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+[{"task_id": "mmlu-3847", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] When a nation is operating at the natural rate of unemployment\nA) there is no cyclical unemployment.\nB) the inflation rate is zero.\nC) there is no structural unemployment.\nD) the nation is experiencing a recession.\n\nAnswer with the letter only.", "response": "A", "cost_usd": 9.2e-06, "tokens_in": 62, "tokens_out": 5, "latency_s": 1.665}, {"task_id": "mmlu-12174", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A 42-year-old man comes to the physician for a follow-up examination 1 week after he passed a renal calculus. X-ray crystallographic analysis of the calculus showed calcium as the primary cation. Physical examination today shows no abnormalities. A 24-hour collection of urine shows increased calcium excretion. Which of the following is the most appropriate pharmacotherapy?\nA) Carbonic anhydrase inhibitor\nB) Na+ \u2013Cl\u2212 symport inhibitor\nC) Na+ \u2013K + \u20132Cl\u2212 symport inhibitor\nD) Osmotic diuretic\n\nAnswer with the letter only.", "response": "B", "cost_usd": 1.61e-05, "tokens_in": 131, "tokens_out": 5, "latency_s": 0.71}, {"task_id": "gsm8k-131", "model": "openai/gpt-5.6-luna", "prompt": "The expenditure of Joseph in May was $500. In June, his expenditure was $60 less. How much was his total expenditure for those two months?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and privately verify arithmetic, signs, rounding, and boundary assumptions. Put only the final numeric result on the last line.", "response": "May expenditure: $500  \nJune expenditure: $500 \u2212 $60 = $440  \nTotal: $500 + $440 = $940  \n\n940", "cost_usd": 5.190000000000001e-05, "tokens_in": 81, "tokens_out": 73, "latency_s": 3.055}, {"task_id": "gsm8k-311", "model": "openai/gpt-5.6-luna", "prompt": "In a family of 5, three people eat three eggs each day while the rest eat two eggs each day. If they eat eggs every day, how many eggs will the family consume in a week?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and privately verify arithmetic, signs, rounding, and boundary assumptions. Put only the final numeric result on the last line.", "response": "Three people eat \\(3\\) eggs each:\n\n\\(3 \\times 3 = 9\\) eggs\n\nThe remaining two people eat \\(2\\) eggs each:\n\n\\(2 \\times 2 = 4\\) eggs\n\nDaily total:\n\n\\(9 + 4 = 13\\) eggs\n\nWeekly total:\n\n\\(13 \\times 7 = 91\\)\n\n91", "cost_usd": 8.59e-05, "tokens_in": 91, "tokens_out": 128, "latency_s": 2.632}, {"task_id": "lcb-abc399_b", "model": "openai/gpt-5.6-luna", "prompt": "N people labeled from 1 to N participated in a certain contest. The score of person i (1 \\leq i \\leq N) was P_i.\nIn this contest, the rank of each of the N people is determined by the following procedure:\n\n- Prepare a variable r, and initialize r = 1. Initially, the ranks of the N people are all undetermined.\n- Repeat the following operation until the ranks of all N people are determined:\n- Let x be the maximum score among the people whose ranks are currently undetermined, and let k be the number of people whose score is x. Determine the rank of those k people with score x to be r, and then add k to r.\n\n\n\nPrint the rank of each of the N people.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\n\nOutput\n\nPrint N lines. The i-th line (1 \\leq i \\leq N) should contain the rank of person i as an integer.\n\nConstraints\n\n\n- 1\\leq N \\leq 100\n- 1\\leq P_i \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n4\r\n3 12 9 9\n\nSample Output 1\n\n4\r\n1\r\n2\r\n2\r\n\nThe ranks of the N\\ (=4) people are determined as follows:\n\n- Prepare a variable r and initialize r=1. At first, the ranks of all 4 people are undetermined.\n- Currently, persons 1, 2, 3, 4 have undetermined ranks. The maximum score among them is P_2\\ (=12). Therefore, determine the rank of person 2 to be r\\ (=1), and then add 1 to r, making r=2.\n- Currently, persons 1, 3, 4 have undetermined ranks. The maximum score among them is P_3=P_4\\ (=9). Therefore, determine the ranks of persons 3 and 4 to be r\\ (=2), and then add 2 to r, making r=4.\n- Currently, person 1 has an undetermined rank. The maximum score among them is P_1\\ (=3). Therefore, determine the rank of person 1 to be r\\ (=4), and then add 1 to r, making r=5.\n- The ranks of all 4 people are now determined, so the process ends.