc3[def4[ghi]]]\") == \"abcdefghighighighidefghighighighidefghighighighiabcdefghighighighidefghighighighidefghighighighi\"\n assert candidate(s = \"5[ab2[c]]3[xy]2[de]\") == \"abccabccabccabccabccxyxyxydede\"\n assert candidate(s = \"5[abc2[de]]\") == \"abcdedeabcdedeabcdedeabcdedeabcdede\"\n assert candidate(s = \"7[k2[3[xyz]]]\") == \"kxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyz\"\n assert candidate(s = \"1[abc2[def]]\") == \"abcdefdef\"\n assert candidate(s = \"3[2[1[x]]]\") == \"xxxxxx\"\n assert candidate(s = \"5[ab2[cd]]\") == \"abcdcdabcdcdabcdcdabcdcdabcdcd\"\n assert candidate(s = \"6[5[4[3[2[1[a]]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"7[xyz]3[abc2[def1[ghi]]]\") == \"xyzxyzxyzxyzxyzxyzxyzabcdefghidefghiabcdefghidefghiabcdefghidefghi\"\n assert candidate(s = \"x1[y2[z3[a4[b5[c]]]]]\") == \"xyzabcccccbcccccbcccccbcccccabcccccbcccccbcccccbcccccabcccccbcccccbcccccbccccczabcccccbcccccbcccccbcccccabcccccbcccccbcccccbcccccabcccccbcccccbcccccbccccc\"\n assert candidate(s = \"3[ab2[c3[d]]]\") == \"abcdddcdddabcdddcdddabcdddcddd\"\n assert candidate(s = \"6[a2[b3[c4[d]]]]\") == \"abcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcdddd\"\n assert candidate(s = \"15[a]\") == \"aaaaaaaaaaaaaaa\"\n assert candidate(s = \"5[2[3[a]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"2[xy3[z]]4[ab]\") == \"xyzzzxyzzzabababab\"\n assert candidate(s = \"1[a2[b3[c4[d5[e]]]]]\") == \"abcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeebcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeee\"\n assert candidate(s = \"4[a3[b]]\") == \"abbbabbbabbbabbb\"\n assert candidate(s = \"2[ab]3[cd]4[ef]\") == \"ababcdcdcdefefefef\"\n assert candidate(s = \"1[2[3[4[5[6[x]]]]]]\") == \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n assert candidate(s = \"2[a3[b4[c5[d6[e7[f]]]]]]\") == \"abcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffabcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffff\"\n assert candidate(s = \"4[a3[b2[c1[d]]]]\") == \"abcdcdbcdcdbcdcdabcdcdbcdcdbcdcdabcdcdbcdcdbcdcdabcdcdbcdcdbcdcd\"\n assert candidate(s = \"3[2[3[4[5[a]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"3[xyz2[abc]4[def]]5[ghi]\") == \"xyzabcabcdefdefdefdefxyzabcabcdefdefdefdefxyzabcabcdefdefdefdefghighighighighi\"\n assert candidate(s = \"2[2[2[2[2[abc]]]]]\") == \"abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc\"\n assert candidate(s = \"3[b2[c]1[d]]4[e]\") == \"bccdbccdbccdeeee\"\n assert candidate(s = \"a2[b3[c4[d5[e]]]]\") == \"abcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeebcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeee\"\n", "comparison": "exact"}, "public_tests": ["\"3[a]2[bc]\"", "\"3[a2[c]]\"", "\"2[abc]3[cd]ef\""], "hints": [], "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().decodeString", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:47:50+00:00", "tests_total": 133, "tests_dropped": 5, "flags": [], "topic_tags": ["string", "stack", "recursion"]}, "language": "cpp", "interface": {"raw_signature": "string decodeString(string s) {", "container": "Solution", "callable": "decodeString", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} @@ -229,7 +229,7 @@ {"question_id": 441, "task_id": "arranging-coins", "difficulty": "Easy", "problem_description": "You have n coins and you want to build a staircase with these coins. The staircase consists of k rows where the i^th row has exactly i coins. The last row of the staircase may be incomplete.\n\nGiven the integer n, return the number of complete rows of the staircase you will build.\n\nExample 1:\n\nInput: n = 5\nOutput: 2\nExplanation: Because the 3^rd row is incomplete, we return 2.\n\nExample 2:\n\nInput: n = 8\nOutput: 3\nExplanation: Because the 4^th row is incomplete, we return 3.\n\nConstraints:\n\n- 1 <= n <= 2^31 - 1\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == 3\n assert candidate(n = 100) == 13\n assert candidate(n = 30) == 7\n assert candidate(n = 15) == 5\n assert candidate(n = 22) == 6\n assert candidate(n = 21) == 6\n assert candidate(n = 2147483647) == 65535\n assert candidate(n = 1804289383) == 60070\n assert candidate(n = 1) == 1\n assert candidate(n = 180) == 18\n assert candidate(n = 10) == 4\n assert candidate(n = 5) == 2\n assert candidate(n = 210) == 20\n assert candidate(n = 45) == 9\n assert candidate(n = 171) == 18\n assert candidate(n = 3) == 2\n assert candidate(n = 576) == 33\n assert candidate(n = 2147483646) == 65535\n assert candidate(n = 12) == 4\n assert candidate(n = 7) == 3\n assert candidate(n = 70) == 11\n assert candidate(n = 1000) == 44\n assert candidate(n = 28) == 7\n assert candidate(n = 64) == 10\n assert candidate(n = 16) == 5\n assert candidate(n = 10000) == 140\n assert candidate(n = 1001) == 44\n assert candidate(n = 2) == 1\n assert candidate(n = 80) == 12\n assert candidate(n = 165) == 17\n assert candidate(n = 6678) == 115\n assert candidate(n = 101) == 13\n assert candidate(n = 100000) == 446\n assert candidate(n = 18) == 5\n assert candidate(n = 256) == 22\n assert candidate(n = 36) == 8\n assert candidate(n = 500) == 31\n assert candidate(n = 1000000000) == 44720\n assert candidate(n = 1999) == 62\n assert candidate(n = 987654321) == 44443\n assert candidate(n = 5000000) == 3161\n assert candidate(n = 325) == 25\n assert candidate(n = 441) == 29\n assert candidate(n = 136) == 16\n assert candidate(n = 500000000) == 31622\n assert candidate(n = 1000000) == 1413\n assert candidate(n = 6) == 3\n assert candidate(n = 123456789) == 15712\n assert candidate(n = 120) == 15\n assert candidate(n = 1999999999) == 63245\n assert candidate(n = 123456) == 496\n assert candidate(n = 5050) == 100\n assert candidate(n = 55) == 10\n assert candidate(n = 84) == 12\n", "comparison": "exact"}, "public_tests": ["5", "8"], "hints": [], "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().arrangeCoins", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:19+00:00", "tests_total": 54, "tests_dropped": 0, "flags": ["has_images"], "topic_tags": ["math", "binary-search"]}, "language": "cpp", "interface": {"raw_signature": "int arrangeCoins(int n) {", "container": "Solution", "callable": "arrangeCoins", "parameters": [{"name": "n", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 442, "task_id": "find-all-duplicates-in-an-array", "difficulty": "Medium", "problem_description": "Given an integer array nums of length n where all the integers of nums are in the range [1, n] and each integer appears at most twice, return an array of all the integers that appears twice.\n\nYou must write an algorithm that runs in O(n) time and uses only constant auxiliary space, excluding the space needed to store the output\n\nExample 1:\n\nInput: nums = [4,3,2,7,8,2,3,1]\nOutput: [2,3]\n\nExample 2:\n\nInput: nums = [1,1,2]\nOutput: [1]\n\nExample 3:\n\nInput: nums = [1]\nOutput: []\n\nConstraints:\n\n- n == nums.length\n- 1 <= n <= 10^5\n- 1 <= nums[i] <= n\n- Each element in nums appears once or twice.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 2]) == [1]\n assert candidate(nums = [5, 3, 2, 3, 5, 1]) == [3, 5]\n assert candidate(nums = [1]) == []\n assert candidate(nums = [5, 3, 1, 2, 4, 3, 5]) == [3, 5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9]) == [10, 9]\n assert candidate(nums = [5, 4, 6, 7, 9, 3, 10, 9, 5, 6]) == [5, 6, 9]\n assert candidate(nums = [10, 2, 5, 10, 9, 1, 1, 4, 3, 7]) == [1, 10]\n assert candidate(nums = [4, 3, 2, 7, 8, 2, 3, 1]) == [3, 2]\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 2, 3]) == [1, 2, 3]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5]) == [2, 4, 3]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5]) == [2, 4, 3, 5]\n assert candidate(nums = [5, 3, 4, 5, 3, 2, 1, 2, 4]) == [3, 5, 2, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2]) == [1, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15]) == [10, 13, 5, 8, 15]\n assert candidate(nums = [3, 3, 2, 2, 1, 1, 6, 6, 5, 5, 4, 4, 10, 10, 9, 9, 8, 8, 7, 7]) == [2, 4, 5, 10, 3, 9, 6, 8, 1, 7]\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]\n assert candidate(nums = [2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36]) == [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [3, 6, 2, 7, 4, 8, 1, 9, 5, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [50, 50, 49, 49, 48, 48, 47, 47, 46, 46, 45, 45, 44, 44, 43, 43, 42, 42, 41, 41, 40, 40, 39, 39, 38, 38, 37, 37, 36, 36, 35, 35, 34, 34, 33, 33, 32, 32, 31, 31, 30, 30, 29, 29, 28, 28, 27, 27, 26, 26, 25, 25, 24, 24, 23, 23, 22, 22, 21, 21, 20, 20, 19, 19, 18, 18, 17, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == [38, 25, 39, 24, 31, 23, 40, 22, 35, 21, 41, 20, 30, 19, 42, 18, 36, 17, 43, 16, 29, 15, 44, 14, 33, 13, 45, 12, 28, 11, 46, 10, 37, 9, 47, 8, 27, 7, 48, 6, 32, 5, 49, 4, 26, 3, 50, 2, 34, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4]) == [3, 4]\n assert candidate(nums = [5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == [3, 6, 5, 7, 2, 8, 4, 9, 1, 10]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10]) == [5, 2, 10]\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4]) == [5, 6, 7, 8, 9, 10, 1, 2, 3, 4]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 1, 1, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == [2, 1, 7, 12, 5, 13, 8, 14, 4, 15, 9, 16, 6, 17, 10, 18, 3, 19, 11, 20]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25]) == [19, 2, 20, 16, 10, 22, 14, 18, 24, 12, 25]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 1]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == [3, 6, 2, 7, 4, 8, 1, 9, 5, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25]) == [13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25]\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]) == [2, 4, 5, 6, 7, 8, 9, 10, 1, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == [5, 1, 6, 3, 7, 1, 8, 4, 9, 2]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == [4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == [3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [8, 2, 3, 2, 1, 5, 6, 3, 7, 4, 8, 5]) == [3, 2, 8, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2]\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14]) == [5, 10, 6, 7, 8, 9]\n assert candidate(nums = [5, 5, 5, 5, 5, 1, 2, 3, 4, 1]) == [5, 5, 5, 5, 1]\n", "comparison": "exact"}, "public_tests": ["[4,3,2,7,8,2,3,1]", "[1,1,2]", "[1]"], "hints": [], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findDuplicates", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:21+00:00", "tests_total": 61, "tests_dropped": 0, "flags": [], "topic_tags": ["array", "hash-table", "sorting"]}, "language": "cpp", "interface": {"raw_signature": "vector findDuplicates(vector& nums) {", "container": "Solution", "callable": "findDuplicates", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 446, "task_id": "arithmetic-slices-ii-subsequence", "difficulty": "Hard", "problem_description": "Given an integer array nums, return the number of all the arithmetic subsequences of nums.\n\nA sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.\n\n- For example, [1, 3, 5, 7, 9], [7, 7, 7, 7], and [3, -1, -5, -9] are arithmetic sequences.\n- For example, [1, 1, 2, 5, 7] is not an arithmetic sequence.\n\nA subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.\n\n- For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].\n\nThe test cases are generated so that the answer fits in 32-bit integer.\n\nExample 1:\n\nInput: nums = [2,4,6,8,10]\nOutput: 7\nExplanation: All arithmetic subsequence slices are:\n[2,4,6]\n[4,6,8]\n[6,8,10]\n[2,4,6,8]\n[4,6,8,10]\n[2,4,6,8,10]\n[2,6,10]\n\nExample 2:\n\nInput: nums = [7,7,7,7,7]\nOutput: 16\nExplanation: Any subsequence of this array is arithmetic.\n\nConstraints:\n\n- 1 <= nums.length <= 1000\n- -2^31 <= nums[i] <= 2^31 - 1\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15]) == 29\n assert candidate(nums = [1, 2, 3, 8, 9]) == 1\n assert candidate(nums = [2, 4, 6, 8, 10]) == 7\n assert candidate(nums = [1, 3, 5, 7, 9]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [10, 20, 30, 40, 50]) == 7\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 55\n assert candidate(nums = [1, 1, 2, 5, 7]) == 0\n assert candidate(nums = [0, 2000000000, -294967296, -294967296]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 7\n assert candidate(nums = [10, 9, 4, 6, 8, 4, 3, 9, 1, 3, 5, 7]) == 10\n assert candidate(nums = [1, 2, 3, 8, 13, 18]) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11]) == 12\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1]) == 99\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34]) == 6\n assert candidate(nums = [7, 7, 7, 7, 7]) == 16\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 968\n assert candidate(nums = [1, 2, 3, 4, 5, 6]) == 12\n assert candidate(nums = [1, 2]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3]) == 99\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64]) == 0\n assert candidate(nums = [1, 2, 3]) == 1\n assert candidate(nums = [1, 2, 3, 8, 9, 10]) == 2\n assert candidate(nums = [3, 1, 2, 2, 4, 5]) == 1\n assert candidate(nums = [3, 1, 2, 5, 7]) == 1\n assert candidate(nums = [1, 7, 10, 15, 27, 29]) == 1\n assert candidate(nums = [1, 2, 1, 2, 1]) == 1\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]) == 9\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 968\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 194\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 55\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96]) == 198\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 55\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36]) == 90\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 0\n assert candidate(nums = [1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 602\n assert candidate(nums = [10, 7, 4, 3, 2, 1, -1, -2, -3, -4]) == 20\n assert candidate(nums = [1000, 990, 980, 970, 960, 950, 940, 930, 920, 910, 900, 890, 880, 870, 860, 850, 840, 830, 820, 810, 800]) == 390\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52]) == 263\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256]) == 0\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]) == 13\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 164\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33]) == 72\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45]) == 1\n assert candidate(nums = [-5, -1, 3, 7, 11, 15, 19, 23]) == 29\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49, 55]) == 55\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 72\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1048365\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]) == 55\n assert candidate(nums = [10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40, 40]) == 139\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 164\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 344\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 946\n assert candidate(nums = [5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35]) == 72\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 60\n assert candidate(nums = [1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91]) == 72\n assert candidate(nums = [1, 3, 5, 7, 9, 12, 15, 18, 21, 24]) == 22\n assert candidate(nums = [5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47]) == 164\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 55\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 604\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 0\n assert candidate(nums = [10, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38]) == 55\n assert candidate(nums = [1, 7, 10, 15, 27, 29, 33, 51]) == 3\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 100\n assert candidate(nums = [1, 3, 5, 9, 15, 25, 39, 57, 79, 105, 135]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 164\n assert candidate(nums = [10, 12, 14, 18, 22, 26, 30, 34, 38, 42, 46]) == 56\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 55\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 72\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1981\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6]) == 4172\n assert candidate(nums = [1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28]) == 62\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 65294\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1048365\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 32647\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 4256\n assert candidate(nums = [1, 7, 10, 15, 27, 29, 33, 37, 41, 45, 49]) == 13\n assert candidate(nums = [5, 8, 11, 14, 17, 20, 23, 26, 29, 32]) == 55\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6]) == 160\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == 164\n assert candidate(nums = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 32\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 90\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57]) == 164\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == 1936\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40]) == 137\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]) == 8\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 604\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == 772\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77]) == 344\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1294\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35]) == 263\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 344\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58]) == 344\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 14, 16, 18, 20, 24, 26, 28, 30, 34, 36, 38, 40]) == 72\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 344\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 114\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 56\n assert candidate(nums = [-2, -1, 1, 4, 8, 13, 19, 