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+[{"task_id": "mmlu-2226", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] All of Bella\u2019s photos are in 8 photo books. Each photo book has 25 photos. Which expression shows how to find the total number of photos Bella has?\nA) 25 \u00f7 8\nB) 25 \u2013 8\nC) 25 + 8\nD) 25 \u00d7 8\n\nAnswer with the letter only.", "response": "D", "cost_usd": 1.13e-05, "tokens_in": 83, "tokens_out": 5, "latency_s": 1.688}, {"task_id": "mmlu-4042", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] If the economy is experiencing a recession how will a plan to decrease taxes for consumers and increase spending on government purchases affect real gross domestic product (GDP) and the price level?\nA) real GDP rises and the price level falls.\nB) real GDP falls and the price level rises.\nC) real GDP rises and the price level rises.\nD) real GDP falls and the price level falls.\n\nAnswer with the letter only.", "response": "C", "cost_usd": 1.2500000000000002e-05, "tokens_in": 95, "tokens_out": 5, "latency_s": 0.755}, {"task_id": "gsm8k-324", "model": "openai/gpt-5.6-luna", "prompt": "Ralph has a record store where people can trade their own records for new ones. People can trade 2 old records for 1 new one. 5 people come in with old records and leave with 7 new records between them. How many old records did the 5 people bring in?\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": "Each new record requires 2 old records.\n\nFor 7 new records:\n\n\\(7 \\times 2 = 14\\) old records.\n\n14", "cost_usd": 8.24e-05, "tokens_in": 110, "tokens_out": 119, "latency_s": 2.939}, {"task_id": "gsm8k-1302", "model": "openai/gpt-5.6-luna", "prompt": "Matthew has a collection of 12 unique toy soldiers. He wants to sell them for a fair price. He found a buyer who is willing to pay for half his collection $5 per toy, and for the other half $7 per toy. If Matthew would agree to that offer, how much money would he earn?\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": "1. Half of 12 toy soldiers is 6.\n2. Six sold at $5 each earn \\(6 \\times 5 = 30\\).\n3. The other six sold at $7 each earn \\(6 \\times 7 = 42\\).\n4. Total earnings: \\(30 + 42 = 72\\).\n\n72", "cost_usd": 8.999999999999999e-05, "tokens_in": 114, "tokens_out": 131, "latency_s": 2.789}, {"task_id": "lcb-abc398_a", "model": "openai/gpt-5.6-luna", "prompt": "Find a length-N string that satisfies all of the following conditions:\n\n- Each character is - or =.\n- It is a palindrome.\n- It contains exactly one or exactly two =s. If it contains two =s, they are adjacent.\n\nSuch a string is unique.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- N is an integer.\n\nSample Input 1\n\n4\n\nSample Output 1\n\n-==-\n\nSample Input 2\n\n7\n\nSample Output 2\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 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": "n = int(input())\nif n % 2:\n    k = n // 2\n    print(\"-\" * k + \"=\" + \"-\" * k)\nelse:\n    k = n // 2 - 1\n    print(\"-\" * k + \"==\" + \"-\" * k)", "cost_usd": 0.0001356, "tokens_in": 282, "tokens_out": 179, "latency_s": 4.807}, {"task_id": "lcb-abc398_a", "model": "openai/gpt-5.6-luna", "prompt": "Find a length-N string that satisfies all of the following conditions:\n\n- Each character is - or =.\n- It is a palindrome.\n- It contains exactly one or exactly two =s. If it contains two =s, they are adjacent.\n\nSuch a string is unique.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- N is an integer.\n\nSample Input 1\n\n4\n\nSample Output 1\n\n-==-\n\nSample Input 2\n\n7\n\nSample Output 2\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 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\nimport itertools\n\ndef solve(n):\n    for chars in itertools.product(\"-=\", repeat=n):\n        s = \"\".join(chars)\n        if s != s[::-1]:\n            continue\n        positions = [i for i, c in enumerate(s) if c == \"=\"]\n        if len(positions) == 1:\n            return s\n        if len(positions) == 2 and positions[1] == positions[0] + 1:\n            return s\n    raise ValueError(\"No valid string\")\n\nn = int(sys.stdin.readline())\nprint(solve(n))\n```\n\n```generator\nimport random\nimport sys\n\nseed = int(sys.argv[1])\nsize = max(1, int(sys.argv[2]))\nrandom.seed(seed)\n\nchoices = list(range(1, size + 1))\nif size >= 2:\n    choices.extend([1, 2, size])\nif size >= 3:\n    choices.extend([3, size - 1])\nn = random.choice(choices)\n\nprint(n)\n```", "cost_usd": 0.00047509999999999995, "tokens_in": 335, "tokens_out": 736, "latency_s": 10.332}, {"task_id": "lcb-abc400_d", "model": "openai/gpt-5.6-luna", "prompt": "Takahashi is about to go buy eel at a fish shop.