\n\nSample Input 2\n\n3\r\n3 9 6\n\nSample Output 2\n\n3\r\n1\r\n2\n\nSample Input 3\n\n4\r\n100 100 100 100\n\nSample Output 3\n\n1\r\n1\r\n1\r\n1\n\nSample Input 4\n\n8\r\n87 87 87 88 41 38 41 38\n\nSample Output 4\n\n2\r\n2\r\n2\r\n1\r\n5\r\n7\r\n5\r\n7\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\nDerive the algorithm from the complete specification and maximum constraints. Privately construct a small direct specification and try to falsify the proposed algorithm. Check ordering, multiplicity, repeated values, boundaries, state changes, and complexity. Trace every published example. The execution harness compares output tokens exactly even when the problem prose grants mathematical tolerance. Match the required canonical representation, precision, rounding, ordering, and separators shown by the statement and examples. Do not print extra precision merely because it is available. Return only one complete raw Python 3 program without Markdown, fences, or explanation.", "response": "import sys\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    n = data[0]\n    scores = data[1:1 + n]\n\n    rank = [0] * n\n    current_rank = 1\n    for score in sorted(set(scores), reverse=True):\n        indices = [i for i, value in enumerate(scores) if value == score]\n        for i in indices:\n            rank[i] = current_rank\n        current_rank += len(indices)\n\n    sys.stdout.write(\"\\n\".join(map(str, rank)))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.0001558, "tokens_in": 766, "tokens_out": 132, "latency_s": 1.562}, {"task_id": "lcb-abc399_b", "model": "openai/gpt-5.6-luna", "prompt": "N people labeled from 1 to N participated in a certain contest. The score of person i (1 \\leq i \\leq N) was P_i.\nIn this contest, the rank of each of the N people is determined by the following procedure:\n\n- Prepare a variable r, and initialize r = 1. Initially, the ranks of the N people are all undetermined.\n- Repeat the following operation until the ranks of all N people are determined:\n- Let x be the maximum score among the people whose ranks are currently undetermined, and let k be the number of people whose score is x. Determine the rank of those k people with score x to be r, and then add k to r.\n\n\n\nPrint the rank of each of the N people.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\n\nOutput\n\nPrint N lines. The i-th line (1 \\leq i \\leq N) should contain the rank of person i as an integer.\n\nConstraints\n\n\n- 1\\leq N \\leq 100\n- 1\\leq P_i \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n4\r\n3 12 9 9\n\nSample Output 1\n\n4\r\n1\r\n2\r\n2\r\n\nThe ranks of the N\\ (=4) people are determined as follows:\n\n- Prepare a variable r and initialize r=1. At first, the ranks of all 4 people are undetermined.\n- Currently, persons 1, 2, 3, 4 have undetermined ranks. The maximum score among them is P_2\\ (=12). Therefore, determine the rank of person 2 to be r\\ (=1), and then add 1 to r, making r=2.\n- Currently, persons 1, 3, 4 have undetermined ranks. The maximum score among them is P_3=P_4\\ (=9). Therefore, determine the ranks of persons 3 and 4 to be r\\ (=2), and then add 2 to r, making r=4.\n- Currently, person 1 has an undetermined rank. The maximum score among them is P_1\\ (=3). Therefore, determine the rank of person 1 to be r\\ (=4), and then add 1 to r, making r=5.\n- The ranks of all 4 people are now determined, so the process ends.\n\nSample Input 2\n\n3\r\n3 9 6\n\nSample Output 2\n\n3\r\n1\r\n2\n\nSample Input 3\n\n4\r\n100 100 100 100\n\nSample Output 3\n\n1\r\n1\r\n1\r\n1\n\nSample Input 4\n\n8\r\n87 87 87 88 41 38 41 38\n\nSample Output 4\n\n2\r\n2\r\n2\r\n1\r\n5\r\n7\r\n5\r\n7\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\nWork independently from the statement and do not assume any candidate implementation. Write a correctness-first oracle for small legal inputs using direct simulation or exhaustive search. Also write a generator accepting seed and size arguments, seeding Python random, and printing one varied legal input. Systematically include legal ties and equalities, repeated values, minimum counts, endpoints, mandatory final transitions, and choices where an equal local action changes a later opportunity. Vary these boundary families from the seed instead of emitting a fixed example. The oracle must not reuse the efficient algorithm requested by the statement. The execution harness compares output tokens exactly even when the prose permits numerical tolerance. Reproduce every published output token exactly and infer one canonical representation for unseen outputs from the statement and examples without inventing extra precision. Return exactly two fenced blocks named oracle and generator, with no other text.", "response": "```oracle\nimport sys\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    if not data:\n        return\n\n    n = data[0]\n    scores = data[1:1 + n]\n    undetermined = [True] * n\n    ranks = [0] * n\n    current_rank = 1\n    remaining = n\n\n    while remaining:\n        maximum = max(scores[i] for i in range(n) if undetermined[i])\n        