26, 34, 43, 53, 64]) == 4\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 946\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 391\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90]) == 41\n assert candidate(nums = [2, 4, 6, 8, 12, 14, 16, 20, 22, 24, 28]) == 32\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]) == 72\n assert candidate(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 28\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 164\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 72\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54]) == 264\n assert candidate(nums = [10, 7, 4, 1, -2, -5, -8, -11, -14]) == 41\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45]) == 41\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 364\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 113\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91]) == 3\n assert candidate(nums = [1, 3, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37]) == 355\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73]) == 113\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61]) == 72\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 57\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 48\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768]) == 0\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40]) == 164\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 968\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]) == 90\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13]) == 25208\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 344\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31]) == 72\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800]) == 29\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49]) == 41\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45]) == 90\n assert candidate(nums = [10, 7, 4, 3, 2, 1, -1, -4, -7, -10]) == 16\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 55\n assert candidate(nums = [1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100]) == 90\n assert candidate(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 17\n assert candidate(nums = [1, 3, 5, 3, 1, -1, -3, -5, -3, -1, 1, 3, 5]) == 53\n assert candidate(nums = [10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 72\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39]) == 113\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21]) == 21\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 1584\n assert candidate(nums = [1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9]) == 323\n assert candidate(nums = [1, 2, 3, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3]) == 1370\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 55\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 55\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 0\n assert candidate(nums = [3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 160\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 72\n assert candidate(nums = [3, 6, 9, 15, 18, 21, 27, 30, 33, 39, 42, 45]) == 40\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 968\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7]) == 165\n assert candidate(nums = [5, 10, 15, 25, 35, 45, 55, 65, 75, 85]) == 42\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 32647\n assert candidate(nums = [1, 7, 10, 15, 27, 29, 33, 18]) == 1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7]) == 5029\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23]) == 90\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45]) == 164\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 55\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 164\n assert candidate(nums = [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79]) == 4\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 32647\n", "comparison": "exact"}, "public_tests": ["[2,4,6,8,10]", "[7,7,7,7,7]"], "hints": [], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().numberOfArithmeticSlices", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:31+00:00", "tests_total": 164, "tests_dropped": 1, "flags": [], "topic_tags": ["array", "dynamic-programming"]}, "language": "cpp", "interface": {"raw_signature": "int numberOfArithmeticSlices(vector& nums) {", "container": "Solution", "callable": "numberOfArithmeticSlices", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} -{"question_id": 447, "task_id": "number-of-boomerangs", "difficulty": "Medium", "problem_description": "You are given n points in the plane that are all distinct, where points[i] = [x_i, y_i]. A boomerang is a tuple of points (i, j, k) such that the distance between i and j equals the distance between i and k (the order of the tuple matters).\n\nReturn the number of boomerangs.\n\nExample 1:\n\nInput: points = [[0,0],[1,0],[2,0]]\nOutput: 2\nExplanation: The two boomerangs are [[1,0],[0,0],[2,0]] and [[1,0],[2,0],[0,0]].\n\nExample 2:\n\nInput: points = [[1,1],[2,2],[3,3]]\nOutput: 2\n\nExample 3:\n\nInput: points = [[1,1]]\nOutput: 0\n\nConstraints:\n\n- n == points.length\n- 1 <= n <= 500\n- points[i].length == 2\n- -10^4 <= x_i, y_i <= 10^4\n- All the points are unique.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0]]) == 8\n assert candidate(points = [[1, 0], [0, 0], [0, 1]]) == 2\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [0, 2]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [2, 0]]) == 2\n assert candidate(points = [[0, 0], [1, 0], [-1, 0], [0, 1], [0, -1]]) == 20\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4]]) == 4\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 0]]) == 4\n assert candidate(points = [[10000, 10000], [-10000, -10000], [0, 0]]) == 2\n assert candidate(points = [[1, 1], [2, 2], [3, 3]]) == 2\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1]]) == 8\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3]]) == 4\n assert candidate(points = [[0, 0], [0, 1], [1, 0], [1, 1]]) == 8\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [2, 0]]) == 8\n assert candidate(points = [[-1, 0], [0, 0], [1, 0]]) == 2\n assert candidate(points = [[1, 1]]) == 0\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [2, 3], [3, 2], [1, 2], [2, 1]]) == 38\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 2], [2, 1], [1, 2]]) == 38\n assert candidate(points = [[-2, -2], [-1, -1], [1, 1], [2, 2], [-3, -3], [3, 3], [-4, -4], [4, 4]]) == 16\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10]]) == 8\n assert candidate(points = [[-1, 0], [0, -1], [1, 0], [0, 1], [0, 0]]) == 20\n assert candidate(points = [[-1, -1], [1, 1], [2, 2], [3, 3], [4, 4], [-1, 1], [1, -1], [-2, -2], [-3, -3], [-4, -4]]) == 48\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [2, 1]]) == 24\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 8\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4]]) == 64\n assert candidate(points = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 3], [3, 4], [4, 5]]) == 16\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [4, 0], [4, 2], [0, 4], [2, 4], [4, 4]]) == 88\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 40\n assert candidate(points = [[1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2]]) == 40\n assert candidate(points = [[5, 5], [5, 10], [10, 5], [10, 10], [7, 7], [8, 8]]) == 16\n assert candidate(points = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 24\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [1, 1], [-1, -1], [-1, 1], [1, -1]]) == 48\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 1], [1, 3], [3, 1], [2, 3], [3, 2], [2, 0], [0, 2], [3, 0], [0, 3]]) == 192\n assert candidate(points = [[-10000, -10000], [10000, 10000], [0, 0], [5000, 5000], [-5000, -5000], [2000, 2000], [-2000, -2000]]) == 10\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [0, 2], [0, 3], [0, 4]]) == 18\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [2, 0], [2, 1], [0, 1], [0, 2], [1, 2], [2, 2], [3, 2]]) == 104\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 2], [3, 3], [4, 4]]) == 104\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 18\n assert candidate(points = [[100, 100], [101, 101], [102, 102], [100, 102], [102, 100], [101, 100], [100, 101], [102, 101], [101, 102]]) == 88\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 12\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [-1, 1], [-2, 2], [-3, 3], [1, -1], [2, -2], [3, -3]]) == 78\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [1, -1], [-1, 1], [-1, -1]]) == 20\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1]]) == 20\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, -1], [0, 1]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13]]) == 72\n assert candidate(points = [[0, 0], [10000, 10000], [-10000, -10000], [10000, -10000], [-10000, 10000]]) == 20\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [1, 1]]) == 12\n assert candidate(points = [[0, 0], [0, 5], [5, 0], [5, 5], [2, 2], [3, 3], [4, 4]]) == 24\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [2, 1], [2, 2], [3, 2], [3, 3], [4, 3], [4, 4], [5, 4]]) == 40\n assert candidate(points = [[0, 0], [0, 1], [1, 0], [1, 1], [2, 2], [2, 1], [1, 2]]) == 38\n assert candidate(points = [[0, 1], [1, 0], [1, 2], [2, 1], [2, 3], [3, 2]]) == 24\n assert candidate(points = [[0, 0], [1, 2], [1, -2], [2, 4], [2, -4], [-1, 2], [-1, -2]]) == 18\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9]]) == 40\n assert candidate(points = [[0, 0], [10, 0], [20, 0], [0, 10], [10, 10], [20, 10], [0, 20], [10, 20], [20, 20]]) == 88\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]) == 18\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2]]) == 164\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [1, 1], [1, -1]]) == 20\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [1, 1]]) == 20\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [0, 1], [2, 2], [2, 0], [0, 2]]) == 42\n assert candidate(points = [[-1000, -1000], [-1000, -999], [-999, -1000], [-999, -999], [-1001, -1001], [-1001, -1000], [-1000, -1001]]) == 38\n assert candidate(points = [[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [0, 1], [0.5, 0.5], [1.5, 0.5], [1.5, 1.5], [0.5, 1.5]]) == 60\n assert candidate(points = [[-5, 5], [-3, -3], [-1, 1], [-2, -2], [0, 0], [2, 2], [3, 3], [5, -5], [4, 4]]) == 32\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, 1], [0, -1]]) == 20\n assert candidate(points = [[10, 10], [10, 20], [20, 20], [20, 10], [10, 15]]) == 12\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [1, 0], [0, 1], [2, 0], [0, 2]]) == 42\n assert candidate(points = [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], [-1, 1], [0, 1], [1, 1], [-1, 2], [0, 2], [1, 2]]) == 164\n assert candidate(points = [[-1, 0], [0, 1], [1, -1], [-2, 0], [0, 2], [2, -2], [-3, 0], [0, 3], [3, -3], [-4, 0]]) == 32\n assert candidate(points = [[-10000, -10000], [-9999, -9999], [-9998, -9998], [-9997, -9997], [-9996, -9996]]) == 8\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [0, 1], [1, 1], [2, 1], [0, 2], [1, 2], [2, 2]]) == 88\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1]]) == 6\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2]]) == 24\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 1], [2, 2]]) == 12\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12]]) == 12\n assert candidate(points = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2], [2, 1], [1, 2], [2, 2], [3, 3]]) == 104\n assert candidate(points = [[100, 100], [101, 100], [100, 101], [101, 101], [102, 102], [102, 101], [101, 102]]) == 38\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [1, 1], [1, 3], [3, 1], [3, 3], [2, 3], [3, 2]]) == 92\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == 12\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 24\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [0, 0]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12]]) == 60\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [1, 2], [2, 1]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2], [1, 2]]) == 38\n assert candidate(points = [[100, 100], [101, 100], [100, 101], [101, 101], [100, 99], [101, 99], [99, 100], [99, 101], [99, 99]]) == 88\n assert candidate(points = [[-2, -2], [-1, -1], [0, 0], [1, 1], [2, 2], [1, 0], [0, 1]]) == 26\n assert candidate(points = [[0, 0], [1, 2], [2, 1], [2, 3], [3, 2], [1, 3]]) == 18\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2], [3, 0], [3, 1], [3, 2], [4, 0]]) == 94\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, -1], [0, 1], [1, 1], [-1, -1], [1, -1], [-1, 1]]) == 88\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1], [1, 1], [-1, -1]]) == 38\n assert candidate(points = [[-5, -5], [-5, 0], [0, -5], [0, 0], [2, 2], [3, 3], [4, 4]]) == 18\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]) == 60\n", "comparison": "exact"}, "public_tests": ["[[0,0],[1,0],[2,0]]", "[[1,1],[2,2],[3,3]]", "[[1,1]]"], "hints": [], "metadata": {"canonical_parameter_names": ["points"], "leetcode_dataset_entry_point": "Solution().numberOfBoomerangs", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:33+00:00", "tests_total": 105, "tests_dropped": 3, "flags": [], "topic_tags": ["array", "hash-table", "math"]}, "language": "cpp", "interface": {"raw_signature": "int numberOfBoomerangs(vector>& points) {", "container": "Solution", "callable": "numberOfBoomerangs", "parameters": [{"name": "points", "type": "vector>&"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 447, "task_id": "number-of-boomerangs", "difficulty": "Medium", "problem_description": "You are given n points in the plane that are all distinct, where points[i] = [x_i, y_i]. A boomerang is a tuple of points (i, j, k) such that the distance between i and j equals the distance between i and k (the order of the tuple matters).\n\nReturn the number of boomerangs.\n\nExample 1:\n\nInput: points = [[0,0],[1,0],[2,0]]\nOutput: 2\nExplanation: The two boomerangs are [[1,0],[0,0],[2,0]] and [[1,0],[2,0],[0,0]].\n\nExample 2:\n\nInput: points = [[1,1],[2,2],[3,3]]\nOutput: 2\n\nExample 3:\n\nInput: points = [[1,1]]\nOutput: 0\n\nConstraints:\n\n- n == points.length\n- 1 <= n <= 500\n- points[i].length == 2\n- -10^4 <= x_i, y_i <= 10^4\n- All the points are unique.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0]]) == 8\n assert candidate(points = [[1, 0], [0, 0], [0, 1]]) == 2\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [0, 2]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [2, 0]]) == 2\n assert candidate(points = [[0, 0], [1, 0], [-1, 0], [0, 1], [0, -1]]) == 20\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4]]) == 4\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 0]]) == 4\n assert candidate(points = [[10000, 10000], [-10000, -10000], [0, 0]]) == 2\n assert candidate(points = [[1, 1], [2, 2], [3, 3]]) == 2\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1]]) == 8\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3]]) == 4\n assert candidate(points = [[0, 0], [0, 1], [1, 0], [1, 1]]) == 8\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [2, 0]]) == 8\n assert candidate(points = [[-1, 0], [0, 0], [1, 0]]) == 2\n assert candidate(points = [[1, 1]]) == 0\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [2, 3], [3, 2], [1, 2], [2, 1]]) == 38\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 2], [2, 1], [1, 2]]) == 38\n assert candidate(points = [[-2, -2], [-1, -1], [1, 1], [2, 2], [-3, -3], [3, 3], [-4, -4], [4, 4]]) == 16\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10]]) == 8\n assert candidate(points = [[-1, 0], [0, -1], [1, 0], [0, 1], [0, 0]]) == 20\n assert candidate(points = [[-1, -1], [1, 1], [2, 2], [3, 3], [4, 4], [-1, 1], [1, -1], [-2, -2], [-3, -3], [-4, -4]]) == 48\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [2, 1]]) == 24\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 8\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4]]) == 64\n assert candidate(points = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 3], [3, 4], [4, 5]]) == 16\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [4, 0], [4, 2], [0, 4], [2, 4], [4, 4]]) == 88\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 40\n assert candidate(points = [[1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2]]) == 40\n assert candidate(points = [[5, 5], [5, 10], [10, 5], [10, 10], [7, 7], [8, 8]]) == 16\n assert candidate(points = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 24\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [1, 1], [-1, -1], [-1, 1], [1, -1]]) == 48\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 1], [1, 3], [3, 1], [2, 3], [3, 2], [2, 0], [0, 2], [3, 0], [0, 3]]) == 192\n assert candidate(points = [[-10000, -10000], [10000, 10000], [0, 0], [5000, 5000], [-5000, -5000], [2000, 2000], [-2000, -2000]]) == 10\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [0, 2], [0, 3], [0, 4]]) == 18\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [2, 0], [2, 1], [0, 1], [0, 2], [1, 2], [2, 2], [3, 2]]) == 104\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 2], [3, 3], [4, 4]]) == 104\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 18\n assert candidate(points = [[100, 100], [101, 101], [102, 102], [100, 102], [102, 100], [101, 100], [100, 101], [102, 101], [101, 102]]) == 88\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 12\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [-1, 1], [-2, 2], [-3, 3], [1, -1], [2, -2], [3, -3]]) == 78\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [1, -1], [-1, 1], [-1, -1]]) == 20\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1]]) == 20\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, -1], [0, 1]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13]]) == 72\n assert candidate(points = [[0, 0], [10000, 10000], [-10000, -10000], [10000, -10000], [-10000, 10000]]) == 20\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [1, 