\nThe town where he lives is divided into a grid of H rows and W columns. Each cell is either a road or a wall.\r\nLet us denote the cell at the i-th row from the top (1\\leq i \\leq H) and the j-th column from the left (1\\leq j \\leq W) as cell (i,j).\r\nInformation about each cell is given by H strings S_1,S_2,\\ldots,S_H, each of length W. Specifically, if the j-th character of S_i (1\\leq i \\leq H,1\\leq j\\leq W) is ., cell (i,j) is a road; if it is #, cell (i,j) is a wall.\nHe can repeatedly perform the following two types of actions in any order:\n\n- Move to an adjacent cell (up, down, left, or right) that is within the town and is a road.\n- Choose one of the four directions (up, down, left, or right) and perform a front kick in that direction.\r\n  When he performs a front kick, for each of the cells at most 2 steps away in that direction from the cell he is currently in, if that cell is a wall, it becomes a road.\r\n  If some of the cells at most 2 steps away are outside the town, a front kick can still be performed, but anything outside the town does not change.\n\nHe starts in cell (A,B), and he wants to move to the fish shop in cell (C,D).\r\nIt is guaranteed that both the cell where he starts and the cell with the fish shop are roads.\r\nFind the minimum number of front kicks he needs in order to reach the fish shop.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W\r\nS_1\r\nS_2\r\n\\vdots\r\nS_H\r\nA B C D\n\nOutput\n\nPrint the minimum number of front kicks needed for Takahashi to reach the fish shop.\n\nConstraints\n\n\n- 1\\leq H\\leq 1000\n- 1\\leq W\\leq 1000\n- Each S_i is a string of length W consisting of . and #.\n- 1\\leq A,C\\leq H\n- 1\\leq B,D\\leq W\n- (A,B)\\neq (C,D)\n- H, W, A, B, C, and D are integers.\n- The cell where Takahashi starts and the cell with the fish shop are roads.\n\nSample Input 1\n\n10 10\r\n..........\r\n#########.\r\n#.......#.\r\n#..####.#.\r\n##....#.#.\r\n#####.#.#.\r\n.##.#.#.#.\r\n###.#.#.#.\r\n###.#.#.#.\r\n#.....#...\r\n1 1 7 1\n\nSample Output 1\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nBy repeatedly moving to adjacent road cells, he can reach cell (7,4).\r\nIf he performs a front kick to the left from cell (7,4), cells (7,3) and (7,2) turn from walls to roads.\r\nThen, by continuing to move through road cells (including those that have become roads), he can reach the fish shop in cell (7,1).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 2\n\n2 2\r\n.#\r\n#.\r\n1 1 2 2\n\nSample Output 2\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nWhen he performs a front kick to the right, cell (1,2) turns from a wall to a road.\r\nThe cell two steps to the right of (1,1) is outside the town, so it does not change.\r\nThen, he can move to cell (1,2) and then to the fish shop in cell (2,2).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 3\n\n1 3\r\n.#.\r\n1 1 1 3\n\nSample Output 3\n\n1\r\n\nWhen performing a front kick, it is fine if the fish shop\u2019s cell is within the cells that could be turned into a road. Specifically, the fish shop\u2019s cell is a road from the beginning, so it remains unchanged; particularly, the shop is not destroyed by the front kick.\n\nSample Input 4\n\n20 20\r\n####################\r\n##...##....###...###\r\n#.....#.....#.....##\r\n#..#..#..#..#..#..##\r\n#..#..#....##..#####\r\n#.....#.....#..#####\r\n#.....#..#..#..#..##\r\n#..#..#.....#.....##\r\n#..#..#....###...###\r\n####################\r\n####################\r\n##..#..##...###...##\r\n##..#..#.....#.....#\r\n##..#..#..#..#..#..#\r\n##..#..#..#..#..#..#\r\n##.....#..#..#..#..#\r\n###....#..#..#..#..#\r\n#####..#.....#.....#\r\n#####..##...###...##\r\n####################\r\n3 3 18 18\n\nSample Output 4\n\n3\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 deque\nfrom array import array\n\ninput = sys.stdin.buffer.readline\n\nH, W = map(int, input().split())\nrows = [input().strip() for _ in range(H)]\ngrid = b\"\".join(rows)\nN = H * W\n\nopened = bytearray(grid.translate(bytes.maketrans(b\".