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+[{"task_id": "mmlu-4134", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] In order to go from national income to GDP one must\nA) add depreciation expenses\nB) add indirect taxes\nC) subtract subsidies\nD) all of the above\n\nAnswer with the letter only.", "response": "D", "cost_usd": 4.6e-05, "tokens_in": 52, "tokens_out": 68, "latency_s": 3.349}, {"task_id": "mmlu-6905", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] You've just finished training a decision tree for spam classification, and it is getting abnormally bad performance on both your training and test sets. You know that your implementation has no bugs, so what could be causing the problem?\nA) Your decision trees are too shallow.\nB) You need to increase the learning rate.\nC) You are overfitting.\nD) None of the above.\n\nAnswer with the letter only.", "response": "A", "cost_usd": 3.399999999999999e-05, "tokens_in": 94, "tokens_out": 41, "latency_s": 2.385}, {"task_id": "gsm8k-898", "model": "openai/gpt-5.6-luna", "prompt": "Dijana and Anis live near a lake, and every weekend they go out rowing into the lake. On a Sunday morning, both went out rowing, and Dijana rowed for 50 miles the whole day. Anis rowed 1/5 times more miles than Dijana. Calculate the total distance the two of them rowed on that day.\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and put only the final numeric result on the last line. Audit marker 11392010794869878572 is answer-independent metadata; do not reproduce it.", "response": "Dijana rowed 50 miles.\n\nAnis rowed \\( \\frac{1}{5} \\) more than Dijana:\n\n\\[\n50+\\frac{1}{5}\\times 50=50+10=60\n\\]\n\nTogether, they rowed:\n\n\\[\n50+60=110\n\\]\n\n110", "cost_usd": 0.0001068, "tokens_in": 132, "tokens_out": 156, "latency_s": 2.821}, {"task_id": "gsm8k-697", "model": "openai/gpt-5.6-luna", "prompt": "Great Grandma Jones has three children.  And each of her children has three children of their own, who are Great Grandma Jones' grandchildren.  And each of these grandchildren has three babies of their own, who are Great Grandma Jones' great grand-babies.  If all of the family show up at the family reunion, how many great grand-babies will be there for Great Grandma Jones to kiss?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and put only the final numeric result on the last line. Audit marker 11235256677412606211 is answer-independent metadata; do not reproduce it.", "response": "Great Grandma Jones has 3 children.\n\nEach child has 3 children:\n3 \u00d7 3 = 9 grandchildren.\n\nEach of the 9 grandchildren has 3 babies:\n9 \u00d7 3 = 27 great-grandbabies.\n\n27", "cost_usd": 8.830000000000003e-05, "tokens_in": 139, "tokens_out": 124, "latency_s": 2.664}, {"task_id": "lcb-abc395_b", "model": "openai/gpt-5.6-luna", "prompt": "Overview: Create an N \\times N pattern as follows.\n\n###########\n#.........#\n#.#######.#\n#.#.....#.#\n#.#.###.#.#\n#.#.#.#.#.#\n#.#.###.#.#\n#.#.....#.#\n#.#######.#\n#.........#\n###########\n\n\nYou are given a positive integer N.\nConsider an N \\times N grid. Let (i,j) denote the cell at the i-th row from the top and the j-th column from the left. Initially, no cell is colored.\nThen, for i = 1,2,\\dots,N in order, perform the following operation:\n\n- Let j = N + 1 - i.\n- If i \\leq j, fill the rectangular region whose top-left cell is (i,i) and bottom-right cell is (j,j) with black if i is odd, or white if i is even. If some cells are already colored, overwrite their colors.  \n- If i > j, do nothing.\n\nAfter all these operations, it can be proved that there are no uncolored cells. Determine the final color of each cell.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint N lines. The i-th line should contain a length-N string S_i representing the colors of the i-th row of the grid after all operations, as follows:\n\n- If cell (i,j) is finally colored black, the j-th character of S_i should be #.