1]]) == 12\n assert candidate(points = [[0, 0], [0, 5], [5, 0], [5, 5], [2, 2], [3, 3], [4, 4]]) == 24\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [2, 1], [2, 2], [3, 2], [3, 3], [4, 3], [4, 4], [5, 4]]) == 40\n assert candidate(points = [[0, 0], [0, 1], [1, 0], [1, 1], [2, 2], [2, 1], [1, 2]]) == 38\n assert candidate(points = [[0, 1], [1, 0], [1, 2], [2, 1], [2, 3], [3, 2]]) == 24\n assert candidate(points = [[0, 0], [1, 2], [1, -2], [2, 4], [2, -4], [-1, 2], [-1, -2]]) == 18\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9]]) == 40\n assert candidate(points = [[0, 0], [10, 0], [20, 0], [0, 10], [10, 10], [20, 10], [0, 20], [10, 20], [20, 20]]) == 88\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]) == 18\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2]]) == 164\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [1, 1], [1, -1]]) == 20\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [1, 1]]) == 20\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [0, 1], [2, 2], [2, 0], [0, 2]]) == 42\n assert candidate(points = [[-1000, -1000], [-1000, -999], [-999, -1000], [-999, -999], [-1001, -1001], [-1001, -1000], [-1000, -1001]]) == 38\n assert candidate(points = [[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1]]) == 40\n assert candidate(points = [[-5, 5], [-3, -3], [-1, 1], [-2, -2], [0, 0], [2, 2], [3, 3], [5, -5], [4, 4]]) == 32\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, 1], [0, -1]]) == 20\n assert candidate(points = [[10, 10], [10, 20], [20, 20], [20, 10], [10, 15]]) == 12\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [1, 0], [0, 1], [2, 0], [0, 2]]) == 42\n assert candidate(points = [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], [-1, 1], [0, 1], [1, 1], [-1, 2], [0, 2], [1, 2]]) == 164\n assert candidate(points = [[-1, 0], [0, 1], [1, -1], [-2, 0], [0, 2], [2, -2], [-3, 0], [0, 3], [3, -3], [-4, 0]]) == 32\n assert candidate(points = [[-10000, -10000], [-9999, -9999], [-9998, -9998], [-9997, -9997], [-9996, -9996]]) == 8\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [0, 1], [1, 1], [2, 1], [0, 2], [1, 2], [2, 2]]) == 88\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1]]) == 6\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2]]) == 24\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 1], [2, 2]]) == 12\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12]]) == 12\n assert candidate(points = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2], [2, 1], [1, 2], [2, 2], [3, 3]]) == 104\n assert candidate(points = [[100, 100], [101, 100], [100, 101], [101, 101], [102, 102], [102, 101], [101, 102]]) == 38\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [1, 1], [1, 3], [3, 1], [3, 3], [2, 3], [3, 2]]) == 92\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == 12\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 24\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [0, 0]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12]]) == 60\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [1, 2], [2, 1]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2], [1, 2]]) == 38\n assert candidate(points = [[100, 100], [101, 100], [100, 101], [101, 101], [100, 99], [101, 99], [99, 100], [99, 101], [99, 99]]) == 88\n assert candidate(points = [[-2, -2], [-1, -1], [0, 0], [1, 1], [2, 2], [1, 0], [0, 1]]) == 26\n assert candidate(points = [[0, 0], [1, 2], [2, 1], [2, 3], [3, 2], [1, 3]]) == 18\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2], [3, 0], [3, 1], [3, 2], [4, 0]]) == 94\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, -1], [0, 1], [1, 1], [-1, -1], [1, -1], [-1, 1]]) == 88\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1], [1, 1], [-1, -1]]) == 38\n assert candidate(points = [[-5, -5], [-5, 0], [0, -5], [0, 0], [2, 2], [3, 3], [4, 4]]) == 18\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]) == 60\n", "comparison": "exact"}, "public_tests": ["[[0,0],[1,0],[2,0]]", "[[1,1],[2,2],[3,3]]", "[[1,1]]"], "hints": [], "metadata": {"canonical_parameter_names": ["points"], "leetcode_dataset_entry_point": "Solution().numberOfBoomerangs", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:33+00:00", "tests_total": 105, "tests_dropped": 4, "flags": [], "topic_tags": ["array", "hash-table", "math"]}, "language": "cpp", "interface": {"raw_signature": "int numberOfBoomerangs(vector>& points) {", "container": "Solution", "callable": "numberOfBoomerangs", "parameters": [{"name": "points", "type": "vector>&"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 448, "task_id": "find-all-numbers-disappeared-in-an-array", "difficulty": "Easy", "problem_description": "Given an array nums of n integers where nums[i] is in the range [1, n], return an array of all the integers in the range [1, n] that do not appear in nums.\n\nExample 1:\n\nInput: nums = [4,3,2,7,8,2,3,1]\nOutput: [5,6]\n\nExample 2:\n\nInput: nums = [1,1]\nOutput: [2]\n\nConstraints:\n\n- n == nums.length\n- 1 <= n <= 10^5\n- 1 <= nums[i] <= n\n\nFollow up: Could you do it without extra space and in O(n) runtime? You may assume the returned list does not count as extra space.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 4, 3, 2, 1]) == []\n assert candidate(nums = [10, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == []\n assert candidate(nums = [1, 1]) == [2]\n assert candidate(nums = [4, 3, 2, 7, 8, 2, 3, 1]) == [5, 6]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5]) == [6, 7, 8, 9]\n assert candidate(nums = [3, 3, 3, 3, 3]) == [1, 2, 4, 5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [2, 2, 2, 2]) == [1, 3, 4]\n assert candidate(nums = [1, 2, 3, 4, 5]) == []\n assert candidate(nums = [1, 2, 2, 3, 3]) == [4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 1, 1, 1, 1]) == [6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [21, 22, 23, 24, 25]\n assert candidate(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10]) == [11, 12, 13]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [1, 2, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8]) == [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == []\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2]) == [21]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == []\n assert candidate(nums = [5, 5, 5, 5, 5]) == [1, 2, 3, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 19, 18, 17, 16]) == [21, 22, 23, 24, 25]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [3, 1, 2, 5, 3, 3, 4, 6, 8, 7, 9, 10, 10]) == [11, 12, 13]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16]) == [1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]) == [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == []\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [1, 2, 3, 4, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [5, 3, 1, 2, 3, 6, 7, 4, 9, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == [41]\n assert candidate(nums = [3, 3, 3, 1, 2, 2, 2, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 1, 1, 1]) == [2, 3, 4]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 20]) == [11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1]) == [21, 22, 23, 24, 25]\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == [17, 18, 19, 20]\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 2, 4, 5]) == [6, 7, 8, 9]\n assert candidate(nums = [1, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9]) == [2, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == []\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(nums = [2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1]) == [101]\n", "comparison": "exact"}, "public_tests": ["[4,3,2,7,8,2,3,1]", "[1,1]"], "hints": ["This is a really easy problem if you decide to use additional memory. For those trying to write an initial solution using additional memory, think counters!", "However, the trick really is to not use any additional space than what is already available to use. Sometimes, multiple passes over the input array help find the solution. However, there's an interesting piece of information in this problem that makes it easy to re-use the input array itself for the solution.", "The problem specifies that the numbers in the array will be in the range [1, n] where n is the number of elements in the array. Can we use this information and modify the array in-place somehow to find what we need?"], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findDisappearedNumbers", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:35+00:00", "tests_total": 68, "tests_dropped": 13, "flags": [], "topic_tags": ["array", "hash-table"]}, "language": "cpp", "interface": {"raw_signature": "vector findDisappearedNumbers(vector& nums) {", "container": "Solution", "callable": "findDisappearedNumbers", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 451, "task_id": "sort-characters-by-frequency", "difficulty": "Medium", "problem_description": "Given a string s, sort it in decreasing order based on the frequency of the characters. The frequency of a character is the number of times it appears in the string.\n\nReturn the sorted string. If there are multiple answers, return any of them.\n\nExample 1:\n\nInput: s = \"tree\"\nOutput: \"eert\"\nExplanation: 'e' appears twice while 'r' and 't' both appear once.\nSo 'e' must appear before both 'r' and 't'. Therefore \"eetr\" is also a valid answer.\n\nExample 2:\n\nInput: s = \"cccaaa\"\nOutput: \"aaaccc\"\nExplanation: Both 'c' and 'a' appear three times, so both \"cccaaa\" and \"aaaccc\" are valid answers.\nNote that \"cacaca\" is incorrect, as the same characters must be together.\n\nExample 3:\n\nInput: s = \"Aabb\"\nOutput: \"bbAa\"\nExplanation: \"bbaA\" is also a valid answer, but \"Aabb\" is incorrect.\nNote that 'A' and 'a' are treated as two different characters.\n\nConstraints:\n\n- 1 <= s.length <= 5 * 10^5\n- s consists of uppercase and lowercase English letters and digits.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aA\") == \"aA\"\n assert candidate(s = \"2a554442f544asf\") == \"4444455522aaffs\"\n assert candidate(s = \"2a554442f544asfasss\") == \"44444ssssaaa55522ff\"\n assert candidate(s = \"zzzzZZZZ\") == \"zzzzZZZZ\"\n assert candidate(s = \"bbaaccdd\") == \"bbaaccdd\"\n assert candidate(s = \"1223334444\") == \"4444333221\"\n assert candidate(s = \"cccaaa\") == \"cccaaa\"\n assert candidate(s = \"tree\") == \"eetr\"\n assert candidate(s = \"aAaaaAaA\") == \"aaaaaAAA\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"aAaaaAaaAAaAa\") == \"aaaaaaaaAAAAA\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"aAaaaAaaAA\") == \"aaaaaaAAAA\"\n assert candidate(s = \"Aabb\") == \"bbAa\"\n assert candidate(s = \"1234567890\") == \"1234567890\"\n assert candidate(s = \"bbaacc\") == \"bbaacc\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiiiiiijjjjjjjjjkkkkkkkkkkllllllllllllmmmmmmmmmmmmm\") == \"mmmmmmmmmmmmmllllllllllllkkkkkkkkkkjjjjjjjjjiiiiiiiaaaabbbbccccddddeeeeffffgggghhhh\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzAA\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzzAA\"\n assert candidate(s = \"AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\") == \"AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\"\n assert candidate(s = \"a1b2c3d4e5f6g7h8i9j0a1b2c3d4e5f6g7h8i9j0a1b2c3d4e5f6g7h8i9j0\") == \"aaa111bbb222ccc333ddd444eee555fff666ggg777hhh888iii999jjj000\"\n assert candidate(s = \"eLeetCoDe\") == \"eeeeLtCoD\"\n assert candidate(s = \"112233445566778899001122334455\") == \"111122223333444455556677889900\"\n assert candidate(s = \"abcABC123abcABC123abcABC\") == \"aaabbbcccAAABBBCCC112233\"\n assert candidate(s = \"anagram\") == \"aaangrm\"\n assert candidate(s = \"a1b2c3d4e5f6g7h8i9j0A1B2C3D4E5F6G7H8I9J0\") == \"11223344556677889900abcdefghijABCDEFGHIJ\"\n assert candidate(s = \"frequencysorttestcase\") == \"eeeessstttrrccfqunyoa\"\n assert candidate(s = \"frequencySort\") == \"rreefquncySot\"\n assert candidate(s = \"aaaaaaaaaabbccccdddd\") == \"aaaaaaaaaaccccddddbb\"\n assert candidate(s = \"leetcode\") == \"eeeltcod\"\n assert candidate(s = \"ZzYyXxWwVvUuTtSsRrQqPpOoNnMmLlKkJjIiHhGgFfEeDdCcBbAa1234567890\") == \"ZzYyXxWwVvUuTtSsRrQqPpOoNnMmLlKkJjIiHhGgFfEeDdCcBbAa1234567890\"\n assert candidate(s = \"01233210\") == \"00112233\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzABCDEFGHIJKLMNOPQRSTUVWXYZ\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzzABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n assert candidate(s = \"111222333444555666777888999000\") == \"111222333444555666777888999000\"\n assert candidate(s = \"repeatedcharactersaretestedhere\") == \"eeeeeeeeerrrrraaaattttddcchhssp\"\n assert candidate(s = \"aaAAbbBBccCCddDDeeEEffFFggGGhhHHiiIIjjJJkkKKllLLmmMMnnNNooppQQrrSSttUUvvWWxxYYzzZZ\") == \"aaAAbbBBccCCddDDeeEEffFFggGGhhHHiiIIjjJJkkKKllLLmmMMnnNNooppQQrrSSttUUvvWWxxYYzzZZ\"\n assert candidate(s = \"1234567890abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\") == \"1234567890abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n assert candidate(s = \"mississippi\") == \"iiiissssppm\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\") == \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"Mississippi\") == \"iiiissssppM\"\n assert candidate(s = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == \"aaaaaaaaaaaaaaaaaaaaAAAAAAAAAAAAAAAAAAAA\"\n assert candidate(s = \"123456789012345678901234567890\") == \"111222333444555666777888999000\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == \"zyxwvutsrqponmlkjihgfedcba\"\n", "comparison": "exact"}, "public_tests": ["\"tree\"", "\"cccaaa\"", "\"Aabb\""], "hints": [], "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().frequencySort", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:40+00:00", "tests_total": 54, "tests_dropped": 5, "flags": ["multiple_answers"], "topic_tags": ["hash-table", "string", "sorting", "heap-priority-queue", "bucket-sort", "counting"]}, "language": "cpp", "interface": {"raw_signature": "string frequencySort(string s) {", "container": "Solution", "callable": "frequencySort", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 452, "task_id": "minimum-number-of-arrows-to-burst-balloons", "difficulty": "Medium", "problem_description": "There are some spherical balloons taped onto a flat wall that represents the XY-plane. The balloons are represented as a 2D integer array points where points[i] = [x_start, x_end] denotes a balloon whose horizontal diameter stretches between x_start and x_end. You do not know the exact y-coordinates of the balloons.\n\nArrows can be shot up directly vertically (in the positive y-direction) from different points along the x-axis. A balloon with x_start and x_end is burst by an arrow shot at x if x_start <= x <= x_end. There is no limit to the number of arrows that can be shot. A shot arrow keeps traveling up infinitely, bursting any balloons in its path.\n\nGiven the array points, return the minimum number of arrows that must be shot to burst all balloons.\n\nExample 1:\n\nInput: points = [[10,16],[2,8],[1,6],[7,12]]\nOutput: 2\nExplanation: The balloons can be burst by 2 arrows:\n- Shoot an arrow at x = 6, bursting the balloons [2,8] and [1,6].\n- Shoot an arrow at x = 11, bursting the balloons [10,16] and [7,12].\n\nExample 2:\n\nInput: points = [[1,2],[3,4],[5,6],[7,8]]\nOutput: 4\nExplanation: One arrow needs to be shot for each balloon for a total of 4 arrows.\n\nExample 3:\n\nInput: points = [[1,2],[2,3],[3,4],[4,5]]\nOutput: 2\nExplanation: The balloons can be burst by 2 arrows:\n- Shoot an arrow at x = 2, bursting the balloons [1,2] and [2,3].\n- Shoot an arrow at x = 4, bursting the balloons [3,4] and [4,5].