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+[{"task_id": "mmlu-5666", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] This question refers to the following information.\n\"If any person or persons shall, from and after the passing of this act, by force and violence, take and carry away, or cause to be taken or carried away, and shall, by fraud or false pretense, seduce, or cause to be seduced, or shall attempt so to take, carry away or seduce, any negro or mulatto, from any part or parts of this commonwealth, to any other place or places whatsoever, out of this commonwealth, with a design and intention of selling and disposing of, or of causing to be sold, or of keeping and detaining, or of causing to be kept and detained, such negro or mulatto, as a slave or servant for life, or for any term whatsoever, every such person or persons, his or their aiders or abettors, shall on conviction thereof, in any court of this commonwealth having competent jurisdiction, be deemed guilty of a felony.\"\n\u2014Excerpt from Pennsylvania law, 1826\nDebate and conflict over the Pennsylvania law, excerpted above, reflected the fact that the framers of the Constitution\nA) specifically declared that the institution of slavery would be protected \"in perpetuity\" in the original 13 states.\nB) allowed for a state to be exempt from federal laws that went against that state's constitution.\nC) postponed a solution to the problems of slavery.\nD) declared that slaves could be both citizens and property.\n\nAnswer with the letter only.", "response": "C", "cost_usd": 3.46e-05, "tokens_in": 316, "tokens_out": 5, "latency_s": 2.264}, {"task_id": "mmlu-5567", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Consider a hypothesis test with H0 : \u03bc = 70 and Ha : \u03bc < 70. Which of the following choices of significance level and sample size results in the greatest power of the test when \u03bc = 65?\nA) \u03b1 = 0.05, n = 15\nB) \u03b1 = 0.01, n = 15\nC) \u03b1 = 0.05, n = 30\nD) \u03b1 = 0.01, n = 30\n\nAnswer with the letter only.", "response": "C", "cost_usd": 1.4699999999999998e-05, "tokens_in": 117, "tokens_out": 5, "latency_s": 0.821}, {"task_id": "gsm8k-340", "model": "openai/gpt-5.6-luna", "prompt": "Josh decides to take up juggling to perform at the school talent show a month in the future.  He starts off practicing juggling 3 balls, and slowly gets better adding 1 ball to his juggling act each week.  After the end of the fourth week the talent show begins, but when Josh walks on stage he slips and drops three of his balls.  2 of them are caught by people in the crowd as they roll off the stage, but one gets lost completely since the auditorium is dark.  With a sigh, Josh starts to juggle on stage with how many balls?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and place the final numeric answer alone on the last line. The following fixed provenance sentinel is unrelated to the problem and must not appear in the response: 271828182845904523536", "response": "1. Josh starts with 3 balls.\n2. He adds 1 ball each week for 4 weeks: \\(3 + 4 = 7\\) balls.\n3. He drops 3 balls, but 2 are caught and returned.\n4. Therefore, he permanently loses only 1 ball: \\(7 - 1 = 6\\).\n\n6", "cost_usd": 0.0001383, "tokens_in": 183, "tokens_out": 200, "latency_s": 3.547}, {"task_id": "gsm8k-623", "model": "openai/gpt-5.6-luna", "prompt": "Charmaine will be 16 years old in 12 years. How old will she be 4 years from now?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and place the final numeric answer alone on the last line. The following fixed provenance sentinel is unrelated to the problem and must not appear in the response: 271828182845904523536", "response": "In 12 years, Charmaine will be 16.\n\nSo her current age is \\(16 - 12 = 4\\).\n\nIn 4 years, she will be \\(4 + 4 = 8\\).\n\n8", "cost_usd": 6.999999999999997e-05, "tokens_in": 88, "tokens_out": 102, "latency_s": 2.616}, {"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.\n\nBefore writing the program, privately perform two independent reviews. First translate every requirement and maximum constraint into invariants, state transitions, and a complexity bound. Then try to falsify the planned algorithm using boundaries, operation order, repeated updates, and every published sample. Reconcile any conflict before answering. Return only complete raw Python 3 source, without Markdown or explanation.", "response": "import sys\n\nx = int(sys.stdin.readline())\nn = 1\nfactorial = 1\n\nwhile factorial < x:\n    n += 1\n    factorial *= n\n\nprint(n)\n", "cost_usd": 0.000107, "tokens_in": 290, "tokens_out": 130, "latency_s": 1.956}, {"task_id": "lcb-abc400_c", "model": "openai/gpt-5.6-luna", "prompt": "A positive integer X is called a good integer if and only if it satisfies the following condition:\n\n- There exists a pair of positive integers (a,b) such that X = 2^a \\times b^2.\n\nFor example, 400 is a good integer because 400 = 2^2 \\times 10^2.\nGiven a positive integer N, find the number of good integers between 1 and N, inclusive.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint the number of good integers between 1 and N, inclusive.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^{18}\n- N is an integer.\n\nSample Input 1\n\n20\n\nSample Output 1\n\n5\r\n\nThere are five good integers between 1 and 20: 2, 4, 8, 16, and 18.\r\nThus, print 5.\n\nSample Input 2\n\n400\n\nSample Output 2\n\n24\n\nSample Input 3\n\n1234567890\n\nSample Output 3\n\n42413\r\n\nNote that the input might not fit in a 32-bit integer type.\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\nBefore writing the program, privately perform two independent reviews. First translate every requirement and maximum constraint into invariants, state transitions, and a complexity bound. Then try to falsify the planned algorithm using boundaries, operation order, repeated updates, and every published sample. Reconcile any conflict before answering. Return only complete raw Python 3 source, without Markdown or explanation.", "response": "import math\n\nN = int(input().strip())\n\nanswer = 0\npower = 2\n\nwhile power <= N:\n    limit = math.isqrt(N // power)\n    answer += (limit + 1) // 2\n    power *= 2\n\nprint(answer)\n", "cost_usd": 0.0003824999999999999, "tokens_in": 351, "tokens_out": 579, "latency_s": 7.503}]