\n- If cell (i,j) is finally colored white, the j-th character of S_i should be ..\n\nConstraints\n\n\n- 1 \\leq N \\leq 50\n- All input values are integers.\n\nSample Input 1\n\n11\n\nSample Output 1\n\n###########\n#.........#\n#.#######.#\n#.#.....#.#\n#.#.###.#.#\n#.#.#.#.#.#\n#.#.###.#.#\n#.#.....#.#\n#.#######.#\n#.........#\n###########\n\nThis matches the pattern shown in the Overview.\n\nSample Input 2\n\n5\n\nSample Output 2\n\n#####\n#...#\n#.#.#\n#...#\n#####\n\nColors are applied as follows, where ? denotes a cell not yet colored:\n         i=1      i=2      i=3      i=4      i=5\n?????    #####    #####    #####    #####    #####\n?????    #####    #...#    #...#    #...#    #...#\n????? -> ##### -> #...# -> #.#.# -> #.#.# -> #.#.#\n?????    #####    #...#    #...#    #...#    #...#\n?????    #####    #####    #####    #####    #####\n\nSample Input 3\n\n8\n\nSample Output 3\n\n########\n#......#\n#.####.#\n#.#..#.#\n#.#..#.#\n#.####.#\n#......#\n########\n\nSample Input 4\n\n2\n\nSample Output 4\n\n##\n##\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 a complete solution from the full statement and constraints. Privately create a small-state specification and use it to challenge your algorithm. Check boundaries, ordering, multiplicity, repeated values, overflow, and complexity. Trace every published example and return only complete raw Python 3 source with no Markdown or prose.", "response": "import sys\n\nn = int(sys.stdin.buffer.readline())\n\ngrid = [['?'] * n for _ in range(n)]\n\nfor i in range(n):\n    j = n - 1 - i\n    if i <= j:\n        color = '#' if i % 2 == 0 else '.'\n        for r in range(i, j + 1):\n            for c in range(i, j + 1):\n                grid[r][c] = color\n\nprint('\\n'.join(''.join(row) for row in grid))", "cost_usd": 0.00037280000000000006, "tokens_in": 728, "tokens_out": 500, "latency_s": 4.714}, {"task_id": "lcb-abc395_b", "model": "google/gemini-3.6-flash", "prompt": "Overview: Create an N \\times N pattern as follows.\n\n###########\n#.........#\n#.#######.#\n#.#.....#.#\n#.#.###.#.#\n#.#.#.#.#.#\n#.#.###.#.#\n#.#.....#.#\n#.#######.#\n#.........#\n###########\n\n\nYou are given a positive integer N.\nConsider an N \\times N grid. Let (i,j) denote the cell at the i-th row from the top and the j-th column from the left. Initially, no cell is colored.\nThen, for i = 1,2,\\dots,N in order, perform the following operation:\n\n- Let j = N + 1 - i.\n- If i \\leq j, fill the rectangular region whose top-left cell is (i,i) and bottom-right cell is (j,j) with black if i is odd, or white if i is even. If some cells are already colored, overwrite their colors.  \n- If i > j, do nothing.\n\nAfter all these operations, it can be proved that there are no uncolored cells. Determine the final color of each cell.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint N lines. The i-th line should contain a length-N string S_i representing the colors of the i-th row of the grid after all operations, as follows:\n\n- If cell (i,j) is finally colored black, the j-th character of S_i should be #.\n- If cell (i,j) is finally colored white, the j-th character of S_i should be ..\n\nConstraints\n\n\n- 1 \\leq N \\leq 50\n- All input values are integers.\n\nSample Input 1\n\n11\n\nSample Output 1\n\n###########\n#.........#\n#.#######.#\n#.#.....#.#\n#.#.###.#.#\n#.#.#.#.#.#\n#.#.###.#.#\n#.#.....#.#\n#.#######.#\n#.........#\n###########\n\nThis matches the pattern shown in the Overview.\n\nSample Input 2\n\n5\n\nSample Output 2\n\n#####\n#...#\n#.#.#\n#...#\n#####\n\nColors are applied as follows, where ? denotes a cell not yet colored:\n         i=1      i=2      i=3      i=4      i=5\n?????    #####    #####    #####    #####    #####\n?????    #####    #...#    #...#    #...#    #...#\n????? -> ##### -> #...# -> #.#.# -> #.#.# -> #.#.#\n?????    #####    #...#    #...#    #...#    #...#\n?????    #####    #####    #####    #####    #####\n\nSample Input 3\n\n8\n\nSample Output 3\n\n########\n#......