\n\nConstraints:\n\n- 1 <= points.length <= 10^5\n- points[i].length == 2\n- -2^31 <= x_start < x_end <= 2^31 - 1\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5]]) == 2\n assert candidate(points = [[10, 16], [2, 8], [1, 6], [7, 12]]) == 2\n assert candidate(points = [[1, 100], [2, 99], [3, 98]]) == 1\n assert candidate(points = [[3, 9], [7, 12], [3, 8], [6, 8], [9, 10], [2, 9], [0, 9], [3, 9], [0, 6], [2, 8]]) == 2\n assert candidate(points = [[1, 2], [3, 4], [5, 6], [7, 8]]) == 4\n assert candidate(points = [[0, 9], [0, 5], [4, 8], [7, 8], [9, 10], [9, 12], [4, 5], [4, 9], [5, 9], [8, 10]]) == 3\n assert candidate(points = [[-2147483646, -2147483645], [2147483646, 2147483647]]) == 2\n assert candidate(points = [[-1000000000, 1000000000], [-999999999, 999999999], [-999999998, 999999998], [1, 2], [2, 3], [3, 4]]) == 2\n assert candidate(points = [[-100, 0], [-90, 10], [-80, 20], [-70, 30], [-60, 40], [-50, 50], [-40, 60], [-30, 70], [-20, 80], [-10, 90]]) == 1\n assert candidate(points = [[1, 2], [2, 5], [5, 7], [6, 10], [10, 15], [15, 20]]) == 3\n assert candidate(points = [[5, 10], [15, 20], [25, 30], [5, 15], [10, 20], [15, 25]]) == 3\n assert candidate(points = [[1, 2], [2, 5], [5, 8], [8, 10], [10, 12], [12, 15], [15, 18], [18, 20], [20, 22], [22, 25], [25, 30], [30, 35], [35, 40]]) == 7\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [1, 10]]) == 5\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [-4, 4], [-5, 5], [-6, 6], [-7, 7], [-8, 8], [-9, 9], [-10, 10]]) == 1\n assert candidate(points = [[-1000, -500], [-499, -300], [-299, -100], [-99, 0], [1, 100], [101, 200], [201, 300], [301, 400], [401, 500], [501, 600]]) == 10\n assert candidate(points = [[-10, 0], [0, 10], [5, 15], [10, 20]]) == 2\n assert candidate(points = [[1, 10], [11, 20], [21, 30], [31, 40], [41, 50], [51, 60], [61, 70], [71, 80], [81, 90], [91, 100]]) == 10\n assert candidate(points = [[-2147483648, 2147483647], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 4\n assert candidate(points = [[1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == 2\n assert candidate(points = [[1, 5], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 4\n assert candidate(points = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12]]) == 4\n assert candidate(points = [[1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [21, 25], [25, 29], [29, 33], [33, 37]]) == 5\n assert candidate(points = [[-10, 15], [-5, 20], [0, 25], [5, 30], [10, 35], [15, 40], [20, 45], [25, 50]]) == 2\n assert candidate(points = [[-100, -50], [-50, 0], [0, 50], [50, 100], [25, 75]]) == 2\n assert candidate(points = [[-100, -90], [-90, -80], [-80, -70], [-70, -60], [-60, -50], [-50, -40], [-40, -30], [-30, -20], [-20, -10]]) == 5\n assert candidate(points = [[-100, -50], [-75, -25], [-50, 0], [-25, 25], [0, 50], [25, 75], [50, 100], [-100, 0], [0, 100]]) == 3\n assert candidate(points = [[-100, -90], [-80, -70], [-60, -50], [-40, -30], [-20, -10], [0, 10], [20, 30], [40, 50], [60, 70], [80, 90], [100, 110]]) == 11\n assert candidate(points = [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) == 1\n assert candidate(points = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [1, 100]]) == 5\n assert candidate(points = [[-10, -8], [-7, -5], [-3, -1], [0, 2], [3, 5], [6, 8], [9, 11], [12, 14]]) == 8\n assert candidate(points = [[-5, -3], [-4, -2], [-3, -1], [-2, 0], [-1, 1], [0, 2], [1, 3], [2, 4], [3, 5]]) == 3\n assert candidate(points = [[-1000, 1000], [500, 1500], [-1500, -500], [0, 500], [500, 1000]]) == 2\n assert candidate(points = [[1, 1000], [2, 999], [3, 998], [4, 997], [5, 996], [6, 995], [7, 994], [8, 993], [9, 992], [10, 991], [11, 990], [12, 989], [13, 988], [14, 987]]) == 1\n assert candidate(points = [[-5, -3], [-4, -2], [-1, 1], [0, 2], [1, 3], [2, 4]]) == 3\n assert candidate(points = [[1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == 2\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15]]) == 7\n assert candidate(points = [[-1, 1], [-1, 2], [0, 2], [1, 3], [0, 3], [-1, 3]]) == 1\n assert candidate(points = [[1, 5], [2, 8], [3, 9], [4, 10], [5, 11], [6, 12], [7, 13], [8, 14], [9, 15]]) == 2\n assert candidate(points = [[-10, 5], [0, 10], [5, 15], [10, 20], [15, 25], [20, 30], [25, 35]]) == 3\n assert candidate(points = [[-5, 5], [0, 10], [-10, 0], [5, 15], [-15, -5], [10, 20], [-20, -10], [15, 25], [-25, -15], [20, 30]]) == 4\n assert candidate(points = [[-2147483648, 2147483647], [-2147483647, 2147483646], [-2147483646, 2147483645], [-2147483645, 2147483644], [-2147483644, 2147483643]]) == 1\n assert candidate(points = [[-10, -1], [0, 1], [2, 3], [5, 7], [10, 12], [15, 17], [20, 22], [25, 27], [30, 32]]) == 9\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 3\n assert candidate(points = [[1, 5], [2, 8], [3, 10], [4, 12], [5, 14], [6, 16]]) == 2\n assert candidate(points = [[1, 100], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == 5\n assert candidate(points = [[1, 5], [2, 3], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12], [11, 13]]) == 4\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 5\n assert candidate(points = [[1, 20], [2, 19], [3, 18], [4, 17], [5, 16], [6, 15], [7, 14], [8, 13], [9, 12], [10, 11]]) == 1\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16]]) == 8\n assert candidate(points = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == 5\n assert candidate(points = [[-1000000, 1000000], [0, 1000000], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 4\n assert candidate(points = [[1, 50], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [1, 3], [3, 5], [5, 7], [7, 9], [2, 4], [4, 6], [6, 8], [8, 10]]) == 5\n assert candidate(points = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == 10\n assert candidate(points = [[100, 150], [120, 200], [130, 180], [160, 210], [170, 220], [180, 230]]) == 2\n assert candidate(points = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400], [350, 450], [400, 500], [450, 550], [500, 600]]) == 3\n assert candidate(points = [[-2, -1], [-1, 0], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [1, 3], [3, 4], [4, 5], [1, 5], [5, 6], [6, 7], [1, 7], [7, 8]]) == 4\n assert candidate(points = [[10, 16], [2, 8], [1, 6], [7, 12], [3, 11], [14, 17], [9, 13], [6, 10]]) == 3\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [-4, 4], [-5, 5], [-6, 6], [-7, 7], [-8, 8], [-9, 9], [-10, 10]]) == 1\n assert candidate(points = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11]]) == 1\n assert candidate(points = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10]]) == 1\n assert candidate(points = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10]]) == 3\n assert candidate(points = [[1, 10], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [11, 12], [12, 13], [13, 14]]) == 6\n assert candidate(points = [[0, 9], [2, 8], [3, 7], [6, 10], [1, 5], [4, 6], [7, 11], [8, 12], [9, 13], [10, 14]]) == 2\n assert candidate(points = [[1, 2], [2, 5], [5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45]]) == 5\n assert candidate(points = [[1, 5], [5, 10], [10, 15], [15, 20], [20, 25]]) == 3\n assert candidate(points = [[-5, -1], [0, 5], [10, 15], [1, 9]]) == 3\n assert candidate(points = [[-10, -5], [-5, 0], [0, 5], [5, 10], [10, 15], [15, 20], [20, 25]]) == 4\n assert candidate(points = [[1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5]]) == 1\n assert candidate(points = [[1, 2], [3, 5], [4, 8], [5, 10], [6, 12], [7, 15], [8, 20]]) == 3\n assert candidate(points = [[-10, -1], [1, 2], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17]]) == 9\n assert candidate(points = [[-2147483646, -2147483645], [-2147483645, -2147483644], [-2147483644, -2147483643]]) == 2\n assert candidate(points = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 4\n assert candidate(points = [[1000, 2000], [1500, 2500], [2000, 3000], [2500, 3500], [3000, 4000], [3500, 4500], [4000, 5000]]) == 3\n assert candidate(points = [[-10, 0], [-5, 5], [0, 10], [5, 15], [10, 20]]) == 2\n assert candidate(points = [[1, 1000], [2, 999], [3, 998], [4, 997], [5, 996], [6, 995], [7, 994], [8, 993], [9, 992], [10, 991]]) == 1\n assert candidate(points = [[1, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [100, 110]]) == 5\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [11, 20], [12, 19], [13, 18], [14, 17], [15, 16]]) == 2\n assert candidate(points = [[5, 10], [15, 20], [10, 15], [25, 30], [18, 25]]) == 3\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15]]) == 7\n assert candidate(points = [[10, 20], [15, 25], [20, 30], [25, 35], [30, 40], [35, 45], [40, 50], [45, 55], [50, 60]]) == 3\n assert candidate(points = [[1, 10], [5, 15], [10, 20], [15, 25], [20, 30]]) == 2\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60]]) == 4\n assert candidate(points = [[1, 10], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80]]) == 4\n assert candidate(points = [[1, 2], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21]]) == 10\n assert candidate(points = [[1, 1000000], [2, 999999], [3, 999998], [4, 999997], [5, 999996], [6, 999995], [7, 999994], [8, 999993], [9, 999992], [10, 999991]]) == 1\n", "comparison": "exact"}, "public_tests": ["[[10,16],[2,8],[1,6],[7,12]]", "[[1,2],[3,4],[5,6],[7,8]]", "[[1,2],[2,3],[3,4],[4,5]]"], "hints": [], "metadata": {"canonical_parameter_names": ["points"], "leetcode_dataset_entry_point": "Solution().findMinArrowShots", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:49:42+00:00", "tests_total": 110, "tests_dropped": 21, "flags": [], "topic_tags": ["array", "greedy", "sorting"]}, "language": "cpp", "interface": {"raw_signature": "int findMinArrowShots(vector>& points) {", "container": "Solution", "callable": "findMinArrowShots", "parameters": [{"name": "points", "type": "vector>&"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} @@ -339,7 +339,7 @@ {"question_id": 649, "task_id": "dota2-senate", "difficulty": "Medium", "problem_description": "In the world of Dota2, there are two parties: the Radiant and the Dire.\n\nThe Dota2 senate consists of senators coming from two parties. Now the Senate wants to decide on a change in the Dota2 game. The voting for this change is a round-based procedure. In each round, each senator can exercise one of the two rights:\n\n- Ban one senator's right: A senator can make another senator lose all his rights in this and all the following rounds.\n- Announce the victory: If this senator found the senators who still have rights to vote are all from the same party, he can announce the victory and decide on the change in the game.\n\nGiven a string senate representing each senator's party belonging. The character 'R' and 'D' represent the Radiant party and the Dire party. Then if there are n senators, the size of the given string will be n.\n\nThe round-based procedure starts from the first senator to the last senator in the given order. This procedure will last until the end of voting. All the senators who have lost their rights will be skipped during the procedure.\n\nSuppose every senator is smart enough and will play the best strategy for his own party. Predict which party will finally announce the victory and change the Dota2 game. The output should be \"Radiant\" or \"Dire\".\n\nExample 1:\n\nInput: senate = \"RD\"\nOutput: \"Radiant\"\nExplanation:\nThe first senator comes from Radiant and he can just ban the next senator's right in round 1.\nAnd the second senator can't exercise any rights anymore since his right has been banned.\nAnd in round 2, the first senator can just announce the victory since he is the only guy in the senate who can vote.\n\nExample 2:\n\nInput: senate = \"RDD\"\nOutput: \"Dire\"\nExplanation:\nThe first senator comes from Radiant and he can just ban the next senator's right in round 1.\nAnd the second senator can't exercise any rights anymore since his right has been banned.\nAnd the third senator comes from Dire and he can ban the first senator's right in round 1.\nAnd in round 2, the third senator can just announce the victory since he is the only guy in the senate who can vote.\n\nConstraints:\n\n- n == senate.length\n- 1 <= n <= 10^4\n- senate[i] is either 'R' or 'D'.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(senate = \"RDDRDR\") == \"Dire\"\n assert candidate(senate = \"RDD\") == \"Dire\"\n assert candidate(senate = \"DRDR\") == \"Dire\"\n assert candidate(senate = \"RDDRRD\") == \"Radiant\"\n assert candidate(senate = \"RDRDRDRDRDRDRD\") == \"Radiant\"\n assert candidate(senate = \"RD\") == \"Radiant\"\n assert candidate(senate = \"DRDRDR\") == \"Dire\"\n assert candidate(senate = \"RRRDDD\") == \"Radiant\"\n assert candidate(senate = \"DDDD\") == \"Dire\"\n assert candidate(senate = \"RRDDRR\") == \"Radiant\"\n assert candidate(senate = \"DDDDRRRRRDDDDRRRR\") == \"Dire\"\n assert candidate(senate = \"RRDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDRRRR\") == \"Dire\"\n assert candidate(senate = \"RDRDRD\") == \"Radiant\"\n assert candidate(senate = \"DDRRR\") == \"Dire\"\n assert candidate(senate = \"DDDRRR\") == \"Dire\"\n assert candidate(senate = \"DDDDDDRRRRRR\") == \"Dire\"\n assert candidate(senate = \"RRDD\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDDRRDDRR\") == \"Radiant\"\n assert candidate(senate = \"RRDDD\") == \"Radiant\"\n assert candidate(senate = \"DRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"DRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"DDRR\") == \"Dire\"\n assert candidate(senate = \"DDRDRR\") == \"Dire\"\n assert candidate(senate = \"RRRRDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRR\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRRDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RDRD\") == \"Radiant\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRD\") == \"Dire\"\n assert candidate(senate = \"RRDDDRRRRDDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RDRRDDRRDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"DDDDDRRRRRRDDDDRRRRRRRRDDDRRR\") == \"Radiant\"\n assert candidate(senate = \"RDDDRDRDRRDDRR\") == \"Dire\"\n assert candidate(senate = \"DDDDDDDDRRRRRDDD\") == \"Dire\"\n assert candidate(senate = \"RRDDRRDDRRDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRRRRRDDDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RDRDRDRDRDRDRDRD\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDRRDDDRRDDDRRDDRRRRRR\") == \"Radiant\"\n assert candidate(senate = \"DDDRRDDDRRRDDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDDDRRRRRR\") == \"Dire\"\n assert candidate(senate = \"RDRRDDDRRDDDRRDDDRDD\") == \"Dire\"\n assert candidate(senate = \"RRDDDDRRRRDDDDRR\") == \"Radiant\"\n assert candidate(senate = \"DRRDDDDDDRRRRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRRRRRRRDDDDDDDDDDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRDRRDDDRRDDDRRDDDRRDDDRRDDDR\") == \"Radiant\"\n assert candidate(senate = \"RDDDRRDDDRRDDDRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRDDDDRRRDDDDRRRDDDDRRRDDDD\") == \"Dire\"\n assert candidate(senate = \"DDRDRDRDRDRDRDRDRDRD\") == \"Dire\"\n assert candidate(senate = \"RRDDDDDDRRRRRRDDDDDDRRRRRRDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRRDDDDDDRRRRRRDDDDDDRRRRRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRDDDDDRDDRRDDDR\") == \"Dire\"\n assert candidate(senate = \"DDDDDDRRRRRRRRRR\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDRRDDDRRDDDRRDDRR\") == \"Radiant\"\n assert candidate(senate = \"RRDDDDDDRRRDDDRRRRDD\") == \"Dire\"\n assert candidate(senate = \"RDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRD\") == \"Radiant\"\n assert candidate(senate = \"DDDDRRRRRDRRDDDD\") == \"Dire\"\n assert candidate(senate = \"RDDDRRRRDDDDRRRR\") == \"Radiant\"\n assert candidate(senate = \"RRDRRDDDRRDDDRDD\") == \"Radiant\"\n assert candidate(senate = \"DDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDDRDD\") == \"Dire\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"RRRRRRRDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"RRRDDDDRRRRRDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDRRDDDRRDDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRRRDDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"DRRDDDRRDDDRRDDDRRDDDDDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDDRRRRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRRRRRDDDDDDDDDDDDDDDDDDDD\") == \"Dire\"\n assert candidate(senate = \"RRDDDDRRRRRDDDDRRRR\") == \"Radiant\"\n assert candidate(senate = \"DDDDDDRRRRRRRRRRRRRR\") == \"Radiant\"\n assert candidate(senate = \"DDDDRRRRDDRRRDDRRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRRDDDDDDRRRRRDDDDDDRRRRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRDDRRRDRDDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRDDDDRRDDDDRRDDDDRRDDDDRRDDDD\") == \"Dire\"\n assert candidate(senate = \"RRDDDRRDDDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RDDRRRDDDDRRRDDDDRRRDD\") == \"Dire\"\n assert candidate(senate = \"DRRDDDRRDDDRRDDDRRDDDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDRRRDDDDRRRDDDDRRRDDDDRRRDD\") == \"Dire\"\n assert candidate(senate = \"RRDRDRDRDRDRDRDRDRDR\") == \"Radiant\"\n assert candidate(senate = \"RRDDRRDDRRDDRRDDRRDDRRDDRRDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDRRDDDRRDDDRRDDRRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DDRRDDRRDDRRDDRRDDRRDDRRDDRRDDRRDDRRDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDRRRDDDRRRDD\") == \"Dire\"\n assert candidate(senate = \"DRRRRRDDDDDDD\") == \"Dire\"\n assert candidate(senate = \"RDRDRDRDRDRDRDRDRDRDRDRDRDRDRD\") == \"Radiant\"\n assert candidate(senate = \"DDDDDDRRRRRRDDDDDDRRRRRRDDDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRDDDDRRRDDRRRRRR\") == \"Radiant\"\n assert candidate(senate = \"DDRRDDRRDDRRDDRRDDRRDDRRDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DRDDRRDDRRDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RDDDRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRRRDRDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"DDDRRRDDRRRDD\") == \"Dire\"\n assert candidate(senate = \"DDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRD\") == \"Dire\"\n assert candidate(senate = \"RRRRDDDDDDDDRRRRRRDDDD\") == \"Dire\"\n assert candidate(senate = \"DDRDRDRDRDRDRDRDRDRDRDRDRDRD\") == \"Dire\"\n assert candidate(senate = \"DRRDDDRRDDDRRDDDRRDDRRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDDDDDRRRRRRRRRR\") == \"Dire\"\n assert candidate(senate = \"DRDDRRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"RRRRDDDDDDDDRRRR\") == \"Radiant\"\n assert candidate(senate = \"DDDDRRRRDDD\") == \"Dire\"\n assert candidate(senate = \"DDRRRRRRRRDD\") == \"Radiant\"\n assert candidate(senate = \"DDDDRRRRRRRRRRRRRDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDRDDRRRDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRDDDDDDDDDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDDDRRRRDDDD\") == \"Radiant\"\n assert candidate(senate = \"DDDDRRRRRR\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRDDDDRRDDRRDDRRDDRRDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRRRRRRRRDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"DRRDDDRRDDDRRDDDRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRDDDDRRRDDDDRRRDDDDRRRDDDDRRRDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDDDRRRRRRRRDDDDDDDDRRRRRRRR\") == \"Dire\"\n assert candidate(senate = \"DDRRRRDDDDRRRRDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDRRDDDRRDDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRDRRDDRRRDDRRDR\") == \"Radiant\"\n assert candidate(senate = \"RRRRRDDDDDRRRRDDDDDRRRRDDDDD\") == \"Radiant\"\n assert candidate(senate = \"DRRRRDDDDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDDDDDDDDDRRRRRRRRRRRRRR\") == \"Dire\"\n assert candidate(senate = \"RRRRRRRDDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRDRRDDDRRDRRDDDRRDRRDDDRRD\") == \"Radiant\"\n assert candidate(senate = \"DRRDDDRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"RDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDR\") == \"Radiant\"\n assert candidate(senate = \"RRRDDDDRRRDDDDRRRDDDDRRRDDDDRR\") == \"Dire\"\n assert candidate(senate = \"RDRDRDRDRDRDRDRDRDRD\") == \"Radiant\"\n assert candidate(senate = \"RRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDR\") == \"Radiant\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"RRRDRDDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDRDRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"DDDDDDRRRRDDDDDDRRRRDDDDDDRRRR\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDDDDRRRRRDDDDDDRRRRRDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRDDDDRRRRDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRRRRRRRRRRRRDDDDDDDDDDDDDDDDDRRRRRRRRRRRRRRRRDDDDDDDDDDDDDDDDDRRRRRRRRRRRRRRRRDDDDDDDDDDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRDDRRDDRRDDRRDDRRDDRRDD\") == \"Radiant\"\n assert candidate(senate = \"RRDRDRDRDRDRDR\") == \"Radiant\"\n assert candidate(senate = \"DRDDDRRDDDRRDDDRRDDDRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDRRRRRRDDDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDRRRRRRDDRRRRR\") == \"Dire\"\n assert candidate(senate = \"DDDRRRDDDDRRRRRDDDDDDRRRRRDDDDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDRRRRDDDDRRRRDDDDRRRRDDDDRRRRDDDDRRRR\") == \"Dire\"\n assert candidate(senate = \"RRDDRRDDRRDDRRDDRRDDRRDDRRDDRR\") == \"Radiant\"\n assert candidate(senate = \"DRRDDDRRDDDRRDDDRRDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDDDRRRRDDDDRRRRRDDDDDRR\") == \"Radiant\"\n assert candidate(senate = \"RRRRRDDDDDDDDDRRRRDDDDDDDDDRRRRDDDDDDDDDRRRRDDDDDDDDDRRRRDDDDDD\") == \"Dire\"\n assert candidate(senate = \"DDDDDDDDDDRRRRRRR\") == \"Dire\"\n assert candidate(senate = \"DDDDRRRRDDDDRRRR\") == \"Dire\"\n assert candidate(senate = \"DDDDRRDDDDRRDDDDRRDDDDRRDDDDRR\") == \"Dire\"\n assert candidate(senate = \"RRRRRDDDDDDDDDRRRDDDRRDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRRDDDDRRRRDDDDRRRRDDDDRRRRDDDDRRRRDDDD\") == \"Radiant\"\n assert candidate(senate = \"RRRRRRRRRRRRRDDDDDDDDDDDDDRRRRRRRRRRRRDDDDDDDDDDDDDRRRRRRRRRRRRDDDDDDDDD\") == \"Radiant\"\n assert candidate(senate = \"DDDDDDDDRRRRRRRR\") == \"Dire\"\n assert candidate(senate = \"DDRRRDDDDRRRRDDDRRR\") == \"Dire\"\n assert candidate(senate = \"DDRRDDRRDDRRDDRR\") == \"Dire\"\n assert candidate(senate = \"RRDDDRRDDDRRDDDRRDDDRRDDDRRDDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DDDDRRDDRRDDRRDDRRDD\") == \"Dire\"\n assert candidate(senate = \"DRDDRRDDRRDDRRDR\") == \"Dire\"\n assert candidate(senate = \"DRDRDRDRDRDRDRDR\") == \"Dire\"\n assert candidate(senate = \"RRRDDDDDRRRRDDDDDRRRRDDDDDRRRRDDDDDRRRRDDDD\") == \"Dire\"\n assert candidate(senate = \"RRRDDDDRRRDDDDRR\") == \"Radiant\"\n assert candidate(senate = \"RDDDRDDDRDDDRDDD\") == \"Dire\"\n assert candidate(senate = \"RRDRDRDRDRDRDRDRDRDRDRDRDRDR\") == \"Radiant\"\n assert candidate(senate = \"DDRRDDRRDDRRDDRRDDRRDDRRDDRRDDRR\") == \"Dire\"\n assert candidate(senate = \"DDRDRDRDRDRDRDRD\") == \"Dire\"\n assert candidate(senate = \"DDRDDDRRDDDRRDDDRRDDDRRDDDRRDDDR\") == \"Dire\"\n assert candidate(senate = \"RRRDDDRRDDDRRDDDRRDDRRRR\") == \"Radiant\"\n assert candidate(senate = \"RRRRRDDDDRRRDDDDRRRDDDDRRRDD\") == \"Radiant\"\n", "comparison": "exact"}, "public_tests": ["\"RD\"", "\"RDD\""], "hints": [], "metadata": {"canonical_parameter_names": ["senate"], "leetcode_dataset_entry_point": "Solution().predictPartyVictory", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:14+00:00", "tests_total": 177, "tests_dropped": 11, "flags": [], "topic_tags": ["string", "greedy", "queue"]}, "language": "cpp", "interface": {"raw_signature": "string predictPartyVictory(string senate) {", "container": "Solution", "callable": "predictPartyVictory", "parameters": [{"name": "senate", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 650, "task_id": "2-keys-keyboard", "difficulty": "Medium", "problem_description": "There is only one character 'A' on the screen of a notepad. You can perform one of two operations on this notepad for each step:\n\n- Copy All: You can copy all the characters present on the screen (a partial copy is not allowed).\n- Paste: You can paste the characters which are copied last time.\n\nGiven an integer n, return the minimum number of operations to get the character 'A' exactly n times on the screen.\n\nExample 1:\n\nInput: n = 3\nOutput: 3\nExplanation: Initially, we have one character 'A'.\nIn step 1, we use Copy All operation.\nIn step 2, we use Paste operation to get 'AA'.\nIn step 3, we use Paste operation to get 'AAA'.\n\nExample 2:\n\nInput: n = 1\nOutput: 0\n\nConstraints:\n\n- 1 <= n <= 1000\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == 3\n assert candidate(n = 12) == 7\n assert candidate(n = 100) == 14\n assert candidate(n = 10) == 7\n assert candidate(n = 1000) == 21\n assert candidate(n = 5) == 5\n assert candidate(n = 4) == 4\n assert candidate(n = 16) == 8\n assert candidate(n = 17) == 17\n assert candidate(n = 2) == 2\n assert candidate(n = 8) == 6\n assert candidate(n = 27) == 9\n assert candidate(n = 18) == 8\n assert candidate(n = 20) == 9\n assert candidate(n = 19) == 19\n assert candidate(n = 11) == 11\n assert candidate(n = 15) == 8\n assert candidate(n = 14) == 9\n assert candidate(n = 9) == 6\n assert candidate(n = 6) == 5\n assert candidate(n = 1) == 0\n assert candidate(n = 7) == 7\n assert candidate(n = 13) == 13\n assert candidate(n = 625) == 20\n assert candidate(n = 97) == 97\n assert candidate(n = 729) == 18\n assert candidate(n = 144) == 14\n assert candidate(n = 49) == 14\n assert candidate(n = 125) == 15\n assert candidate(n = 300) == 17\n assert candidate(n = 841) == 58\n assert candidate(n = 60) == 12\n assert candidate(n = 30) == 10\n assert candidate(n = 600) == 19\n assert candidate(n = 64) == 12\n assert candidate(n = 72) == 12\n assert candidate(n = 99) == 17\n assert candidate(n = 343) == 21\n assert candidate(n = 225) == 16\n assert candidate(n = 819) == 26\n assert candidate(n = 128) == 14\n assert candidate(n = 999) == 46\n assert candidate(n = 96) == 13\n assert candidate(n = 256) == 16\n assert candidate(n = 997) == 997\n assert candidate(n = 36) == 10\n assert candidate(n = 529) == 46\n assert candidate(n = 91) == 20\n assert candidate(n = 77) == 18\n assert candidate(n = 81) == 12\n assert candidate(n = 48) == 11\n assert candidate(n = 961) == 62\n assert candidate(n = 200) == 16\n assert candidate(n = 400) == 18\n assert candidate(n = 512) == 18\n assert candidate(n = 196) == 18\n assert candidate(n = 750) == 20\n assert candidate(n = 121) == 22\n assert candidate(n = 361) == 38\n assert candidate(n = 441) == 20\n assert candidate(n = 500) == 19\n assert candidate(n = 55) == 16\n assert candidate(n = 25) == 10\n", "comparison": "exact"}, "public_tests": ["3", "1"], "hints": ["How many characters may be there in the clipboard at the last step if n = 3? n = 7? n = 10? n = 24?"], "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().minSteps", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:17+00:00", "tests_total": 65, "tests_dropped": 2, "flags": [], "topic_tags": ["math", "dynamic-programming"]}, "language": "cpp", "interface": {"raw_signature": "int minSteps(int n) {", "container": "Solution", "callable": "minSteps", "parameters": [{"name": "n", "type": "int"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 657, "task_id": "robot-return-to-origin", "difficulty": "Easy", "problem_description": "There is a robot starting at the position (0, 0), the origin, on a 2D plane. Given a sequence of its moves, judge if this robot ends up at (0, 0) after it completes its moves.\n\nYou are given a string moves that represents the move sequence of the robot where moves[i] represents its i^th move. Valid moves are 'R' (right), 'L' (left), 'U' (up), and 'D' (down).\n\nReturn true if the robot returns to the origin after it finishes all of its moves, or false otherwise.\n\nNote: The way that the robot is \"facing\" is irrelevant. 'R' will always make the robot move to the right once, 'L' will always make it move left, etc. Also, assume that the magnitude of the robot's movement is the same for each move.\n\nExample 1:\n\nInput: moves = \"UD\"\nOutput: true\nExplanation: The robot moves up once, and then down once. All moves have the same magnitude, so it ended up at the origin where it started. Therefore, we return true.\n\nExample 2:\n\nInput: moves = \"LL\"\nOutput: false\nExplanation: The robot moves left twice. It ends up two \"moves\" to the left of the origin. We return false because it is not at the origin at the end of its moves.\n\nConstraints:\n\n- 1 <= moves.length <= 2 * 10^4\n- moves only contains the characters 'U', 'D', 'L' and 'R'.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(moves = \"LULLDDRRUURRDDLL\") == False\n assert candidate(moves = \"UUUUUUUUUUDDDDDDDDDDLLLLRRRR\") == True\n assert candidate(moves = \"UDLR\") == True\n assert candidate(moves = \"UUDDRRLL\") == True\n assert candidate(moves = \"LUDD\") == False\n assert candidate(moves = \"RLUD\") == True\n assert candidate(moves = \"RRDDLLUURR\") == False\n assert candidate(moves = \"LRLRLRLR\") == True\n assert candidate(moves = \"ULDRULDRULDR\") == True\n assert candidate(moves = \"LDRU\") == True\n assert candidate(moves = \"UDLRUDLRUDLR\") == True\n assert candidate(moves = \"UUUUUUUUUUUUUUDDDDDDDDDDDDDDLLLLLLLLRRRRRRRRRRRR\") == False\n assert candidate(moves = \"LDRRLU\") == True\n assert candidate(moves = \"UUDDLLRR\") == True\n assert candidate(moves = \"RLUDRLUD\") == True\n assert candidate(moves = \"LLLLRRRR\") == True\n assert candidate(moves = \"RULD\") == True\n assert candidate(moves = \"UUUUUUUUUUDDDDDDDDDDLLLLLLLLRRRRRRRR\") == True\n assert candidate(moves = \"UDUDUDUD\") == True\n assert candidate(moves = \"UUUUUUUUUUUUUUUUDDDDDDDDDDDDDDDDLLLLLLLLLLLLRRRRRRRRRRRRRR\") == False\n assert candidate(moves = \"RRDDLLUU\") == True\n assert candidate(moves = \"LL\") == False\n assert candidate(moves = \"UUUUDDDDLLLLRRRR\") == True\n assert candidate(moves = \"LRUD\") == True\n assert candidate(moves = \"UUDDLLRRUUDDLLRR\") == True\n assert candidate(moves = \"UUUUDDDD\") == True\n assert candidate(moves = \"RRDD\") == False\n assert candidate(moves = \"UUUUUUUUUUUUDDDDDDDDDDDDLLLLRRRRRRRRRRRR\") == False\n assert candidate(moves = \"RRRLLLDDDUUU\") == True\n assert candidate(moves = \"UD\") == True\n assert candidate(moves = \"UUUUUUUUUUUUUUUUUUDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRR\") == True\n assert candidate(moves = \"UDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLR\") == True\n assert candidate(moves = \"LDDRUURLDDRUURLDDRUURLDDRUURLDDR\") == False\n assert candidate(moves = \"LLLLLRRRRRRLLLLRRRRRRLLL\") == True\n assert candidate(moves = \"UUDDDDUUUUUUUUUUDDDD\") == False\n assert candidate(moves = \"UDUDUDUDUDUDUDUDUDUDUDUDUDUD\") == True\n assert candidate(moves = \"UDUDUDUDUDUDUDUD\") == True\n assert candidate(moves = \"LLLLRRRRUUUUDDDDLRRRLLLLUUUUDDDD\") == False\n assert candidate(moves = \"RRDDLLUURRDDLLUURRDDLLUU\") == True\n assert candidate(moves = \"LRLRLRLRLRLRLRLR\") == True\n assert candidate(moves = \"LLRRLLRRLLRRLLRRLLRRLLRRLLRR\") == True\n assert candidate(moves = \"LDRULDRULDRU\") == True\n assert candidate(moves = \"LLLLRRRRLLLLRRRRLLLLRRRRLLLLRRRR\") == True\n assert candidate(moves = \"LLRRDDUULLRRDDUULLRRDDUULLRRDDUULL\") == False\n assert candidate(moves = \"RULLDDRRULLDDRRULLDDRR\") == False\n assert candidate(moves = \"LLLLUUUUUURRRRRRRRDDDDDD\") == False\n assert candidate(moves = \"RULLDRLDURDURLDLURDURLDLURDURLDL\") == False\n assert candidate(moves = \"UDLRUDLRUDLRUDLR\") == True\n assert candidate(moves = \"UUDDUUDDUUDDUUDDLLLLRRRRLLLLRRRR\") == True\n assert candidate(moves = \"RLRLRLRLRLRLRLRL\") == True\n assert candidate(moves = \"UUDDUUDDUUDDUUDDUUDDUUDD\") == True\n assert candidate(moves = \"UDLLRRUUDDLLRRUUDDLLRRUUDDLLRR\") == True\n assert candidate(moves = \"UUUDDDLLLRRR\") == True\n assert candidate(moves = \"UUUUDDDDLLLLRRRRUUUUDDDDLLLLRRRRUUUUDDDDLLLLRRRR\") == True\n assert candidate(moves = \"UUDDUUDDUUDDUUDDUUDDUUDDUUDD\") == True\n assert candidate(moves = \"UUUUDDDDLLLLRRRRUUUUDDDDLLLLRRRR\") == True\n assert candidate(moves = \"UUDDLLLLRRRRUUDDLLRR\") == True\n assert candidate(moves = \"UDUDUDUDUD\") == True\n assert candidate(moves = \"RLRLRLRLUDUDUDUD\") == True\n assert candidate(moves = \"URDLURDLURDLURDL\") == True\n assert candidate(moves = \"ULDRULDRLDURDLURDLURDLURDLURDL\") == False\n assert candidate(moves = \"RRDDLLUURRDDLLUURRDDLLUURRDDLLUU\") == True\n assert candidate(moves = \"LUDRLUDRLUDRLUDRLUDRLUDR\") == True\n assert candidate(moves = \"LRRLRLRLUDUDUDUD\") == True\n assert candidate(moves = \"UUDDUUDDUUDDUUDD\") == True\n assert candidate(moves = \"RRDDUULLRRDDUULL\") == True\n assert candidate(moves = \"LRUDLRUDLRUD\") == True\n assert candidate(moves = \"LURDLURDLURDLURD\") == True\n assert candidate(moves = \"LLLLRRRRUUDDUUDD\") == True\n assert candidate(moves = \"UDUDLRRLRLUDUDLR\") == True\n assert candidate(moves = \"LLLLLLLLRRRRRRRRUUUUUUUUDDDDDDDD\") == True\n assert candidate(moves = \"UDLRUDLRUDLRUDLRUDLRUDLR\") == True\n assert candidate(moves = \"UUDDDDUUDDDDUUDD\") == False\n assert candidate(moves = \"LLLLRRRRLLLLRRRR\") == True\n assert candidate(moves = \"ULLDRRDUULLDRRDU\") == True\n assert candidate(moves = \"UUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDD\") == True\n assert candidate(moves = \"RRRRRRRRRRLLLLLLLLLLDDDDDDDDDDUUUUUUUUUU\") == True\n assert candidate(moves = \"RLRLRLRLRL\") == True\n assert candidate(moves = \"LLLLDDDDUUUURRRR\") == True\n assert candidate(moves = \"UUDDLLRRUUDDDDLLRRUUDDLLRR\") == False\n assert candidate(moves = \"LLRRUUDDUUDDLLRR\") == True\n assert candidate(moves = \"LRRLRLRLUDUDUDUDLRRLRLRLUDUDUDUD\") == True\n assert candidate(moves = \"RLRLRLRLRLRLRLRLRLRL\") == True\n assert candidate(moves = \"UUDDUURRDD\") == False\n assert candidate(moves = \"UUDDUULLRR\") == False\n assert candidate(moves = \"RRRRDDDDLLLLUUUU\") == True\n assert candidate(moves = \"UDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLR\") == True\n assert candidate(moves = \"LLLLRRRRUUUDDDUUUDDDLLLLRRRR\") == True\n assert candidate(moves = \"UUUUUUUUDDDDDDDDLLLLLLLLRRRRRRRRRRLLRRUUDDLL\") == True\n assert candidate(moves = \"DDUUUUDDLLRRRR\") == False\n assert candidate(moves = \"UUDDLLUURRDDDDLLRR\") == False\n assert candidate(moves = \"RURURURURURURULULULULULULULU\") == False\n assert candidate(moves = \"UUUUUUDDDDDDLLLLRRRRRR\") == False\n assert candidate(moves = \"UUDDDDLLLLRRRRUUDDDD\") == False\n assert candidate(moves = \"LLLLLLLLRRRRRRRRUUUUUUUUDDDDDDDDLLLLLLLLRRRRRRRRUUUUUUUUDDDDDDDD\") == True\n assert candidate(moves = \"RRRDDDLLLUUUUUDDDD\") == False\n assert candidate(moves = \"UUUUUUUUUUDDDDDDDDDDLLLLLLLLRRRRRRRRRR\") == False\n assert candidate(moves = \"RUDLRUDLRUDLRUDL\") == True\n assert candidate(moves = \"UUDDLLRRUUDDLLRRUUDDLLRR\") == True\n assert candidate(moves = \"RUDLRULDRLUDLRULDRLUDLRULDRL\") == False\n assert candidate(moves = \"UDUDUDUDUDUDUDUDUDUDUDUD\") == True\n assert candidate(moves = \"URDLURDLURDL\") == True\n assert candidate(moves = \"UUDDDDDDDLLLLRRRRUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUDDDDDDDLLLLRRRR\") == False\n assert candidate(moves = \"RRDDLLUURRDDLLUU\") == True\n assert candidate(moves = \"UUUUUUUUDDDDDDDDLLLLRRRR\") == True\n assert candidate(moves = \"RRRLLLLDDDUUUUUDDDLLLLURRRDDDDUUU\") == False\n assert candidate(moves = \"DDDDLLLLUUUUUUUUDDDDLLLLRRRRRRRR\") == True\n assert candidate(moves = \"UDUDUDUDLRRLRLRL\") == True\n assert candidate(moves = \"LURDLURDLURDLURDLURDLURDLURDLURDL\") == False\n assert candidate(moves = \"UUUUUUUUDDDDDDDDLLLLRRRRRRRR\") == False\n assert candidate(moves = \"RRUUDDLLDDUURLLR\") == True\n assert candidate(moves = \"ULURDLDRULURDLDRULURDLDRULURDLDR\") == True\n", "comparison": "exact"}, "public_tests": ["\"UD\"", "\"LL\""], "hints": [], "metadata": {"canonical_parameter_names": ["moves"], "leetcode_dataset_entry_point": "Solution().judgeCircle", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:30+00:00", "tests_total": 112, "tests_dropped": 0, "flags": [], "topic_tags": ["string", "simulation"]}, "language": "cpp", "interface": {"raw_signature": "bool judgeCircle(string moves) {", "container": "Solution", "callable": "judgeCircle", "parameters": [{"name": "moves", "type": "string"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} -{"question_id": 658, "task_id": "find-k-closest-elements", "difficulty": "Medium", "problem_description": "Given a sorted integer array arr, two integers k and x, return the k closest integers to x in the array. The result should also be sorted in ascending order.\n\nAn integer a is closer to x than an integer b if:\n\n- |a - x| < |b - x|, or\n- |a - x| == |b - x| and a < b\n\nExample 1:\n\nInput: arr = [1,2,3,4,5], k = 4, x = 3\nOutput: [1,2,3,4]\n\nExample 2:\n\nInput: arr = [1,1,2,3,4,5], k = 4, x = -1\nOutput: [1,1,2,3]\n\nConstraints:\n\n- 1 <= k <= arr.length\n- 1 <= arr.length <= 10^4\n- arr is sorted in ascending order.