group = [\n            i for i in range(n)\n            if undetermined[i] and scores[i] == maximum\n        ]\n\n        for i in group:\n            undetermined[i] = False\n            ranks[i] = current_rank\n\n        current_rank += len(group)\n        remaining -= len(group)\n\n    sys.stdout.write(\"\\n\".join(map(str, ranks)))\n\nif __name__ == \"__main__\":\n    main()\n```\n\n```generator\nimport random\nimport sys\n\ndef main():\n    if len(sys.argv) != 3:\n        raise SystemExit(\"usage: generator SEED SIZE\")\n\n    seed = int(sys.argv[1])\n    n = int(sys.argv[2])\n\n    if not 1 <= n <= 100:\n        raise SystemExit(\"SIZE must be between 1 and 100\")\n\n    random.seed(seed)\n    family = random.randrange(8)\n\n    if n == 1:\n        scores = [random.choice([1, 2, 50, 99, 100])]\n    elif family == 0:\n        value = random.randint(1, 100)\n        scores = [value] * n\n    elif family == 1:\n        values = random.sample(range(1, 101), min(n, 100))\n        scores = values[:n]\n    elif family == 2:\n        a = random.randint(1, 99)\n        b = random.randint(a + 1, 100)\n        scores = [random.choice([a, b]) for _ in range(n)]\n    elif family == 3:\n        palette_size = random.randint(2, min(8, n))\n        palette = random.sample(range(1, 101), palette_size)\n        scores = [random.choice(palette) for _ in range(n)]\n    elif family == 4:\n        scores = [\n            random.choice([1, 2, 3, 98, 99, 100])\n            for _ in range(n)\n        ]\n    elif family == 5:\n        scores = [\n            max(1, min(100, 50 + ((i % 7) - 3) * random.randint(1, 8)))\n            for i in range(n)\n        ]\n        random.shuffle(scores)\n    elif family == 6:\n        scores = [random.randint(1, 100) for _ in range(n)]\n        if n >= 2:\n            scores[0] = 1\n            scores[1] = 100\n        if n >= 4:\n            scores[2] = scores[3] = random.choice([1, 50, 100])\n    else:\n        scores = [random.randint(1, 5) for _ in range(n)]\n        if n >= 3:\n            scores[0] = 100\n            scores[-1] = 1\n\n    print(n)\n    print(*scores)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0006927000000000001, "tokens_in": 819, "tokens_out": 1018, "latency_s": 8.106}, {"task_id": "lcb-abc395_c", "model": "openai/gpt-5.6-luna", "prompt": "You are given a positive integer N and an integer sequence A = (A_1,A_2,\\dots,A_N) of length N.\nDetermine whether there exists a non-empty (contiguous) subarray of A that has a repeated value, occurring multiple times in A. If such a subarray exists, find the length of the shortest such subarray.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\dots A_N\n\nOutput\n\nIf there is no (contiguous) subarray satisfying the condition in the problem statement, print -1. Otherwise, print the length of the shortest such subarray.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq A_i \\leq 10^6 \\ (1 \\leq i \\leq N)\n- All input values are integers.\n\nSample Input 1\n\n5\r\n3 9 5 3 1\n\nSample Output 1\n\n4\r\n\n(3,9,5,3) and (3,9,5,3,1) satisfy the condition. The shorter one is (3,9,5,3), which has length 4.\n\nSample Input 2\n\n4\r\n2 5 3 1\n\nSample Output 2\n\n-1\r\n\nThere is no subarray that satisfies the condition.\n\nSample Input 3\n\n10\r\n1 1 2 3 5 8 13 21 34 55\n\nSample Output 3\n\n2\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\nDerive the algorithm from the complete specification and maximum constraints. Privately construct a small direct specification and try to falsify the proposed algorithm. Check ordering, multiplicity, repeated values, boundaries, state changes, and complexity. Trace every published example. The execution harness compares output tokens exactly even when the problem prose grants mathematical tolerance. Match the required canonical representation, precision, rounding, ordering, and separators shown by the statement and examples. Do not print extra precision merely because it is available. Return only one complete raw Python 3 program without Markdown, fences, or explanation.", "response": "import sys\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    n = data[0]\n    a = data[1:1 + n]\n\n    last = {}\n    ans = n + 1\n\n    for i, x in enumerate(a):\n        if x in last:\n            ans = min(ans, i - last[x] + 1)\n        last[x] = i\n\n    print(-1 if ans == n + 1 else ans)\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.00017639999999999995, "tokens_in": 480, "tokens_out": 214, "latency_s": 2.688}, {"task_id": "lcb-abc395_c", "model": "openai/gpt-5.6-luna", "prompt": "You are given a positive integer N and an integer sequence A = (A_1,A_2,\\dots,A_N) of length N.