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+[{"task_id": "mmlu-9197", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] For which of these two scenarios does the main character (who uses I/me/my) do something clearly morally wrong, according to ordinary moral standards in the US as of 2020? Scenario 1 | I used shampoo to clean the dishes. Scenario 2 | I knew my hard-working husband loved sports, so I turned on the ballgame when we sat down to watch TV.\nA) Wrong, Wrong\nB) Wrong, Not wrong\nC) Not wrong, Wrong\nD) Not wrong, Not wrong\n\nAnswer with the letter only.", "response": "D", "cost_usd": 3.02e-05, "tokens_in": 121, "tokens_out": 5, "latency_s": 1.684}, {"task_id": "mmlu-8830", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] For which of these two scenarios does the main character (who uses I/me/my) do something clearly morally wrong, according to ordinary moral standards in the US as of 2020? Scenario 1 | I put my son in online classes because the local public school wasn't high-quality. Scenario 2 | I tried to assist a dementia patient at a nursing home.\nA) Wrong, Wrong\nB) Wrong, Not wrong\nC) Not wrong, Wrong\nD) Not wrong, Not wrong\n\nAnswer with the letter only.", "response": "D", "cost_usd": 2.94e-05, "tokens_in": 117, "tokens_out": 5, "latency_s": 1.291}, {"task_id": "gsm8k-139", "model": "openai/gpt-5.6-luna", "prompt": "In a candy machine, there are 22 more than four times the number of pink gumballs as there are blue gumballs. If there are 12 blue gumballs how many pink ones are there?\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": "Let \\(p\\) be the number of pink gumballs and \\(b\\) the number of blue gumballs.\n\nThe relationship is:\n\\[\np=4b+22\n\\]\n\nSubstitute \\(b=12\\):\n\\[\np=4(12)+22=48+22=70\n\\]\n\n70", "cost_usd": 0.000158, "tokens_in": 94, "tokens_out": 116, "latency_s": 2.943}, {"task_id": "gsm8k-409", "model": "openai/gpt-5.6-luna", "prompt": "Carolyn works for a delivery service company that hires on a contract basis. In May, they hired 40 employees, paying each employee $15 per hour for a 40-hour workweek. In June, 1/4 of the employees' contracts expired. Calculate the total amount of money the company paid to the employees in the 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:\n- 40 employees \u00d7 $15/hour \u00d7 40 hours = $24,000\n\nJune:\n- 1/4 of 40 = 10 contracts expired\n- 40 \u2212 10 = 30 employees\n- 30 \u00d7 $15/hour \u00d7 40 hours = $18,000\n\nTotal:\n- $24,000 + $18,000 = $42,000\n\n42000", "cost_usd": 0.000234, "tokens_in": 120, "tokens_out": 175, "latency_s": 2.722}, {"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    ranks = [0] * n\n    rank = 1\n\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            ranks[i] = rank\n        rank += len(indices)\n\n    sys.stdout.write(\"\\n\".join(map(str, ranks)))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.00030800000000000006, "tokens_in": 766, "tokens_out": 129, "latency_s": 1.718}, {"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    determined = [False] * n\n    ranks = [0] * n\n    r = 1\n\n    while not all(determined):\n        maximum = max(scores[i] for i in range(n) if not determined[i])\n        indices = [\n            i for i in range(n)\n            if not determined[i] and scores[i] == maximum\n        ]\n\n        for i in indices:\n            ranks[i] = r\n            determined[i] = True\n\n        r += len(indices)\n\n    sys.stdout.write(\"\\n\".join(map(str, ranks)) + \"\\n\")\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.py SEED SIZE\")\n\n    seed = int(sys.argv[1])\n    n = max(1, min(100, int(sys.argv[2])))\n    random.seed(seed)\n\n    family = seed % 10\n\n    if family == 0:\n        scores = [100] * n\n    elif family == 1:\n        scores = [1] * n\n    elif family == 2:\n        scores = list(range(1, n + 1))\n        random.shuffle(scores)\n    elif family == 3:\n        scores = [100 - (i % 2) for i in range(n)]\n        random.shuffle(scores)\n    elif family == 4:\n        values = [1, 50, 100]\n        scores = [random.choice(values) for _ in range(n)]\n    elif family == 5:\n        scores = [random.randint(1, 100) for _ in range(n)]\n        if n >= 2:\n            scores[0] = 1\n            scores[-1] = 100\n    elif family == 6:\n        scores = [1 + (i * 99 // max(1, n - 1)) for i in range(n)]\n        random.shuffle(scores)\n    elif family == 7:\n        scores = [random.choice([1, 2, 99, 100]) for _ in range(n)]\n        if n >= 3:\n            scores[0] = 100\n            scores[1] = 100\n            scores[2] = 1\n    elif family == 8:\n        scores = [random.randint(1, 5) for _ in range(n)]\n    else:\n        scores = [random.randint(1, 100) for _ in range(n)]\n        if n >= 4:\n            scores[:4] = [1, 1, 100, 100]\n            random.shuffle(scores)\n\n    print(n)\n    print(*scores)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0012929999999999999, "tokens_in": 819, "tokens_out": 941, "latency_s": 11.479}, {"task_id": "lcb-abc392_d", "model": "openai/gpt-5.6-luna", "prompt": "There are N dice.\r\nThe i-th die has K_i faces, with the numbers A_{i,1}, A_{i,2}, \\ldots, A_{i,K_i} written on them.\r\nWhen you roll this die, each face appears with probability \\frac{1}{K_i}.\nYou choose two dice from the N dice and roll them.\r\nDetermine the maximum probability that the two dice show the same number, when the dice are chosen optimally.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nK_1 A_{1,1} A_{1,2} \\dots A_{1,K_1}\r\n\\vdots\r\nK_N A_{N,1} A_{N,2} \\dots A_{N,K_N}\n\nOutput\n\nPrint the answer.\r\nYour answer is considered correct if the absolute or relative error from the true solution does not exceed 10^{-8}.\n\nConstraints\n\n\n- 2 \\leq N \\leq 100\n- 1 \\leq K_i\n- K_1 + K_2 + \\dots + K_N \\leq 10^5\n- 1 \\leq A_{i,j} \\leq 10^5\n- All input values are integers.\n\nSample Input 1\n\n3\r\n3 1 2 3\r\n4 1 2 2 1\r\n6 1 2 3 4 5 6\n\nSample Output 1\n\n0.333333333333333\r\n\n\n- When choosing the 1st and 2nd dice, the probability that the outcomes are the same is \\frac{1}{3}.\n- When choosing the 1st and 3rd dice, the probability is \\frac{1}{6}.\n- When choosing the 2nd and 3rd dice, the probability is \\frac{1}{6}.\n\nTherefore, the maximum probability is \\frac{1}{3} = 0.3333333333\\ldots.\n\nSample Input 2\n\n3\r\n5 1 1 1 1 1\r\n4 2 2 2 2\r\n3 1 1 2\n\nSample Output 2\n\n0.666666666666667\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\nfrom collections import Counter\n\ndata = list(map(int, sys.stdin.buffer.read().split()))\nidx = 0\nn = data[idx]\nidx += 1\n\ndice = []\nfor _ in range(n):\n    k = data[idx]\n    idx += 1\n    counts = Counter(data[idx:idx + k])\n    idx += k\n    dice.append((k, counts))\n\nbest_num = -1\nbest_den = 1\n\nfor i in range(n):\n    k1, c1 = dice[i]\n    for j in range(i + 1, n):\n        k2, c2 = dice[j]\n        if len(c1) <= len(c2):\n            small, large = c1, c2\n        else:\n            small, large = c2, c1\n\n        numerator = sum(count * large.get(value, 0) for value, count in small.items())\n        denominator = k1 * k2\n\n        if numerator * best_den > best_num * denominator:\n            best_num = numerator\n            best_den = denominator\n\nprint(f\"{best_num / best_den:.15f}\")", "cost_usd": 0.0014825999999999997, "tokens_in": 621, "tokens_out": 1132, "latency_s": 14.513}, {"task_id": "lcb-abc392_d", "model": "openai/gpt-5.6-luna", "prompt": "There are N dice.\r\nThe i-th die has K_i faces, with the numbers A_{i,1}, A_{i,2}, \\ldots, A_{i,K_i} written on them.\r\nWhen you roll this die, each face appears with probability \\frac{1}{K_i}.\nYou choose two dice from the N dice and roll them.\r\nDetermine the maximum probability that the two dice show the same number, when the dice are chosen optimally.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nK_1 A_{1,1} A_{1,2} \\dots A_{1,K_1}\r\n\\vdots\r\nK_N A_{N,1} A_{N,2} \\dots A_{N,K_N}\n\nOutput\n\nPrint the answer.\r\nYour answer is considered correct if the absolute or relative error from the true solution does not exceed 10^{-8}.