\n- -10^4 <= arr[i], x <= 10^4\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(arr = [1, 3, 5, 7, 9],k = 4,x = 6) == [3, 5, 7, 9]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 2,x = 6) == [5, 7]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 1,x = 6) == [5]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 5,x = 6) == [1, 3, 5, 7, 9]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 2,x = 3) == [2, 3]\n assert candidate(arr = [1, 1, 1, 1, 1],k = 3,x = 1) == [1, 1, 1]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 5,x = 8) == [1, 3, 5, 7, 9]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 4,x = 3) == [1, 2, 3, 4]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5],k = 4,x = 2) == [1, 2, 2, 2]\n assert candidate(arr = [1, 1, 2, 3, 4, 5],k = 4,x = -1) == [1, 1, 2, 3]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 1,x = 2) == [2]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 5,x = 3) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 3,x = 6) == [3, 5, 7]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 3,x = 6) == [3, 4, 5]\n assert candidate(arr = [0, 0, 1, 2, 3, 3, 4, 7, 7, 8],k = 3,x = 5) == [3, 3, 4]\n assert candidate(arr = [1, 2, 2, 2, 3, 4, 5],k = 3,x = 2) == [2, 2, 2]\n assert candidate(arr = [1, 2, 2, 2, 5, 5, 5, 8, 9],k = 3,x = 4) == [5, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 1,x = 5) == [5]\n assert candidate(arr = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6],k = 7,x = 3) == [2, 2, 2, 3, 3, 3, 4]\n assert candidate(arr = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],k = 7,x = 13) == [6, 8, 10, 12, 14, 16, 18]\n assert candidate(arr = [1, 2, 3, 100, 101, 102],k = 3,x = 99) == [100, 101, 102]\n assert candidate(arr = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],k = 5,x = -90) == [-94, -93, -92, -91, -90]\n assert candidate(arr = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109],k = 4,x = 90) == [100, 101, 102, 103]\n assert candidate(arr = [-10, -5, -2, 0, 3, 8, 12, 16, 20],k = 5,x = -1) == [-10, -5, -2, 0, 3]\n assert candidate(arr = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 4,x = 5) == [10, 10, 10, 10]\n assert candidate(arr = [-10, -5, 0, 5, 10],k = 3,x = -6) == [-10, -5, 0]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 5) == [3, 4, 5, 6, 7]\n assert candidate(arr = [1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10],k = 9,x = 4) == [3, 3, 3, 3, 4, 4, 4, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4,x = 5) == [3, 4, 5, 6]\n assert candidate(arr = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 5,x = 6) == [4, 4, 5, 5, 5]\n assert candidate(arr = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10,x = 0) == [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 15) == [4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20,x = 10) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],k = 5,x = 10) == [5, 7, 9, 11, 13]\n assert candidate(arr = [-100, -50, -30, -20, -10, 0, 10, 20, 30, 50, 100],k = 5,x = -25) == [-50, -30, -20, -10, 0]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 4,x = 12) == [9, 11, 13, 15]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 7,x = 10) == [7, 8, 9, 10, 11, 12, 13]\n assert candidate(arr = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],k = 5,x = -99) == [-100, -99, -98, -97, -96]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 3) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],k = 5,x = 28) == [23, 25, 27, 29, 31]\n assert candidate(arr = [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10],k = 5,x = 1) == [-4, -2, 0, 2, 4]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 4,x = 10) == [7, 9, 11, 13]\n assert candidate(arr = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2],k = 5,x = 1) == [1, 1, 1, 1, 1]\n assert candidate(arr = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 7,x = 0) == [5, 5, 5, 5, 5, 5, 5]\n assert candidate(arr = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],k = 4,x = -5) == [-7, -6, -5, -4]\n assert candidate(arr = [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3],k = 6,x = 1) == [1, 1, 1, 1, 1, 2]\n assert candidate(arr = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 5,x = 0) == [1, 1, 1, 2, 2]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 6,x = 14) == [9, 11, 13, 15, 17, 19]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 10,x = 8) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10,x = 1) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 0) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 5,x = 3) == [2, 2, 3, 3, 3]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 0) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(arr = [1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 4,x = 1) == [1, 1, 1, 2]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 5) == [3, 4, 5, 6, 7]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5],k = 3,x = 5) == [3, 4, 5]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1],k = 4,x = 1) == [1, 1, 1, 1]\n assert candidate(arr = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0],k = 5,x = 0) == [-4, -3, -2, -1, 0]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4,x = 11) == [7, 8, 9, 10]\n assert candidate(arr = [1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10],k = 8,x = 5) == [3, 4, 4, 5, 5, 5, 6, 6]\n assert candidate(arr = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6],k = 15,x = 3) == [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5,x = 1) == [1, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 15) == [6, 7, 8, 9, 10]\n assert candidate(arr = [-10, -5, -3, -1, 0, 1, 3, 5, 7, 10],k = 4,x = 12) == [3, 5, 7, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 0) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 4,x = 15) == [12, 14, 16, 18]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10,x = 10) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(arr = [1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10],k = 10,x = 5) == [4, 4, 4, 4, 5, 5, 5, 5, 5, 6]\n assert candidate(arr = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7],k = 8,x = 4) == [3, 3, 3, 4, 4, 5, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 8,x = 16) == [8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 0) == [1, 2, 3]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 5) == [2, 3, 4, 5, 6, 7, 8]\n assert candidate(arr = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 10,x = 5) == [-40, -30, -20, -10, 0, 10, 20, 30, 40, 50]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 15) == [8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 11) == [6, 7, 8, 9, 10]\n assert candidate(arr = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],k = 5,x = 12) == [7, 9, 11, 13, 15]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10,x = 15) == [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 3,x = 2) == [1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4,x = 10) == [7, 8, 9, 10]\n assert candidate(arr = [1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9],k = 4,x = 4) == [3, 4, 5, 5]\n assert candidate(arr = [-10, -5, -3, -1, 0, 1, 2, 3, 5, 7],k = 3,x = -4) == [-5, -3, -1]\n assert candidate(arr = [-10, -5, -2, 0, 1, 3, 5, 8, 12],k = 3,x = -3) == [-5, -2, 0]\n assert candidate(arr = [1, 2, 3, 3, 3, 3, 4, 5, 6],k = 4,x = 3) == [3, 3, 3, 3]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5],k = 3,x = 1) == [1, 2, 2]\n assert candidate(arr = [1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8],k = 5,x = 2) == [1, 1, 1, 2, 2]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 11) == [8, 9, 10]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 5,x = 10) == [5, 7, 9, 11, 13]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5,x = 1) == [1, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 0) == [1, 2, 3]\n assert candidate(arr = [1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9],k = 6,x = 5) == [4, 5, 5, 5, 6, 6]\n assert candidate(arr = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],k = 5,x = -94) == [-96, -95, -94, -93, -92]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],k = 6,x = 10) == [5, 7, 9, 11, 13, 15]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 9],k = 5,x = 4) == [3, 3, 4, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 12) == [8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 6,x = 5.5) == [3, 4, 5, 6, 7, 8]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7,x = 10) == [7, 8, 9, 10, 11, 12, 13]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 2,x = 5) == [4, 5]\n assert candidate(arr = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 3,x = 55) == [40, 50, 60]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7,x = 7) == [4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],k = 5,x = 12) == [7, 9, 11, 13, 15]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 6,x = 5) == [2, 3, 4, 5, 6, 7]\n assert candidate(arr = [-20, -15, -10, -5, 0, 5, 10, 15, 20],k = 4,x = 0) == [-10, -5, 0, 5]\n assert candidate(arr = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6],k = 10,x = 3) == [1, 2, 2, 2, 3, 3, 3, 4, 4, 4]\n assert candidate(arr = [0, 1, 1, 1, 1, 2, 3, 4, 4, 4, 5, 5, 6, 7, 8, 9],k = 6,x = 0) == [0, 1, 1, 1, 1, 2]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 15,x = 10) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]\n assert candidate(arr = [1, 2, 3, 6, 7, 8, 9, 10],k = 3,x = 5) == [3, 6, 7]\n assert candidate(arr = [-10, -5, -2, -1, 0, 1, 2, 3, 5, 6, 7, 10, 15],k = 5,x = -3) == [-5, -2, -1, 0, 1]\n assert candidate(arr = [0, 0, 1, 1, 1, 1, 2, 2, 3, 3],k = 5,x = 1) == [0, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 11) == [4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = -2) == [1, 2, 3]\n assert candidate(arr = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24],k = 5,x = 16) == [9, 12, 15, 18, 21]\n assert candidate(arr = [-10, -5, -3, -1, 0, 1, 3, 5, 7, 10],k = 5,x = -2) == [-5, -3, -1, 0, 1]\n assert candidate(arr = [-10, -5, -1, 0, 1, 5, 10],k = 3,x = -3) == [-5, -1, 0]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5,x = 2) == [1, 1, 1, 1, 1]\n assert candidate(arr = [1, 3, 3, 3, 5, 5, 5, 7, 7, 9],k = 4,x = 6) == [5, 5, 5, 7]\n assert candidate(arr = [1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5],k = 7,x = 4) == [4, 4, 4, 4, 4, 4, 4]\n assert candidate(arr = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60],k = 5,x = 53) == [40, 45, 50, 55, 60]\n assert candidate(arr = [-5, -3, -2, -1, 0, 1, 2, 3, 4, 5],k = 6,x = -4) == [-5, -3, -2, -1, 0, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10,x = 5) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 12,x = 2) == [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10,x = 5) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 6,x = 15) == [12, 13, 14, 15, 16, 17]\n assert candidate(arr = [-10, -5, 0, 3, 9, 12],k = 3,x = -7) == [-10, -5, 0]\n assert candidate(arr = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5,x = 0) == [0, 0, 0, 0, 0]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 4,x = 10) == [7, 9, 11, 13]\n assert candidate(arr = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50],k = 6,x = 15) == [-10, 0, 10, 20, 30, 40]\n assert candidate(arr = [1, 3, 4, 5, 8, 10, 15, 20, 30, 50, 100],k = 4,x = 12) == [5, 8, 10, 15]\n assert candidate(arr = [1, 3, 3, 4, 4, 4, 4, 5, 6, 8, 9],k = 5,x = 4) == [3, 4, 4, 4, 4]\n", "comparison": "exact"}, "public_tests": ["[1,2,3,4,5]\n4\n3", "[1,1,2,3,4,5]\n4\n-1"], "hints": [], "metadata": {"canonical_parameter_names": ["arr", "k", "x"], "leetcode_dataset_entry_point": "Solution().findClosestElements", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:33+00:00", "tests_total": 129, "tests_dropped": 1, "flags": [], "topic_tags": ["array", "two-pointers", "binary-search", "sliding-window", "sorting", "heap-priority-queue"]}, "language": "cpp", "interface": {"raw_signature": "vector findClosestElements(vector& arr, int k, int x) {", "container": "Solution", "callable": "findClosestElements", "parameters": [{"name": "arr", "type": "vector&"}, {"name": "k", "type": "int"}, {"name": "x", "type": "int"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 658, "task_id": "find-k-closest-elements", "difficulty": "Medium", "problem_description": "Given a sorted integer array arr, two integers k and x, return the k closest integers to x in the array. The result should also be sorted in ascending order.\n\nAn integer a is closer to x than an integer b if:\n\n- |a - x| < |b - x|, or\n- |a - x| == |b - x| and a < b\n\nExample 1:\n\nInput: arr = [1,2,3,4,5], k = 4, x = 3\nOutput: [1,2,3,4]\n\nExample 2:\n\nInput: arr = [1,1,2,3,4,5], k = 4, x = -1\nOutput: [1,1,2,3]\n\nConstraints:\n\n- 1 <= k <= arr.length\n- 1 <= arr.length <= 10^4\n- arr is sorted in ascending order.\n- -10^4 <= arr[i], x <= 10^4\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(arr = [1, 3, 5, 7, 9],k = 4,x = 6) == [3, 5, 7, 9]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 2,x = 6) == [5, 7]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 1,x = 6) == [5]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 5,x = 6) == [1, 3, 5, 7, 9]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 2,x = 3) == [2, 3]\n assert candidate(arr = [1, 1, 1, 1, 1],k = 3,x = 1) == [1, 1, 1]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 5,x = 8) == [1, 3, 5, 7, 9]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 4,x = 3) == [1, 2, 3, 4]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5],k = 4,x = 2) == [1, 2, 2, 2]\n assert candidate(arr = [1, 1, 2, 3, 4, 5],k = 4,x = -1) == [1, 1, 2, 3]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 1,x = 2) == [2]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 5,x = 3) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 3, 5, 7, 9],k = 3,x = 6) == [3, 5, 7]\n assert candidate(arr = [1, 2, 3, 4, 5],k = 3,x = 6) == [3, 4, 5]\n assert candidate(arr = [0, 0, 1, 2, 3, 3, 4, 7, 7, 8],k = 3,x = 5) == [3, 3, 4]\n assert candidate(arr = [1, 2, 2, 2, 3, 4, 5],k = 3,x = 2) == [2, 2, 2]\n assert candidate(arr = [1, 2, 2, 2, 5, 5, 5, 8, 9],k = 3,x = 4) == [5, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 1,x = 5) == [5]\n assert candidate(arr = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6],k = 7,x = 3) == [2, 2, 2, 3, 3, 3, 4]\n assert candidate(arr = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],k = 7,x = 13) == [6, 8, 10, 12, 14, 16, 18]\n assert candidate(arr = [1, 2, 3, 100, 101, 102],k = 3,x = 99) == [100, 101, 102]\n assert candidate(arr = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],k = 5,x = -90) == [-94, -93, -92, -91, -90]\n assert candidate(arr = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109],k = 4,x = 90) == [100, 101, 102, 103]\n assert candidate(arr = [-10, -5, -2, 0, 3, 8, 12, 16, 20],k = 5,x = -1) == [-10, -5, -2, 0, 3]\n assert candidate(arr = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 4,x = 5) == [10, 10, 10, 10]\n assert candidate(arr = [-10, -5, 0, 5, 10],k = 3,x = -6) == [-10, -5, 0]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 5) == [3, 4, 5, 6, 7]\n assert candidate(arr = [1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10],k = 9,x = 4) == [3, 3, 3, 3, 4, 4, 4, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4,x = 5) == [3, 4, 5, 6]\n assert candidate(arr = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 5,x = 6) == [4, 4, 5, 5, 5]\n assert candidate(arr = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10,x = 0) == [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 15) == [4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20,x = 10) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],k = 5,x = 10) == [5, 7, 9, 11, 13]\n assert candidate(arr = [-100, -50, -30, -20, -10, 0, 10, 20, 30, 50, 100],k = 5,x = -25) == [-50, -30, -20, -10, 0]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 4,x = 12) == [9, 11, 13, 15]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 7,x = 10) == [7, 8, 9, 10, 11, 12, 13]\n assert candidate(arr = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],k = 5,x = -99) == [-100, -99, -98, -97, -96]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 3) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],k = 5,x = 28) == [23, 25, 27, 29, 31]\n assert candidate(arr = [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10],k = 5,x = 1) == [-4, -2, 0, 2, 4]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 4,x = 10) == [7, 9, 11, 13]\n assert candidate(arr = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2],k = 5,x = 1) == [1, 1, 1, 1, 1]\n assert candidate(arr = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 7,x = 0) == [5, 5, 5, 5, 5, 5, 5]\n assert candidate(arr = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],k = 4,x = -5) == [-7, -6, -5, -4]\n assert candidate(arr = [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3],k = 6,x = 1) == [1, 1, 1, 1, 1, 2]\n assert candidate(arr = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 5,x = 0) == [1, 1, 1, 2, 2]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 6,x = 14) == [9, 11, 13, 15, 17, 19]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 10,x = 8) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10,x = 1) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 0) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 5,x = 3) == [2, 2, 3, 3, 3]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 0) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(arr = [1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 4,x = 1) == [1, 1, 1, 2]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 5) == [3, 4, 5, 6, 7]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5],k = 3,x = 5) == [3, 4, 5]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1],k = 4,x = 1) == [1, 1, 1, 1]\n assert candidate(arr = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0],k = 5,x = 0) == [-4, -3, -2, -1, 0]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4,x = 11) == [7, 8, 9, 10]\n assert candidate(arr = [1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10],k = 8,x = 5) == [3, 4, 4, 5, 5, 5, 6, 6]\n assert candidate(arr = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6],k = 15,x = 3) == [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5,x = 1) == [1, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 15) == [6, 7, 8, 9, 10]\n assert candidate(arr = [-10, -5, -3, -1, 0, 1, 3, 5, 7, 10],k = 4,x = 12) == [3, 5, 7, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 0) == [1, 2, 3, 4, 5]\n assert candidate(arr = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 4,x = 15) == [12, 14, 16, 18]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10,x = 10) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(arr = [1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10],k = 10,x = 5) == [4, 4, 4, 4, 5, 5, 5, 5, 5, 6]\n assert candidate(arr = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7],k = 8,x = 4) == [3, 3, 3, 4, 4, 5, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 