\nDetermine whether there exists a non-empty (contiguous) subarray of A that has a repeated value, occurring multiple times in A. If such a subarray exists, find the length of the shortest such subarray.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\dots A_N\n\nOutput\n\nIf there is no (contiguous) subarray satisfying the condition in the problem statement, print -1. Otherwise, print the length of the shortest such subarray.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq A_i \\leq 10^6 \\ (1 \\leq i \\leq N)\n- All input values are integers.\n\nSample Input 1\n\n5\r\n3 9 5 3 1\n\nSample Output 1\n\n4\r\n\n(3,9,5,3) and (3,9,5,3,1) satisfy the condition. The shorter one is (3,9,5,3), which has length 4.\n\nSample Input 2\n\n4\r\n2 5 3 1\n\nSample Output 2\n\n-1\r\n\nThere is no subarray that satisfies the condition.\n\nSample Input 3\n\n10\r\n1 1 2 3 5 8 13 21 34 55\n\nSample Output 3\n\n2\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\nWork independently from the statement and do not assume any candidate implementation. Write a correctness-first oracle for small legal inputs using direct simulation or exhaustive search. Also write a generator accepting seed and size arguments, seeding Python random, and printing one varied legal input. Systematically include legal ties and equalities, repeated values, minimum counts, endpoints, mandatory final transitions, and choices where an equal local action changes a later opportunity. Vary these boundary families from the seed instead of emitting a fixed example. The oracle must not reuse the efficient algorithm requested by the statement. The execution harness compares output tokens exactly even when the prose permits numerical tolerance. Reproduce every published output token exactly and infer one canonical representation for unseen outputs from the statement and examples without inventing extra precision. Return exactly two fenced blocks named oracle and generator, with no other text.", "response": "```oracle\nimport sys\n\ndef solve():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    if not data:\n        return\n    n = data[0]\n    a = data[1:1 + n]\n\n    answer = None\n    for left in range(n):\n        seen = set()\n        for right in range(left, n):\n            if a[right] in seen:\n                length = right - left + 1\n                if answer is None or length < answer:\n                    answer = length\n                break\n            seen.add(a[right])\n\n    print(-1 if answer is None else answer)\n\nif __name__ == \"__main__\":\n    solve()\n```\n\n```generator\nimport random\nimport sys\n\ndef main():\n    if len(sys.argv) < 3:\n        raise SystemExit(\"usage: generator SEED SIZE\")\n\n    seed = int(sys.argv[1])\n    n = max(1, min(200000, int(sys.argv[2])))\n    random.seed(seed)\n\n    family = random.randrange(8)\n\n    if family == 0:\n        a = list(range(1, n + 1))\n        random.shuffle(a)\n\n    elif family == 1:\n        value = random.randint(1, 10**6)\n        a = [value] * n\n\n    elif family == 2:\n        a = []\n        next_value = random.randint(1, 10**6 - n)\n        for _ in range(n):\n            a.append(next_value)\n            next_value += 1\n\n        if n >= 2:\n            i = random.randrange(n - 1)\n            a[i + 1] = a[i]\n\n    elif family == 3:\n        base = random.randint(1, 10**6)\n        period = random.randint(1, min(12, n))\n        values = [((base + i * random.randint(1, 97) - 1) % 10**6) + 1\n                  for i in range(period)]\n        a = [values[i % period] for i in range(n)]\n\n    elif family == 4:\n        a = [random.randint(1, min(10**6, max(1, n // 2 + 1)))\n             for _ in range(n)]\n        if n >= 2:\n            a[0] = a[-1]\n\n    elif family == 5:\n        a = [random.randint(1, 10**6) for _ in range(n)]\n        if n >= 3:\n            left = random.randrange(n - 1)\n            right = random.randrange(left + 1, n)\n            a[right] = a[left]\n\n    elif family == 6:\n        a = []\n        for i in range(n):\n            if i % 3 == 0:\n                a.append(random.randint(1, 10**6))\n            elif i % 3 == 1 and a:\n                a.append(a[-1])\n            else:\n                a.append(random.randint(1, 10**6))\n\n    else:\n        a = [random.randint(1, 10**6) for _ in range(n)]\n        if n >= 4:\n            x = random.randint(1, 10**6)\n            left = random.randrange(1, n - 2)\n            right = random.randrange(left + 1, n)\n            a[left] = x\n            a[right] = x\n        if n >= 1 and random.randrange(2):\n            a[0] = random.randint(1, 10**6)\n        if n >= 2 and random.randrange(2):\n            a[-1] = a[0]\n\n    print(n)\n    print(*a)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0006557, "tokens_in": 533, "tokens_out": 1004, "latency_s": 8.105}]