\n\nConstraints\n\n\n- 2 \\leq N \\leq 100\n- 1 \\leq K_i\n- K_1 + K_2 + \\dots + K_N \\leq 10^5\n- 1 \\leq A_{i,j} \\leq 10^5\n- All input values are integers.\n\nSample Input 1\n\n3\r\n3 1 2 3\r\n4 1 2 2 1\r\n6 1 2 3 4 5 6\n\nSample Output 1\n\n0.333333333333333\r\n\n\n- When choosing the 1st and 2nd dice, the probability that the outcomes are the same is \\frac{1}{3}.\n- When choosing the 1st and 3rd dice, the probability is \\frac{1}{6}.\n- When choosing the 2nd and 3rd dice, the probability is \\frac{1}{6}.\n\nTherefore, the maximum probability is \\frac{1}{3} = 0.3333333333\\ldots.\n\nSample Input 2\n\n3\r\n5 1 1 1 1 1\r\n4 2 2 2 2\r\n3 1 1 2\n\nSample Output 2\n\n0.666666666666667\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\n\ndef solve():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    if not data:\n        return\n\n    n = data[0]\n    pos = 1\n    dice = []\n\n    for _ in range(n):\n        k = data[pos]\n        pos += 1\n        faces = data[pos:pos + k]\n        pos += k\n        dice.append(faces)\n\n    best = 0.0\n\n    for i in range(n):\n        for j in range(i + 1, n):\n            same = 0\n            for x in dice[i]:\n                for y in dice[j]:\n                    if x == y:\n                        same += 1\n            probability = same / (len(dice[i]) * len(dice[j]))\n            if probability > best:\n                best = probability\n\n    print(f\"{best:.15f}\")\n\n\nif __name__ == \"__main__\":\n    solve()\n```\n\n```generator\nimport random\nimport sys\n\n\ndef generate(seed, size):\n    random.seed(seed)\n\n    n = max(2, min(100, size if size > 0 else 2))\n    dice = []\n\n    families = [\n        \"constant\",\n        \"range\",\n        \"repeated\",\n        \"mixed\",\n        \"endpoint\",\n        \"pair\",\n    ]\n\n    for i in range(n):\n        family = random.choice(families)\n\n        if family == \"constant\":\n            k = random.randint(1, max(1, min(12, size + 1)))\n            value = random.choice([1, 2, 100000, random.randint(1, 100000)])\n            faces = [value] * k\n\n        elif family == \"range\":\n            k = random.randint(1, max(1, min(15, size + 2)))\n            start = random.randint(1, 100001 - k)\n            faces = list(range(start, start + k))\n            random.shuffle(faces)\n\n        elif family == \"repeated\":\n            k = random.randint(1, max(1, min(20, size + 3)))\n            pool_size = random.randint(1, min(5, k))\n            pool = [\n                random.choice([1, 100000, random.randint(1, 100000)])\n                for _ in range(pool_size)\n            ]\n            faces = [random.choice(pool) for _ in range(k)]\n\n        elif family == \"mixed\":\n            k = random.randint(1, max(1, min(20, size + 4)))\n            faces = []\n            for _ in range(k):\n                choice = random.randrange(5)\n                if choice == 0:\n                    faces.append(1)\n                elif choice == 1:\n                    faces.append(100000)\n                else:\n                    faces.append(random.randint(1, 100000))\n\n        elif family == \"endpoint\":\n            k = random.randint(1, max(1, min(12, size + 2)))\n            faces = [1, 100000][:k]\n            while len(faces) < k:\n                faces.append(random.choice([1, 100000]))\n\n        else:\n            k = random.randint(1, max(1, min(16, size + 3)))\n            a = random.randint(1, 100000)\n            b = random.randint(1, 100000)\n            faces = [a if random.random() < 0.5 else b for _ in range(k)]\n\n        dice.append(faces)\n\n    total = sum(len(x) for x in dice)\n    if total > 100000:\n        scale = 100000 / total\n        dice = [\n            faces[:max(1, int(len(faces) * scale))]\n            for faces in dice\n        ]\n\n    print(n)\n    for faces in dice:\n        print(len(faces), *faces)\n\n\nif __name__ == \"__main__\":\n    seed = int(sys.argv[1]) if len(sys.argv) > 1 else 0\n    size = int(sys.argv[2]) if len(sys.argv) > 2 else 10\n    generate(seed, size)\n```", "cost_usd": 0.0016204000000000001, "tokens_in": 674, "tokens_out": 1238, "latency_s": 11.012}]