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+[{"task_id": "mmlu-6862", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Computational complexity of Gradient descent is,\nA) linear in D\nB) linear in N\nC) polynomial in D\nD) dependent on the number of iterations\n\nAnswer with the letter only.", "response": "D", "cost_usd": 8e-06, "tokens_in": 50, "tokens_out": 5, "latency_s": 1.77}, {"task_id": "mmlu-7753", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] In the movie 'Star Wars' what kind of creature is Chewbacca?\nA) Woolie\nB) Woobie\nC) Wookiee\nD) Klingon\n\nAnswer with the letter only.", "response": "C", "cost_usd": 8.3e-06, "tokens_in": 53, "tokens_out": 5, "latency_s": 1.259}, {"task_id": "gsm8k-305", "model": "openai/gpt-5.6-luna", "prompt": "John arm wrestles 20 people.  He beats 80%.  How many people did he lose to?\n\nReason step by step, then give the final answer as a single number.\n\n[Request tag 12404491281331275243 - bookkeeping for this call only. Ignore it; do not mention or repeat it anywhere in your reply.]", "response": "80% of 20 = 16 wins.  \n20 \u2212 16 = 4 losses.\n\n4", "cost_usd": 5.5599999999999996e-05, "tokens_in": 76, "tokens_out": 80, "latency_s": 2.672}, {"task_id": "gsm8k-1136", "model": "openai/gpt-5.6-luna", "prompt": "Bob has a certain number of marbles. If he receives 2 dozen more marbles, he will have 60 marbles. If he loses 10 of the marbles he has, how many marbles will Bob have?\n\nReason step by step, then give the final answer as a single number.\n\n[Request tag 18683835050829836592 - bookkeeping for this call only. Ignore it; do not mention or repeat it anywhere in your reply.]", "response": "2 dozen = 24 marbles.\n\nBob initially had 60 \u2212 24 = 36 marbles.\n\nAfter losing 10, he has 36 \u2212 10 = 26 marbles.\n\n26", "cost_usd": 7.18e-05, "tokens_in": 100, "tokens_out": 103, "latency_s": 2.415}, {"task_id": "lcb-abc389_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer X not less than 2.\nFind the positive integer N such that N! = X.\nHere, N! denotes the factorial of N, and it is guaranteed that there is exactly one such N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nX\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 2 \\leq X \\leq 3 \\times 10^{18}\n- There is exactly one positive integer N such that N!=X.\n- All input values are integers.\n\nSample Input 1\n\n6\n\nSample Output 1\n\n3\r\n\nFrom 3!=3\\times2\\times1=6, print 3.\n\nSample Input 2\n\n2432902008176640000\n\nSample Output 2\n\n20\r\n\nFrom 20!=2432902008176640000, print 20.\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.", "response": "import sys\n\nx = int(sys.stdin.readline())\nfactorial = 1\nn = 1\n\nwhile factorial < x:\n    n += 1\n    factorial *= n\n\nprint(n)", "cost_usd": 4.8100000000000004e-05, "tokens_in": 217, "tokens_out": 44, "latency_s": 3.071}, {"task_id": "lcb-abc399_d", "model": "openai/gpt-5.6-luna", "prompt": "N couples are seated in a line.\nCount the number of pairs of couples such that neither couple was originally sitting next to each other, and both couples can end up sitting next to each other by swapping seats among those four people.\n\nThere is a sequence A = (A_1, A_2, \\dots, A_{2N}) of length 2N. Each of the integers 1, 2, \\dots, N appears exactly twice in A.\nFind the number of integer pairs (a, b) satisfying 1 \\leq a < b \\leq N and all of the following conditions:\n\n- The two occurrences of a in A are not adjacent.\n- The two occurrences of b in A are not adjacent.\n- By performing the following operation one or more times in any order, it is possible to reach a state where the two occurrences of a in A are adjacent and the two occurrences of b in A are also adjacent.