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+[{"task_id": "mmlu-1820", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Negative residual autocorrelation is indicated by which one of the following?\nA) A cyclical pattern in the residuals\nB) An alternating pattern in the residuals\nC) A complete randomness in the residuals\nD) Residuals that are all close to zero\n\nAnswer with the letter only.", "response": "B", "cost_usd": 1.02e-05, "tokens_in": 72, "tokens_out": 5, "latency_s": 1.806}, {"task_id": "mmlu-6095", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Which of the following does NOT usually occur to the lens of the eye as one grows older?\nA) It becomes thicker\nB) It yellows\nC) It becomes clouded\nD) It fills with fluid\n\nAnswer with the letter only.", "response": "D", "cost_usd": 9.100000000000001e-06, "tokens_in": 61, "tokens_out": 5, "latency_s": 0.81}, {"task_id": "gsm8k-333", "model": "openai/gpt-5.6-luna", "prompt": "Robert wants to buy a bookshelf and a sofa and has received two offers. Furniture United's offer includes a $1,350 advance payment and 6 monthly installments of $350 each. Cozy Homes' offer includes a $1,100 advance payment and 9 monthly installments of $250 each. What is the cost difference between the two offers?\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": "Furniture United: \\(1{,}350 + 6 \\times 350 = 3{,}450\\)\n\nCozy Homes: \\(1{,}100 + 9 \\times 250 = 3{,}350\\)\n\nCost difference: \\(3{,}450 - 3{,}350 = 100\\)\n\n100", "cost_usd": 9.289999999999998e-05, "tokens_in": 119, "tokens_out": 135, "latency_s": 2.615}, {"task_id": "gsm8k-507", "model": "openai/gpt-5.6-luna", "prompt": "Janet takes two bus trips five days a week. If each bus trip costs her $2.20, how much would she save by buying a weekly bus pass for $20?\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": "Two bus trips per day for five days means:\n\n2 \u00d7 5 = 10 trips\n\nAt $2.20 per trip:\n\n10 \u00d7 $2.20 = $22\n\nSavings:\n\n$22 \u2212 $20 = $2\n\n2", "cost_usd": 6.69e-05, "tokens_in": 87, "tokens_out": 97, "latency_s": 2.701}, {"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.read().split()))\n    n = data[0]\n    scores = data[1:1 + n]\n\n    sorted_scores = sorted(scores, reverse=True)\n    rank = {}\n    for i, score in enumerate(sorted_scores, 1):\n        if score not in rank:\n            rank[score] = i\n\n    print(\"\\n\".join(str(rank[score]) for score in scores))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.0001666, "tokens_in": 766, "tokens_out": 150, "latency_s": 3.237}, {"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 = set(range(n))\n    ranks = [0] * n\n    rank = 1\n\n    while undetermined:\n        maximum = max(scores[i] for i in undetermined)\n        group = [i for i in undetermined if scores[i] == maximum]\n\n        for i in group:\n            ranks[i] = rank\n            undetermined.remove(i)\n\n        rank += 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 family == 0:\n        scores = [random.randint(1, 100) for _ in range(n)]\n    elif family == 1:\n        values = random.sample(range(1, 101), min(3, n))\n        scores = [random.choice(values) for _ in range(n)]\n    elif family == 2:\n        scores = [random.choice([1, 100]) for _ in range(n)]\n    elif family == 3:\n        scores = list(range(1, n + 1))\n        random.shuffle(scores)\n    elif family == 4:\n        scores = [random.randint(1, 5) for _ in range(n)]\n    elif family == 5:\n        scores = [100 - (i % min(n, 10)) for i in range(n)]\n        random.shuffle(scores)\n    elif family == 6:\n        scores = [1] * n\n        if n > 1:\n            scores[random.randrange(n)] = 100\n        if n > 2:\n            scores[random.randrange(n)] = 99\n    else:\n        scores = []\n        while len(scores) < n:\n            value = random.choice([1, 2, 50, 51, 99, 100])\n            count = min(n - len(scores), random.randint(1, max(1, n // 3)))\n            scores.extend([value] * count)\n        random.shuffle(scores)\n\n    print(n)\n    print(*scores)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0005781, "tokens_in": 819, "tokens_out": 827, "latency_s": 7.529}, {"task_id": "lcb-abc399_c", "model": "openai/gpt-5.6-luna", "prompt": "You are given a simple undirected graph with N vertices and M edges, where the vertices are labeled 1 to N. The i-th edge connects vertices u_i and v_i.\r\nWhat is the minimum number of edges that need to be deleted from this graph so that the graph becomes a forest?\n\nWhat is a forest?\r\n\r\nA simple undirected graph F is called a forest if and only if F does not contain any cycle.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nu_1 v_1\r\nu_2 v_2\r\n\\vdots\r\nu_M v_M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- 0 \\leq M \\leq \\min \\left( \\frac{N(N-1)}{2}, 2 \\times 10^5\\right)\n- 1 \\leq u_i < v_i \\leq N\n- The given graph is simple.