8,x = 16) == [8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 0) == [1, 2, 3]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 5) == [2, 3, 4, 5, 6, 7, 8]\n assert candidate(arr = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 10,x = 5) == [-40, -30, -20, -10, 0, 10, 20, 30, 40, 50]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 15) == [8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5,x = 11) == [6, 7, 8, 9, 10]\n assert candidate(arr = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],k = 5,x = 12) == [7, 9, 11, 13, 15]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10,x = 15) == [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 3,x = 2) == [1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4,x = 10) == [7, 8, 9, 10]\n assert candidate(arr = [1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9],k = 4,x = 4) == [3, 4, 5, 5]\n assert candidate(arr = [-10, -5, -3, -1, 0, 1, 2, 3, 5, 7],k = 3,x = -4) == [-5, -3, -1]\n assert candidate(arr = [-10, -5, -2, 0, 1, 3, 5, 8, 12],k = 3,x = -3) == [-5, -2, 0]\n assert candidate(arr = [1, 2, 3, 3, 3, 3, 4, 5, 6],k = 4,x = 3) == [3, 3, 3, 3]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5],k = 3,x = 1) == [1, 2, 2]\n assert candidate(arr = [1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8],k = 5,x = 2) == [1, 1, 1, 2, 2]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 11) == [8, 9, 10]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 5,x = 10) == [5, 7, 9, 11, 13]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5,x = 1) == [1, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 0) == [1, 2, 3]\n assert candidate(arr = [1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9],k = 6,x = 5) == [4, 5, 5, 5, 6, 6]\n assert candidate(arr = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],k = 5,x = -94) == [-96, -95, -94, -93, -92]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],k = 6,x = 10) == [5, 7, 9, 11, 13, 15]\n assert candidate(arr = [1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 9],k = 5,x = 4) == [3, 3, 4, 5, 5]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = 12) == [8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7,x = 10) == [7, 8, 9, 10, 11, 12, 13]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 2,x = 5) == [4, 5]\n assert candidate(arr = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 3,x = 55) == [40, 50, 60]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7,x = 7) == [4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],k = 5,x = 12) == [7, 9, 11, 13, 15]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 6,x = 5) == [2, 3, 4, 5, 6, 7]\n assert candidate(arr = [-20, -15, -10, -5, 0, 5, 10, 15, 20],k = 4,x = 0) == [-10, -5, 0, 5]\n assert candidate(arr = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6],k = 10,x = 3) == [1, 2, 2, 2, 3, 3, 3, 4, 4, 4]\n assert candidate(arr = [0, 1, 1, 1, 1, 2, 3, 4, 4, 4, 5, 5, 6, 7, 8, 9],k = 6,x = 0) == [0, 1, 1, 1, 1, 2]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 15,x = 10) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]\n assert candidate(arr = [1, 2, 3, 6, 7, 8, 9, 10],k = 3,x = 5) == [3, 6, 7]\n assert candidate(arr = [-10, -5, -2, -1, 0, 1, 2, 3, 5, 6, 7, 10, 15],k = 5,x = -3) == [-5, -2, -1, 0, 1]\n assert candidate(arr = [0, 0, 1, 1, 1, 1, 2, 2, 3, 3],k = 5,x = 1) == [0, 1, 1, 1, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 7,x = 11) == [4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3,x = -2) == [1, 2, 3]\n assert candidate(arr = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24],k = 5,x = 16) == [9, 12, 15, 18, 21]\n assert candidate(arr = [-10, -5, -3, -1, 0, 1, 3, 5, 7, 10],k = 5,x = -2) == [-5, -3, -1, 0, 1]\n assert candidate(arr = [-10, -5, -1, 0, 1, 5, 10],k = 3,x = -3) == [-5, -1, 0]\n assert candidate(arr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5,x = 2) == [1, 1, 1, 1, 1]\n assert candidate(arr = [1, 3, 3, 3, 5, 5, 5, 7, 7, 9],k = 4,x = 6) == [5, 5, 5, 7]\n assert candidate(arr = [1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5],k = 7,x = 4) == [4, 4, 4, 4, 4, 4, 4]\n assert candidate(arr = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60],k = 5,x = 53) == [40, 45, 50, 55, 60]\n assert candidate(arr = [-5, -3, -2, -1, 0, 1, 2, 3, 4, 5],k = 6,x = -4) == [-5, -3, -2, -1, 0, 1]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10,x = 5) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(arr = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],k = 12,x = 2) == [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3]\n assert candidate(arr = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10,x = 5) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 6,x = 15) == [12, 13, 14, 15, 16, 17]\n assert candidate(arr = [-10, -5, 0, 3, 9, 12],k = 3,x = -7) == [-10, -5, 0]\n assert candidate(arr = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5,x = 0) == [0, 0, 0, 0, 0]\n assert candidate(arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 4,x = 10) == [7, 9, 11, 13]\n assert candidate(arr = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50],k = 6,x = 15) == [-10, 0, 10, 20, 30, 40]\n assert candidate(arr = [1, 3, 4, 5, 8, 10, 15, 20, 30, 50, 100],k = 4,x = 12) == [5, 8, 10, 15]\n assert candidate(arr = [1, 3, 3, 4, 4, 4, 4, 5, 6, 8, 9],k = 5,x = 4) == [3, 4, 4, 4, 4]\n", "comparison": "exact"}, "public_tests": ["[1,2,3,4,5]\n4\n3", "[1,1,2,3,4,5]\n4\n-1"], "hints": [], "metadata": {"canonical_parameter_names": ["arr", "k", "x"], "leetcode_dataset_entry_point": "Solution().findClosestElements", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:33+00:00", "tests_total": 129, "tests_dropped": 2, "flags": [], "topic_tags": ["array", "two-pointers", "binary-search", "sliding-window", "sorting", "heap-priority-queue"]}, "language": "cpp", "interface": {"raw_signature": "vector findClosestElements(vector& arr, int k, int x) {", "container": "Solution", "callable": "findClosestElements", "parameters": [{"name": "arr", "type": "vector&"}, {"name": "k", "type": "int"}, {"name": "x", "type": "int"}], "return_type": "vector", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 659, "task_id": "split-array-into-consecutive-subsequences", "difficulty": "Medium", "problem_description": "You are given an integer array nums that is sorted in non-decreasing order.\n\nDetermine if it is possible to split nums into one or more subsequences such that both of the following conditions are true:\n\n- Each subsequence is a consecutive increasing sequence (i.e. each integer is exactly one more than the previous integer).\n- All subsequences have a length of 3 or more.\n\nReturn true if you can split nums according to the above conditions, or false otherwise.\n\nA subsequence of an array is a new array that is formed from the original array by deleting some (can be none) of the elements without disturbing the relative positions of the remaining elements. (i.e., [1,3,5] is a subsequence of [1,2,3,4,5] while [1,3,2] is not).\n\nExample 1:\n\nInput: nums = [1,2,3,3,4,5]\nOutput: true\nExplanation: nums can be split into the following subsequences:\n[1,2,3,3,4,5] --> 1, 2, 3\n[1,2,3,3,4,5] --> 3, 4, 5\n\nExample 2:\n\nInput: nums = [1,2,3,3,4,4,5,5]\nOutput: true\nExplanation: nums can be split into the following subsequences:\n[1,2,3,3,4,4,5,5] --> 1, 2, 3, 4, 5\n[1,2,3,3,4,4,5,5] --> 3, 4, 5\n\nExample 3:\n\nInput: nums = [1,2,3,4,4,5]\nOutput: false\nExplanation: It is impossible to split nums into consecutive increasing subsequences of length 3 or more.\n\nConstraints:\n\n- 1 <= nums.length <= 10^4\n- -1000 <= nums[i] <= 1000\n- nums is sorted in non-decreasing order.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 3, 4, 4, 5]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 5]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5]) == True\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 6]) == False\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == True\n assert candidate(nums = [1, 2, 3, 4, 4, 5, 5, 5, 6, 7]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 5, 5, 5]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10]) == False\n assert candidate(nums = [-1000, -999, -999, -998, -997, -996, -995, -994, -993, -992, -991, -990, -899, -898, -897, -896, -895, -894, -893, -892, -891, -890]) == False\n assert candidate(nums = [1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16]) == False\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12]) == False\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19]) == True\n assert candidate(nums = [1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20]) == True\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 10, 10, 10, 11, 12, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 18, 19, 20, 20, 21, 22, 23, 24, 25, 25]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == True\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == False\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14]) == False\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11]) == False\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 29, 29, 30]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9, 10, 10]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13]) == True\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [-3, -2, -1, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == True\n assert candidate(nums = [1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 13, 14, 15]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == True\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 14, 15]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12]) == True\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == False\n assert candidate(nums = [1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 15]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15]) == True\n assert candidate(nums = [-5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13]) == False\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17]) == True\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7]) == False\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13]) == False\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20]) == False\n assert candidate(nums = [1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8]) == False\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 20]) == False\n assert candidate(nums = [-1, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10]) == True\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10]) == True\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 22, 23, 24, 25, 25, 25]) == False\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12]) == True\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15]) == False\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16]) == True\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8]) == False\n assert candidate(nums = [5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == True\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15]) == True\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18]) == True\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == True\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13]) == True\n", "comparison": "exact"}, "public_tests": ["[1,2,3,3,4,5]", "[1,2,3,3,4,4,5,5]", "[1,2,3,4,4,5]"], "hints": [], "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().isPossible", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:35+00:00", "tests_total": 123, "tests_dropped": 0, "flags": [], "topic_tags": ["array", "hash-table", "greedy", "heap-priority-queue"]}, "language": "cpp", "interface": {"raw_signature": "bool isPossible(vector& nums) {", "container": "Solution", "callable": "isPossible", "parameters": [{"name": "nums", "type": "vector&"}], "return_type": "bool", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 661, "task_id": "image-smoother", "difficulty": "Easy", "problem_description": "An image smoother is a filter of the size 3 x 3 that can be applied to each cell of an image by rounding down the average of the cell and the eight surrounding cells (i.e., the average of the nine cells in the blue smoother). If one or more of the surrounding cells of a cell is not present, we do not consider it in the average (i.e., the average of the four cells in the red smoother).\n\nGiven an m x n integer matrix img representing the grayscale of an image, return the image after applying the smoother on each cell of it.\n\nExample 1:\n\nInput: img = [[1,1,1],[1,0,1],[1,1,1]]\nOutput: [[0,0,0],[0,0,0],[0,0,0]]\nExplanation:\nFor the points (0,0), (0,2), (2,0), (2,2): floor(3/4) = floor(0.75) = 0\nFor the points (0,1), (1,0), (1,2), (2,1): floor(5/6) = floor(0.83333333) = 0\nFor the point (1,1): floor(8/9) = floor(0.88888889) = 0\n\nExample 2:\n\nInput: img = [[100,200,100],[200,50,200],[100,200,100]]\nOutput: [[137,141,137],[141,138,141],[137,141,137]]\nExplanation:\nFor the points (0,0), (0,2), (2,0), (2,2): floor((100+200+200+50)/4) = floor(137.5) = 137\nFor the points (0,1), (1,0), (1,2), (2,1): floor((200+200+50+200+100+100)/6) = floor(141.666667) = 141\nFor the point (1,1): floor((50+200+200+200+200+100+100+100+100)/9) = floor(138.888889) = 138\n\nConstraints:\n\n- m == img.length\n- n == img[i].length\n- 1 <= m, n <= 200\n- 0 <= img[i][j] <= 255\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(img = [[100, 200, 100], [200, 50, 200], [100, 200, 100]]) == [[137, 141, 137], [141, 138, 141], [137, 141, 137]]\n assert candidate(img = [[10, 20, 30], [40, 50, 60], [70, 80, 90]]) == [[30, 35, 40], [45, 50, 55], [60, 65, 70]]\n assert candidate(img = [[1]]) == [[1]]\n assert candidate(img = [[255, 255, 255], [255, 255, 255], [255, 255, 255]]) == [[255, 255, 255], [255, 255, 255], [255, 255, 255]]\n assert candidate(img = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == [[3, 3, 4], [4, 5, 5], [6, 6, 7]]\n assert candidate(img = [[1, 1, 1], [1, 0, 1], [1, 1, 1]]) == [[0, 0, 0], [0, 0, 0], [0, 0, 0]]\n assert candidate(img = [[1, 2], [3, 4]]) == [[2, 2], [2, 2]]\n assert candidate(img = [[1, 2, 3], [4, 5, 6]]) == [[3, 3, 4], [3, 3, 4]]\n assert candidate(img = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]) == [[3, 4, 5, 5], [5, 6, 7, 7], [9, 10, 11, 11], [11, 12, 13, 13]]\n assert candidate(img = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]) == [[0, 0, 0], [0, 0, 0], [0, 0, 0]]\n assert candidate(img = [[255]]) == [[255]]\n assert candidate(img = [[1, 1], [1, 1]]) == [[1, 1], [1, 1]]\n assert candidate(img = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]) == [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]\n assert candidate(img = [[255, 255, 255, 255], [255, 0, 0, 255], [255, 0, 0, 255], [255, 255, 255, 255]]) == [[191, 170, 170, 191], [170, 141, 141, 170], [170, 141, 141, 170], [191, 170, 170, 191]]\n assert candidate(img = [[128, 64, 32, 16, 8], [8, 128, 64, 32, 16], [16, 8, 128, 64, 32], [32, 16, 8, 128, 64], [64, 32, 16, 8, 128]]) == [[82, 70, 56, 28, 18], [58, 64, 59, 43, 28], [34, 45, 64, 59, 56], [28, 35, 45, 64, 70], [36, 28, 34, 58, 82]]\n assert candidate(img = [[255, 0, 255], [0, 255, 0], [255, 0, 255]]) == [[127, 127, 127], [127, 141, 127], [127, 127, 127]]\n assert candidate(img = [[123, 45, 67], [89, 101, 113], [125, 137, 149], [161, 173, 185], [197, 209, 221]]) == [[89, 89, 81], [103, 105, 102], [131, 137, 143], [167, 173, 179], [185, 191, 197]]\n assert candidate(img = [[255, 0, 0], [0, 255, 0], [0, 0, 255]]) == [[127, 85, 63], [85, 85, 85], [63, 85, 127]]\n assert candidate(img = [[10, 20, 30, 40, 50], [60, 70, 80, 90, 100], [110, 120, 130, 140, 150], [160, 170, 180, 190, 200], [210, 220, 230, 240, 250]]) == [[40, 45, 55, 65, 70], [65, 70, 80, 90, 95], [115, 120, 130, 140, 145], [165, 170, 180, 190, 195], [190, 195, 205, 215, 220]]\n assert candidate(img = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]) == [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]\n assert candidate(img = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30]]) == [[4, 5, 6, 7, 8, 8], [7, 8, 9, 10, 11, 11], [13, 14, 15, 16, 17, 17], [19, 20, 21, 22, 23, 23], [22, 23, 24, 25, 26, 26]]\n assert candidate(img = [[255, 127, 63, 31], [15, 7, 3, 1], [255, 255, 255, 255], [255, 255, 255, 255]]) == [[101, 78, 38, 24], [152, 137, 110, 101], [173, 172, 171, 170], [255, 255, 255, 255]]\n assert candidate(img = [[10, 20], [30, 40]]) == [[25, 25], [25, 25]]\n assert candidate(img = [[200, 150, 100], [50, 0, 50], [100, 150, 200]]) == [[100, 91, 75], [108, 111, 108], [75, 91, 100]]\n assert candidate(img = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]]) == [[3, 3, 4], [4, 5, 5], [7, 8, 8], [10, 11, 11], [12, 12, 13]]\n assert candidate(img = [[0, 1, 0, 1, 0], [1, 0, 1, 0, 1], [0, 1, 0, 1, 0], [1, 0, 1, 0, 1], [0, 1, 0, 1, 0]]) == [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\n assert candidate(img = [[0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0]]) == [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]\n assert candidate(img = [[255, 0, 0, 255], [0, 0, 0, 0], [0, 0, 0, 0], [255, 0, 0, 255]]) == [[63, 42, 42, 63], [42, 28, 28, 42], [42, 28, 28, 42], [63, 42, 42, 63]]\n assert candidate(img = [[50, 50, 50], [50, 50, 50], [50, 50, 50], [50, 50, 50]]) == [[50, 50, 50], [50, 50, 50], [50, 50, 50], [50, 50, 50]]\n assert candidate(img = [[255, 0, 255, 0, 255], [0, 255, 0, 255, 0], [255, 0, 255, 0, 255], [0, 255, 0, 255, 0], [255, 0, 255, 0, 255]]) == [[127, 127, 127, 127, 127], [127, 141, 113, 141, 127], [127, 113, 141, 113, 127], [127, 141, 113, 141, 127], [127, 127, 127, 127, 127]]\n assert candidate(img = [[255, 255, 255, 255, 255], [255, 255, 255, 255, 255], [255, 255, 255, 255, 255], [255, 255, 255, 255, 255], [255, 255, 255, 255, 255]]) == [[255, 255, 255, 255, 255], [255, 255, 255, 255, 255], [255, 255, 255, 255, 255], [255, 255, 255, 255, 255], [255, 255, 255, 255, 255]]\n assert