#\n#.####.#\n#.#..#.#\n#.#..#.#\n#.####.#\n#......#\n########\n\nSample Input 4\n\n2\n\nSample Output 4\n\n##\n##\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 without seeing another solution. Return one raw executable Python program derived by a structurally different route. Oracle must be a simple correctness-first program for small legal inputs and must not reuse the candidate algorithm. Generator must accept seed and size arguments, seed Python random, and print one varied legal input. Append oracle lines between comments `# ORACLE-BEGIN` and `# ORACLE-END`, prefixing every line with `#|`. Append generator lines the same way between `# GENERATOR-BEGIN` and `# GENERATOR-END`. Those comment sections must be inert when the complete response is executed as the candidate.", "response": "import sys\n\n\ndef main():\n    input = sys.stdin.read\n    data = input().split()\n    if not data:\n        return\n    N = int(data[0])\n    ans = []\n    for r in range(N):\n        row = []\n        for c in range(N):\n            d = min(r, N - 1 - r, c, N - 1 - c)\n            if d % 2 == 0:\n                row.append(\"#\")\n            else:\n                row.append(\".\")\n        ans.append(\"\".join(row))\n    print(\"\\n\".join(ans))\n\n\nif __name__ == \"__main__\":\n    main()\n\n# ORACLE-BEGIN\n#| import sys\n#|\n#| def oracle_solve(N):\n#|     grid = [['?'] * N for _ in range(N)]\n#|     for i in range(1, N + 1):\n#|         j = N + 1 - i\n#|         if i <= j:\n#|             color = '#' if i % 2 == 1 else '.'\n#|             for r in range(i - 1, j):\n#|                 for c in range(i - 1, j):\n#|                     grid[r][c] = color\n#|         else:\n#|             break\n#|     return \"\\n\".join(\"\".join(row) for row in grid)\n#|\n#| if __name__ == \"__main__\":\n#|     data = sys.stdin.read().split()\n#|     if data:\n#|         print(oracle_solve(int(data[0])))\n# ORACLE-END\n\n# GENERATOR-BEGIN\n#| import sys\n#| import random\n#|\n#| def main():\n#|     args = sys.argv[1:]\n#|     seed = int(args[0]) if len(args) > 0 else 42\n#|     size = int(args[1]) if len(args) > 1 else 50\n#|     random.seed(seed)\n#|     max_n = max(1, min(50, size))\n#|     N = random.randint(1, max_n)\n#|     print(N)\n#|\n#| if __name__ == \"__main__\":\n#|     main()\n# GENERATOR-END", "cost_usd": 0.00879675, "tokens_in": 824, "tokens_out": 2181, "latency_s": 9.974}, {"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 a complete solution from the full statement and constraints. Privately create a small-state specification and use it to challenge your algorithm. Check boundaries, ordering, multiplicity, repeated values, overflow, and complexity. Trace every published example and return only complete raw Python 3 source with no Markdown or prose.", "response": "import sys\nfrom collections import Counter\n\ndef main():\n    data = iter(map(int, sys.stdin.buffer.read().split()))\n    n = next(data)\n\n    ks = []\n    groups = [[] for _ in range(100001)]\n\n    for i in range(n):\n        k = next(data)\n        ks.append(k)\n        counts = Counter(next(data) for _ in range(k))\n        for value, count in counts.items():\n            groups[value].append((i, count))\n\n    scores = [0] * (n * n)\n\n    for occurrences in groups:\n        m = len(occurrences)\n        for x in range(m):\n            i, ci = occurrences[x]\n            base = i * n\n            for y in range(x + 1, m):\n                j, cj = occurrences[y]\n                scores[base + j] += ci * cj\n\n    answer = 0.0\n    for i in range(n):\n        base = i * n\n        for j in range(i + 1, n):\n            probability = scores[base + j] / (ks[i] * ks[j])\n            if probability > answer:\n                answer = probability\n\n    print(\"{:.15f}\".format(answer))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.0008374000000000003, "tokens_in": 568, "tokens_out": 1301, "latency_s": 14.084}]