\n- Choose an integer pair (i, j) (1 \\leq i \\leq 2N, 1 \\leq j \\leq 2N) such that A_i = a and A_j = b, and swap A_i with A_j.\n\n\n\nYou are given T test cases; solve each of them.\n\nInput\n\nThe input is given from Standard Input in the following format, where \\mathrm{case}_i denotes the i-th test case:\nT\n\\mathrm{case}_1\n\\mathrm{case}_2\n\\vdots\n\\mathrm{case}_T\n\nEach test case is given in the following format:\nN\nA_1 A_2 \\dots A_{2N}\n\nOutput\n\nPrint T lines. The i-th line should contain the answer for the i-th test case.\n\nConstraints\n\n\n- 1 \\leq T \\leq 2 \\times 10^5\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq A_i \\leq N\n- Each of 1, 2, \\dots, N appears exactly twice in A.\n- The sum of N over all test cases is at most 2 \\times 10^5.\n- All input values are integers.\n\nSample Input 1\n\n3\n3\n1 2 3 3 1 2\n4\n1 1 2 2 3 3 4 4\n5\n1 2 3 4 5 1 2 3 4 5\n\nSample Output 1\n\n1\n0\n4\n\nConsider the first test case.\n(a, b) = (1, 2) satisfies the conditions in the problem statement, for the following reasons:\n\n- The two occurrences of 1 in A are not adjacent.\n- The two occurrences of 2 in A are not adjacent.\n- By performing the operation where (i, j) = (1, 6) and swapping A_1 with A_6, you can reach a state where the two occurrences of 1 are adjacent and the two occurrences of 2 are also adjacent.\n\n(1, 2) is the only pair (a, b) that satisfies the conditions.\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.\n\nImplementation blueprint (mandatory): read every token at once with sys.stdin.buffer.read().split() and walk an index across test cases. Per test case over the array A of length 2N: record first[v] and second[v], the two 0-based positions of each value. Build SELF = set of values whose second position equals first position + 1. Scan every consecutive index pair (j, j+1) with u = A[j], w = A[j+1], skipping u == w: when j == first[u] and j+1 == first[w], add the unordered pair {u, w} to a set F; when j == second[u] and j+1 == second[w], add it to a set G. The answer is the number of pairs present in both F and G whose two values are both outside SELF. Never enumerate value pairs in a double loop. Collect all answers and print them joined by newlines with one final write. Return ONLY the complete Python 3 program implementing exactly this blueprint. No code fences, no explanations, no text before or after the program.", "response": "import sys\n\ndata = sys.stdin.buffer.read().split()\nidx = 0\nt = int(data[idx])\nidx += 1\nanswers = []\n\nfor _ in range(t):\n    n = int(data[idx])\n    idx += 1\n\n    a = list(map(int, data[idx:idx + 2 * n]))\n    idx += 2 * n\n\n    first = [-1] * (n + 1)\n    second = [-1] * (n + 1)\n\n    for pos, v in enumerate(a):\n        if first[v] == -1:\n            first[v] = pos\n        else:\n            second[v] = pos\n\n    self_set = {\n        v for v in range(1, n + 1)\n        if second[v] == first[v] + 1\n    }\n\n    f = set()\n    g = set()\n\n    for j in range(2 * n - 1):\n        u = a[j]\n        w = a[j + 1]\n        if u == w:\n            continue\n\n        pair = (u, w) if u < w else (w, u)\n\n        if j == first[u] and j + 1 == first[w]:\n            f.add(pair)\n\n        if j == second[u] and j + 1 == second[w]:\n            g.add(pair)\n\n    answer = sum(\n        1 for u, v in f & g\n        if u not in self_set and v not in self_set\n    )\n    answers.append(str(answer))\n\nsys.stdout.write(\"\\n\".join(answers) + \"\\n\")", "cost_usd": 0.0003951, "tokens_in": 927, "tokens_out": 504, "latency_s": 6.061}]