candidate(img = [[200, 50, 50], [50, 200, 50], [50, 50, 200]]) == [[125, 100, 87], [100, 100, 100], [87, 100, 125]]\n assert candidate(img = [[0, 0, 0, 0], [0, 255, 255, 0], [0, 255, 255, 0], [0, 0, 0, 0]]) == [[63, 85, 85, 63], [85, 113, 113, 85], [85, 113, 113, 85], [63, 85, 85, 63]]\n assert candidate(img = [[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 255, 255, 255, 1, 0], [0, 1, 255, 0, 255, 1, 0], [0, 1, 255, 255, 255, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == [[0, 0, 0, 0, 0, 0, 0], [0, 28, 57, 85, 57, 28, 0], [0, 57, 85, 142, 85, 57, 0], [0, 85, 142, 226, 142, 85, 0], [0, 57, 85, 142, 85, 57, 0], [0, 28, 57, 85, 57, 28, 0], [0, 0, 0, 0, 0, 0, 0]]\n assert candidate(img = [[10, 20, 30], [40, 50, 60], [70, 80, 90], [100, 110, 120], [130, 140, 150]]) == [[30, 35, 40], [45, 50, 55], [75, 80, 85], [105, 110, 115], [120, 125, 130]]\n assert candidate(img = [[255, 0, 0, 0, 255], [0, 255, 255, 255, 0], [0, 255, 0, 255, 0], [0, 255, 255, 255, 0], [255, 0, 0, 0, 255]]) == [[127, 127, 127, 127, 127], [127, 113, 141, 113, 127], [127, 141, 226, 141, 127], [127, 113, 141, 113, 127], [127, 127, 127, 127, 127]]\n assert candidate(img = [[0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 255, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]) == [[0, 0, 0, 0, 0], [0, 28, 28, 28, 0], [0, 28, 29, 28, 0], [0, 28, 28, 28, 0], [0, 0, 0, 0, 0]]\n assert candidate(img = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]) == [[3, 4, 5, 5], [5, 6, 7, 7], [9, 10, 11, 11], [11, 12, 13, 13]]\n assert candidate(img = [[0, 1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23, 24, 25, 26]]) == [[5, 5, 6, 7, 8, 9, 10, 11, 12], [9, 10, 11, 12, 13, 14, 15, 16, 16], [14, 14, 15, 16, 17, 18, 19, 20, 21]]\n assert candidate(img = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]) == [[4, 4, 5, 6, 7], [6, 7, 8, 9, 9], [11, 12, 13, 14, 14], [14, 14, 15, 16, 17]]\n assert candidate(img = [[0, 1, 2, 3, 4, 5], [5, 4, 3, 2, 1, 0], [0, 1, 2, 3, 4, 5], [5, 4, 3, 2, 1, 0], [0, 1, 2, 3, 4, 5], [5, 4, 3, 2, 1, 0]]) == [[2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 3, 3], [3, 3, 2, 2, 2, 1], [1, 2, 2, 2, 3, 3], [3, 3, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2]]\n assert candidate(img = [[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1]]) == [[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1]]\n assert candidate(img = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 0, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == [[1, 1, 1, 1, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 1, 1, 1, 1]]\n assert candidate(img = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120], [130, 140, 150, 160], [170, 180, 190, 200]]) == [[35, 40, 50, 55], [55, 60, 70, 75], [95, 100, 110, 115], [135, 140, 150, 155], [155, 160, 170, 175]]\n assert candidate(img = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\n assert candidate(img = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36]]) == [[4, 5, 6, 7, 8, 8], [7, 8, 9, 10, 11, 11], [13, 14, 15, 16, 17, 17], [19, 20, 21, 22, 23, 23], [25, 26, 27, 28, 29, 29], [28, 29, 30, 31, 32, 32]]\n assert candidate(img = [[255, 100, 50, 25, 0], [25, 50, 100, 255, 255], [0, 25, 50, 100, 255], [255, 255, 100, 50, 25], [25, 100, 255, 255, 0]]) == [[107, 96, 96, 114, 133], [75, 72, 83, 121, 148], [101, 95, 109, 132, 156], [110, 118, 132, 121, 114], [158, 165, 169, 114, 82]]\n assert candidate(img = [[50, 100, 150, 200], [250, 50, 100, 150], [200, 250, 50, 100], [100, 150, 200, 250]]) == [[112, 116, 125, 150], [150, 133, 127, 125], [166, 150, 144, 141], [175, 158, 166, 150]]\n assert candidate(img = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == [[4, 4, 5, 6, 7], [6, 7, 8, 9, 9], [11, 12, 13, 14, 14], [16, 17, 18, 19, 19], [19, 19, 20, 21, 22]]\n assert candidate(img = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]\n assert candidate(img = [[255, 255, 255, 255], [255, 0, 0, 255], [255, 0, 255, 255], [255, 255, 255, 255]]) == [[191, 170, 170, 191], [170, 170, 170, 212], [170, 170, 170, 212], [191, 212, 212, 255]]\n assert candidate(img = [[100, 100, 100, 100, 100], [100, 100, 100, 100, 100], [100, 100, 100, 100, 100], [100, 100, 100, 100, 100], [100, 100, 100, 100, 100]]) == [[100, 100, 100, 100, 100], [100, 100, 100, 100, 100], [100, 100, 100, 100, 100], [100, 100, 100, 100, 100], [100, 100, 100, 100, 100]]\n assert candidate(img = [[10, 10, 10], [10, 10, 10], [10, 10, 10], [10, 10, 10], [10, 10, 10]]) == [[10, 10, 10], [10, 10, 10], [10, 10, 10], [10, 10, 10], [10, 10, 10]]\n assert candidate(img = [[100, 150, 200, 250], [100, 150, 200, 250], [100, 150, 200, 250], [100, 150, 200, 250], [100, 150, 200, 250], [100, 150, 200, 250]]) == [[125, 150, 200, 225], [125, 150, 200, 225], [125, 150, 200, 225], [125, 150, 200, 225], [125, 150, 200, 225], [125, 150, 200, 225]]\n assert candidate(img = [[0, 255, 255], [255, 255, 0], [255, 0, 0]]) == [[191, 170, 191], [170, 141, 127], [191, 127, 63]]\n assert candidate(img = [[100, 200, 150], [175, 200, 125], [100, 150, 200]]) == [[168, 158, 168], [154, 155, 170], [156, 158, 168]]\n assert candidate(img = [[50, 50, 50, 50], [50, 50, 50, 50], [50, 50, 50, 50], [50, 50, 50, 50]]) == [[50, 50, 50, 50], [50, 50, 50, 50], [50, 50, 50, 50], [50, 50, 50, 50]]\n assert candidate(img = [[255, 255, 255], [255, 0, 255], [255, 255, 255]]) == [[191, 212, 191], [212, 226, 212], [191, 212, 191]]\n assert candidate(img = [[128, 64, 32], [16, 8, 4], [2, 1, 0]]) == [[54, 42, 27], [36, 28, 18], [6, 5, 3]]\n assert candidate(img = [[50, 100, 150, 200, 250], [250, 50, 100, 150, 200], [200, 250, 50, 100, 150], [150, 200, 250, 50, 100], [100, 150, 200, 250, 50]]) == [[112, 116, 125, 175, 200], [150, 133, 127, 150, 175], [183, 166, 133, 127, 125], [175, 172, 166, 133, 116], [150, 175, 183, 150, 112]]\n assert candidate(img = [[255, 0, 255, 0], [0, 255, 0, 255], [255, 0, 255, 0], [0, 255, 0, 255]]) == [[127, 127, 127, 127], [127, 141, 113, 127], [127, 113, 141, 127], [127, 127, 127, 127]]\n assert candidate(img = [[100, 200, 150, 125], [250, 50, 75, 200], [150, 250, 100, 50], [200, 100, 250, 150]]) == [[150, 137, 133, 137], [166, 147, 133, 116], [166, 158, 136, 137], [175, 175, 150, 137]]\n assert candidate(img = [[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [65, 70, 75, 80]]) == [[17, 20, 25, 27], [27, 30, 35, 37], [47, 50, 55, 57], [57, 60, 65, 67]]\n assert candidate(img = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15], [16, 17, 18]]) == [[3, 3, 4], [4, 5, 5], [7, 8, 8], [10, 11, 11], [13, 14, 14], [15, 15, 16]]\n assert candidate(img = [[255, 255, 255, 255], [255, 255, 255, 255], [255, 255, 255, 255], [255, 255, 255, 255]]) == [[255, 255, 255, 255], [255, 255, 255, 255], [255, 255, 255, 255], [255, 255, 255, 255]]\n assert candidate(img = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]]) == [[3, 3, 4], [4, 5, 5], [7, 8, 8], [10, 11, 11], [12, 12, 13]]\n assert candidate(img = [[10, 20, 30, 40, 50], [20, 30, 40, 50, 60], [30, 40, 50, 60, 70], [40, 50, 60, 70, 80], [50, 60, 70, 80, 90]]) == [[20, 25, 35, 45, 50], [25, 30, 40, 50, 55], [35, 40, 50, 60, 65], [45, 50, 60, 70, 75], [50, 55, 65, 75, 80]]\n assert candidate(img = [[255, 255, 255, 255], [255, 0, 0, 255], [255, 0, 0, 255], [255, 255, 255, 255]]) == [[191, 170, 170, 191], [170, 141, 141, 170], [170, 141, 141, 170], [191, 170, 170, 191]]\n assert candidate(img = [[50, 60, 70, 80], [40, 50, 60, 70], [30, 40, 50, 60], [20, 30, 40, 50]]) == [[50, 55, 65, 70], [45, 50, 60, 65], [35, 40, 50, 55], [30, 35, 45, 50]]\n assert candidate(img = [[128, 128, 128], [128, 128, 128], [128, 128, 128], [128, 128, 128], [128, 128, 128]]) == [[128, 128, 128], [128, 128, 128], [128, 128, 128], [128, 128, 128], [128, 128, 128]]\n assert candidate(img = [[0, 0, 0, 0, 0], [0, 255, 255, 255, 0], [0, 255, 255, 255, 0], [0, 255, 255, 255, 0], [0, 0, 0, 0, 0]]) == [[63, 85, 127, 85, 63], [85, 113, 170, 113, 85], [127, 170, 255, 170, 127], [85, 113, 170, 113, 85], [63, 85, 127, 85, 63]]\n assert candidate(img = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 7, 5, 3, 1], [2, 4, 6, 8, 10, 8, 6, 4, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2], [3, 2, 1, 4, 5, 6, 9, 8, 7], [7, 8, 9, 6, 5, 4, 1, 2, 3]]) == [[5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 5, 5, 5, 5, 5, 4, 4], [4, 5, 6, 7, 7, 6, 4, 3, 2], [2, 2, 4, 5, 5, 5, 4, 2, 2], [2, 2, 3, 4, 5, 5, 5, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 5, 5, 6, 6, 6, 6], [6, 6, 6, 5, 5, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5]]\n assert candidate(img = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == [[4, 4, 5, 6, 7], [6, 7, 8, 9, 9], [11, 12, 13, 14, 14], [16, 17, 18, 19, 19], [19, 19, 20, 21, 22]]\n assert candidate(img = [[0, 0, 0, 0, 0, 0], [0, 255, 255, 255, 255, 0], [0, 255, 0, 0, 255, 0], [0, 255, 0, 0, 255, 0], [0, 255, 255, 255, 255, 0], [0, 0, 0, 0, 0, 0]]) == [[63, 85, 127, 127, 85, 63], [85, 85, 113, 113, 85, 85], [127, 113, 141, 141, 113, 127], [127, 113, 141, 141, 113, 127], [85, 85, 113, 113, 85, 85], [63, 85, 127, 127, 85, 63]]\n assert candidate(img = [[255, 0, 0, 255, 0], [0, 255, 0, 255, 0], [0, 0, 255, 0, 0], [0, 255, 0, 255, 0], [255, 0, 0, 255, 0]]) == [[127, 85, 127, 85, 127], [85, 85, 113, 85, 85], [85, 85, 141, 85, 85], [85, 85, 113, 85, 85], [127, 85, 127, 85, 127]]\n assert candidate(img = [[255, 0, 255, 0], [0, 255, 0, 255], [255, 0, 255, 0], [0, 255, 0, 255]]) == [[127, 127, 127, 127], [127, 141, 113, 127], [127, 113, 141, 127], [127, 127, 127, 127]]\n assert candidate(img = [[255, 0, 0, 0], [0, 255, 0, 0], [0, 0, 255, 0], [0, 0, 0, 255]]) == [[127, 85, 42, 0], [85, 85, 56, 42], [42, 56, 85, 85], [0, 42, 85, 127]]\n assert candidate(img = [[200, 100, 150, 200, 50], [50, 100, 150, 200, 250], [250, 200, 150, 100, 50], [50, 100, 150, 200, 250], [250, 200, 150, 100, 50]]) == [[112, 125, 150, 166, 175], [150, 150, 150, 144, 141], [125, 133, 150, 166, 175], [175, 166, 150, 133, 125], [150, 150, 150, 150, 150]]\n", "comparison": "exact"}, "public_tests": ["[[1,1,1],[1,0,1],[1,1,1]]", "[[100,200,100],[200,50,200],[100,200,100]]"], "hints": [], "metadata": {"canonical_parameter_names": ["img"], "leetcode_dataset_entry_point": "Solution().imageSmoother", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:39+00:00", "tests_total": 81, "tests_dropped": 3, "flags": ["has_images"], "topic_tags": ["array", "matrix"]}, "language": "cpp", "interface": {"raw_signature": "vector> imageSmoother(vector>& img) {", "container": "Solution", "callable": "imageSmoother", "parameters": [{"name": "img", "type": "vector>&"}], "return_type": "vector>", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} {"question_id": 664, "task_id": "strange-printer", "difficulty": "Hard", "problem_description": "There is a strange printer with the following two special properties:\n\n- The printer can only print a sequence of the same character each time.\n- At each turn, the printer can print new characters starting from and ending at any place and will cover the original existing characters.\n\nGiven a string s, return the minimum number of turns the printer needed to print it.\n\nExample 1:\n\nInput: s = \"aaabbb\"\nOutput: 2\nExplanation: Print \"aaa\" first and then print \"bbb\".\n\nExample 2:\n\nInput: s = \"aba\"\nOutput: 2\nExplanation: Print \"aaa\" first and then print \"b\" from the second place of the string, which will cover the existing character 'a'.\n\nConstraints:\n\n- 1 <= s.length <= 100\n- s consists of lowercase English letters.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"pppppppp\") == 1\n assert candidate(s = \"abcba\") == 3\n assert candidate(s = \"aabbaa\") == 2\n assert candidate(s = \"zzzzy\") == 2\n assert candidate(s = \"abababab\") == 5\n assert candidate(s = \"ppqpqr\") == 4\n assert candidate(s = \"a\") == 1\n assert candidate(s = \"abcabcabc\") == 7\n assert candidate(s = \"aabbc\") == 3\n assert candidate(s = \"aabaa\") == 2\n assert candidate(s = \"abcabc\") == 5\n assert candidate(s = \"abcdabcd\") == 7\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\") == 26\n assert candidate(s = \"abcdabcdabcd\") == 10\n assert candidate(s = \"abc\") == 3\n assert candidate(s = \"abcd\") == 4\n assert candidate(s = \"aaabbb\") == 2\n assert candidate(s = \"zzzzyyyxx\") == 3\n assert candidate(s = \"aabbccddeeff\") == 6\n assert candidate(s = \"aba\") == 2\n assert candidate(s = \"aabbcc\") == 3\n assert candidate(s = \"abacaba\") == 4\n assert candidate(s = \"abca\") == 3\n assert candidate(s = \"abacabadabacabadabacaba\") == 12\n assert candidate(s = \"aabbaabbaabb\") == 4\n assert candidate(s = \"abababababaabababa\") == 9\n assert candidate(s = \"abcabcabcabc\") == 9\n assert candidate(s = \"abacabadabacabadabacabadabacabad\") == 17\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg\") == 43\n assert candidate(s = \"zzyzxzyzxzyzxzyzxzyzxzyzxzyz\") == 14\n assert candidate(s = \"aabbccddeeaabbccddeeaabbcc\") == 11\n assert candidate(s = \"aabbaaabbbaaa\") == 3\n assert candidate(s = \"abcdefghabcdeghijklmno\") == 21\n assert candidate(s = \"aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbcccccccccccccccccc\") == 3\n assert candidate(s = \"aabbccddeeaabbccddeeaabbccddeeaabbcc\") == 15\n assert candidate(s = \"zzzzzyyyzzzzyyy\") == 3\n assert candidate(s = \"ababababababababababababababababababababababababababababababababababababababababababababa\") == 45\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\") == 21\n assert candidate(s = \"abcdefghijabcdefghijabcdefghijabcdefghijabcdefghij\") == 46\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc\") == 33\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz\") == 26\n assert candidate(s = \"abacabad\") == 5\n assert candidate(s = \"aaaabbbbccccddddeeeeaabbcc\") == 7\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"abcabcabcabcabcabc\") == 13\n assert candidate(s = \"zzzzzzzzzzzzzzy\") == 2\n assert candidate(s = \"aabbccddeeffgghhii\") == 9\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzy\") == 2\n assert candidate(s = \"abcdeffedcba\") == 6\n assert candidate(s = \"aaaaaaaaaabbbbbbbbccccccccddddddddeeeeeeeefffffffff\") == 6\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == 1\n assert candidate(s = \"abcdefedcba\") == 6\n assert candidate(s = \"aabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabb\") == 13\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == 1\n assert candidate(s = \"abababababababababababababab\") == 15\n assert candidate(s = \"abcdeedcbaedcbaedcba\") == 13\n assert candidate(s = \"abacabadabacaba\") == 8\n assert candidate(s = \"abababababababababababababababababababababababab\") == 25\n assert candidate(s = \"aaaaaaaaaabbbbbbbbbbcccccccccc\") == 3\n assert candidate(s = \"aaabbbcccdddfffgggaaa\") == 6\n assert candidate(s = \"aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbccccccccccccccccccccdddddddddddddddddd\") == 4\n assert candidate(s = \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccba\") == 26\n assert candidate(s = \"aabbccddeeffaabbccddeeffaabbccddeeffaabbccddeeff\") == 21\n assert candidate(s = \"abcdefghijihgfedcba\") == 10\n assert candidate(s = \"aabbccddeeaabbccddeeaabbccddeeee\") == 13\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\") == 33\n assert candidate(s = \"abacabadabacabadabacabadabacabadabacabad\") == 21\n assert candidate(s = \"zzzyyxxwvvuuttrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == 25\n assert candidate(s = \"ababababababababababababab\") == 14\n assert candidate(s = \"aabbccddeeffgg\") == 7\n assert candidate(s = \"abacabadabacabadabacabadabacabadabacabadabacabadabacabad\") == 29\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 26\n assert candidate(s = \"aabbccddeeffgghhiijj\") == 10\n assert candidate(s = \"abacabadabacabadabacabadabacabadabacabadabacabad\") == 25\n assert candidate(s = \"abcdefg\") == 7\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 26\n assert candidate(s = \"abcabcabcabcabcabcabcabcaabbcc\") == 19\n assert candidate(s = \"abacabadabacabadabacabad\") == 13\n assert candidate(s = \"aaabaaabaaabaaabaaabaaabaaabaaabaaabaaabaaabaaab\") == 13\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 26\n assert candidate(s = \"abcbaabcbaabcba\") == 7\n assert candidate(s = \"aabbbcccdddaaabbccccddeee\") == 8\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllll\") == 12\n assert candidate(s = \"ababababab\") == 6\n assert candidate(s = \"abcddcba\") == 4\n assert candidate(s = \"aabbaabbccddeeffaabb\") == 8\n assert candidate(s = \"abcdabcdabcdabcdabcdabcdabcdabcd\") == 25\n assert candidate(s = \"abcdefghihgfedcba\") == 9\n assert candidate(s = \"abcabcabcabcabcabcabcabcabc\") == 19\n assert candidate(s = \"abcabcabcabcabcabcabcabc\") == 17\n assert candidate(s = \"abcdabcdbaba\") == 8\n assert candidate(s = \"xyzyxzyzyxzyzyxzyz\") == 11\n assert candidate(s = \"abcdefghijhgfedcba\") == 10\n assert candidate(s = \"mississippi\") == 5\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"ababababababababababababababababababababababababababa\") == 27\n assert candidate(s = \"abcabcabcabcabc\") == 11\n assert candidate(s = \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\") == 37\n assert candidate(s = \"aabbccddeeaabbcc\") == 7\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n", "comparison": "exact"}, "public_tests": ["\"aaabbb\"", "\"aba\""], "hints": [], "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().strangePrinter", "problem_source": "newfacade/LeetCodeDataset", "description_source": "leetcode.com", "interface_source": "leetcode/codeSnippets", "fetched_at": "2026-09-30T19:55:46+00:00", "tests_total": 102, "tests_dropped": 1, "flags": [], "topic_tags": ["string", "dynamic-programming"]}, "language": "cpp", "interface": {"raw_signature": "int strangePrinter(string s) {", "container": "Solution", "callable": "strangePrinter", "parameters": [{"name": "s", "type": "string"}], "return_type": "int", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}}