\n- All input values are integers.\n\nSample Input 1\n\n4 4\r\n1 2\r\n1 3\r\n2 4\r\n3 4\n\nSample Output 1\n\n1\r\n\nFor example, if you delete the first edge, the graph becomes a forest.\n\nSample Input 2\n\n5 0\n\nSample Output 2\n\n0\n\nSample Input 3\n\n10 10\r\n7 9\r\n4 6\r\n6 10\r\n2 5\r\n5 6\r\n5 9\r\n6 8\r\n4 8\r\n1 5\r\n1 4\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    if not data:\n        return\n\n    n, m = data[0], data[1]\n    parent = list(range(n + 1))\n    size = [1] * (n + 1)\n\n    def find(x):\n        while parent[x] != x:\n            parent[x] = parent[parent[x]]\n            x = parent[x]\n        return x\n\n    unions = 0\n    idx = 2\n    for _ in range(m):\n        u, v = data[idx], data[idx + 1]\n        idx += 2\n        ru, rv = find(u), find(v)\n        if ru != rv:\n            if size[ru] < size[rv]:\n                ru, rv = rv, ru\n            parent[rv] = ru\n            size[ru] += size[rv]\n            unions += 1\n\n    print(m - unions)\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.00022830000000000007, "tokens_in": 495, "tokens_out": 298, "latency_s": 3.424}, {"task_id": "lcb-abc399_c", "model": "openai/gpt-5.6-luna", "prompt": "You are given a simple undirected graph with N vertices and M edges, where the vertices are labeled 1 to N. The i-th edge connects vertices u_i and v_i.\r\nWhat is the minimum number of edges that need to be deleted from this graph so that the graph becomes a forest?\n\nWhat is a forest?\r\n\r\nA simple undirected graph F is called a forest if and only if F does not contain any cycle.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nu_1 v_1\r\nu_2 v_2\r\n\\vdots\r\nu_M v_M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- 0 \\leq M \\leq \\min \\left( \\frac{N(N-1)}{2}, 2 \\times 10^5\\right)\n- 1 \\leq u_i < v_i \\leq N\n- The given graph is simple.\n- All input values are integers.\n\nSample Input 1\n\n4 4\r\n1 2\r\n1 3\r\n2 4\r\n3 4\n\nSample Output 1\n\n1\r\n\nFor example, if you delete the first edge, the graph becomes a forest.\n\nSample Input 2\n\n5 0\n\nSample Output 2\n\n0\n\nSample Input 3\n\n10 10\r\n7 9\r\n4 6\r\n6 10\r\n2 5\r\n5 6\r\n5 9\r\n6 8\r\n4 8\r\n1 5\r\n1 4\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\nfrom itertools import combinations\n\ndef is_forest(n, edges, mask):\n    parent = list(range(n))\n    size = [1] * n\n\n    def find(x):\n        while parent[x] != x:\n            parent[x] = parent[parent[x]]\n            x = parent[x]\n        return x\n\n    for i, (u, v) in enumerate(edges):\n        if not (mask >> i) & 1:\n            continue\n        ru, rv = find(u), find(v)\n        if ru == rv:\n            return False\n        if size[ru] < size[rv]:\n            ru, rv = rv, ru\n        parent[rv] = ru\n        size[ru] += size[rv]\n    return True\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    if not data:\n        return\n    n, m = data[0], data[1]\n    edges = []\n    p = 2\n    for _ in range(m):\n        edges.append((data[p] - 1, data[p + 1] - 1))\n        p += 2\n\n    best = m\n    for mask in range(1 << m):\n        kept = mask.bit_count()\n        if m - kept >= best:\n            continue\n        if is_forest(n, edges, mask):\n            best = m - kept\n\n    print(best)\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    size = max(1, int(sys.argv[2]))\n    random.seed(seed)\n\n    n = min(2 * 10**5, max(1, size))\n    all_edges = [(u, v) for u in range(1, n + 1) for v in range(u + 1, n + 1)]\n\n    family = seed % 8\n    if n == 1:\n        chosen = []\n    elif family == 0:\n        chosen = all_edges[:min(len(all_edges), max(0, n - 1))]\n    elif family == 1:\n        chosen = all_edges[:min(len(all_edges), n)]\n    elif family == 2:\n        target = min(len(all_edges), max(0, 2 * n - 3))\n        chosen = random.sample(all_edges, target)\n    elif family == 3:\n        target = min(len(all_edges), max(0, n // 2))\n        chosen = random.sample(all_edges, target)\n    elif family == 4:\n        target = min(len(all_edges), max(0, n * 2))\n        chosen = random.sample(all_edges, target)\n    elif family == 5:\n        chosen = []\n        for v in range(2, n + 1):\n            chosen.append((1, v))\n        extra = min(len(all_edges) - len(chosen), max(0, n // 2))\n        remaining = [e for e in all_edges if e not in set(chosen)]\n        chosen += random.sample(remaining, extra)\n    elif family == 6:\n        target = min(len(all_edges), max(0, n - 1))\n        chosen = random.sample(all_edges, target)\n    else:\n        target = min(len(all_edges), max(0, 3 * n - 6))\n        chosen = random.sample(all_edges, target)\n\n    random.shuffle(chosen)\n    print(n, len(chosen))\n    for u, v in chosen:\n        print(u, v)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0006962000000000001, "tokens_in": 548, "tokens_out": 1069, "latency_s": 8.571}]