#\", b\"\\x01\\x00\")))\ndist = array(\"i\", [-1]) * N\n\nA, B, C, D = map(int, input().split())\nstart = (A - 1) * W + (B - 1)\ntarget = (C - 1) * W + (D - 1)\n\ndist[start] = 0\nopened[start] = 1\nq = deque([start])\n\nwhile q:\n    v = q.popleft()\n    if v == target:\n        break\n\n    d = dist[v]\n    r = v // W\n    c = v - r * W\n\n    if r > 0:\n        u = v - W\n        if opened[u] and dist[u] == -1:\n            dist[u] = d\n            q.appendleft(u)\n    if r + 1 < H:\n        u = v + W\n        if opened[u] and dist[u] == -1:\n            dist[u] = d\n            q.appendleft(u)\n    if c > 0:\n        u = v - 1\n        if opened[u] and dist[u] == -1:\n            dist[u] = d\n            q.appendleft(u)\n    if c + 1 < W:\n        u = v + 1\n        if opened[u] and dist[u] == -1:\n            dist[u] = d\n            q.appendleft(u)\n\n    nd = d + 1\n\n    if r > 0:\n        u = v - W\n        opened[u] = 1\n        if dist[u] == -1:\n            dist[u] = nd\n            q.append(u)\n        if r > 1:\n            u -= W\n            opened[u] = 1\n            if dist[u] == -1:\n                dist[u] = nd\n                q.append(u)\n\n    if r + 1 < H:\n        u = v + W\n        opened[u] = 1\n        if dist[u] == -1:\n            dist[u] = nd\n            q.append(u)\n        if r + 2 < H:\n            u += W\n            opened[u] = 1\n            if dist[u] == -1:\n                dist[u] = nd\n                q.append(u)\n\n    if c > 0:\n        u = v - 1\n        opened[u] = 1\n        if dist[u] == -1:\n            dist[u] = nd\n            q.append(u)\n        if c > 1:\n            u -= 1\n            opened[u] = 1\n            if dist[u] == -1:\n                dist[u] = nd\n                q.append(u)\n\n    if c + 1 < W:\n        u = v + 1\n        opened[u] = 1\n        if dist[u] == -1:\n            dist[u] = nd\n            q.append(u)\n        if c + 2 < W:\n            u += 1\n            opened[u] = 1\n            if dist[u] == -1:\n                dist[u] = nd\n                q.append(u)\n\nprint(dist[target])", "cost_usd": 0.0014911750000000002, "tokens_in": 1322, "tokens_out": 2210, "latency_s": 23.651}, {"task_id": "lcb-abc400_d", "model": "openai/gpt-5.6-luna", "prompt": "Takahashi is about to go buy eel at a fish shop.\nThe town where he lives is divided into a grid of H rows and W columns. Each cell is either a road or a wall.\r\nLet us denote the cell at the i-th row from the top (1\\leq i \\leq H) and the j-th column from the left (1\\leq j \\leq W) as cell (i,j).\r\nInformation about each cell is given by H strings S_1,S_2,\\ldots,S_H, each of length W. Specifically, if the j-th character of S_i (1\\leq i \\leq H,1\\leq j\\leq W) is ., cell (i,j) is a road; if it is #, cell (i,j) is a wall.\nHe can repeatedly perform the following two types of actions in any order:\n\n- Move to an adjacent cell (up, down, left, or right) that is within the town and is a road.\n- Choose one of the four directions (up, down, left, or right) and perform a front kick in that direction.\r\n  When he performs a front kick, for each of the cells at most 2 steps away in that direction from the cell he is currently in, if that cell is a wall, it becomes a road.\r\n  If some of the cells at most 2 steps away are outside the town, a front kick can still be performed, but anything outside the town does not change.\n\nHe starts in cell (A,B), and he wants to move to the fish shop in cell (C,D).\r\nIt is guaranteed that both the cell where he starts and the cell with the fish shop are roads.\r\nFind the minimum number of front kicks he needs in order to reach the fish shop.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W\r\nS_1\r\nS_2\r\n\\vdots\r\nS_H\r\nA B C D\n\nOutput\n\nPrint the minimum number of front kicks needed for Takahashi to reach the fish shop.\n\nConstraints\n\n\n- 1\\leq H\\leq 1000\n- 1\\leq W\\leq 1000\n- Each S_i is a string of length W consisting of . and #.\n- 1\\leq A,C\\leq H\n- 1\\leq B,D\\leq W\n- (A,B)\\neq (C,D)\n- H, W, A, B, C, and D are integers.\n- The cell where Takahashi starts and the cell with the fish shop are roads.\n\nSample Input 1\n\n10 10\r\n..........\r\n#########.\r\n#.......#.\r\n#..####.#.\r\n##....#.#.\r\n#####.#.#.\r\n.##.#.#.#.\r\n###.#.#.#.\r\n###.#.#.#.\r\n#.....#...\r\n1 1 7 1\n\nSample Output 1\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nBy repeatedly moving to adjacent road cells, he can reach cell (7,4).\r\nIf he performs a front kick to the left from cell (7,4), cells (7,3) and (7,2) turn from walls to roads.\r\nThen, by continuing to move through road cells (including those that have become roads), he can reach the fish shop in cell (7,1).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 2\n\n2 2\r\n.#\r\n#.\r\n1 1 2 2\n\nSample Output 2\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nWhen he performs a front kick to the right, cell (1,2) turns from a wall to a road.\r\nThe cell two steps to the right of (1,1) is outside the town, so it does not change.\r\nThen, he can move to cell (1,2) and then to the fish shop in cell (2,2).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 3\n\n1 3\r\n.#.\r\n1 1 1 3\n\nSample Output 3\n\n1\r\n\nWhen performing a front kick, it is fine if the fish shop\u2019s cell is within the cells that could be turned into a road. Specifically, the fish shop\u2019s cell is a road from the beginning, so it remains unchanged; particularly, the shop is not destroyed by the front kick.\n\nSample Input 4\n\n20 20\r\n####################\r\n##...##....###...###\r\n#.....#.....#.....##\r\n#..#..#..#..#..#..##\r\n#..#..#....##..#####\r\n#.....#.....#..#####\r\n#.....#..#..#..#..##\r\n#..#..#.....#.....##\r\n#..#..#....###...###\r\n####################\r\n####################\r\n##..#..##...###...##\r\n##..#..#.....#.....#\r\n##..#..#..#..#..#..#\r\n##..#..#..#..#..#..#\r\n##.....#..#..#..#..#\r\n###....#..#..#..#..#\r\n#####..#.....#.....#\r\n#####..##...###...##\r\n####################\r\n3 3 18 18\n\nSample Output 4\n\n3\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\nExecuted evidence disproved the program. Re-derive a general algorithm from the complete statement and constraints. Do not patch, fingerprint, or special-case the failing input. Return only one complete raw Python 3 program without Markdown, fences, or explanation.\nExecuted input:\n10 10\n..........\n#########.\n#.......#.\n#..####.#.\n##....#.#.\n#####.#.#.\n.##.#.#.#.\n###.#.#.#.\n###.#.#.#.\n#.....#...\n1 1 7 1\n\nProgram output:\n3\nTrusted expected output (published sample):\n1", "response": "import sys\nfrom array import array\nfrom collections import deque\n\ndata = sys.stdin.buffer.read().split()\nH = int(data[0])\nW = int(data[1])\nrows = data[2:2 + H]\ngrid = b\"\".join(rows)\n\nA = int(data[2 + H]) - 1\nB = int(data[3 + H]) - 1\nC = int(data[4 + H]) - 1\nD = int(data[5 + H]) - 1\n\nstart = A * W + B\ntarget = C * W + D\nn = H * W\n\nINF = 10**9\ndist = array('i', [INF]) * n\ndone = bytearray(n)\ndist[start] = 0\n\nq = deque([start])\nappend = q.append\nappendleft = q.appendleft\n\nwhile q:\n    v = q.popleft()\n    if done[v]:\n        continue\n    done[v] = 1\n\n    if v == target:\n        break\n\n    d = dist[v]\n    r = v // W\n    c = v - r * W\n\n    if r > 0:\n        p = v - W\n        if grid[p] == 46:\n            if d < dist[p]:\n                dist[p] = d\n                appendleft(p)\n        else:\n            nd = d + 1\n            if nd < dist[p]:\n                dist[p] = nd\n                append(p)\n            if r > 1:\n                p2 = p - W\n                if nd < dist[p2]:\n                    dist[p2] = nd\n                    append(p2)\n\n    if r + 1 < H:\n        p = v + W\n        if grid[p] == 46:\n            if d < dist[p]:\n                dist[p] = d\n                appendleft(p)\n        else:\n            nd = d + 1\n            if nd < dist[p]:\n                dist[p] = nd\n                append(p)\n            if r + 2 < H:\n                p2 = p + W\n                if nd < dist[p2]:\n                    dist[p2] = nd\n                    append(p2)\n\n    if c > 0:\n        p = v - 1\n        if grid[p] == 46:\n            if d < dist[p]:\n                dist[p] = d\n                appendleft(p)\n        else:\n            nd = d + 1\n            if nd < dist[p]:\n                dist[p] = nd\n                append(p)\n            if c > 1:\n                p2 = p - 1\n                if nd < dist[p2]:\n                    dist[p2] = nd\n                    append(p2)\n\n    if c + 1 < W:\n        p = v + 1\n        if grid[p] == 46:\n            if d < dist[p]:\n                dist[p] = d\n                appendleft(p)\n        else:\n            nd = d + 1\n            if nd < dist[p]:\n                dist[p] = nd\n                append(p)\n            if c + 2 < W:\n                p2 = p + 1\n                if nd < dist[p2]:\n                    dist[p2] = nd\n                    append(p2)\n\nprint(dist[target])", "cost_usd": 0.0029067250000000006, "tokens_in": 1328, "tokens_out": 4568, "latency_s": 69.406}]