list[list[int]]:`\\n- Input `grid` is a 2D list of integers (0-9 representing colors: 0=black, 1=blue, 2=red, 3=green, 4=yellow, 5=gray, 6=magenta, 7=orange, 8=cyan, 9=brown)\\n- Return a 2D list representing the output grid\\n- Wrap code in: ```python ... ```\\n- Available imports: numpy, scipy, torch, itertools, collections\\n- Write modular code with clear variable names\\n\\n**Part 3: Response Format**\\n\\nBefore your code, provide 3 sentences of reasoning explaining:\\n- What pattern you identified\\n- Why this rule works for all examples\\n\\n**Code Examples:**\\n\\nExample 1 - Color replacement:\\n```python\\nimport numpy as np\\n\\ndef transform(grid: list[list[int]]) -> list[list[int]]:\\n \\\"\\\"\\\"Replace all 0s with 1s.\\\"\\\"\\\"\\n arr = np.array(grid)\\n return np.where(arr == 0, 1, arr).tolist()\\n```\\n\\nExample 2 - Spatial operation:\\n```python\\nimport numpy as np\\n\\ndef transform(grid: list[list[int]]) -> list[list[int]]:\\n \\\"\\\"\\\"Rotate grid 90 degrees clockwise.\\\"\\\"\\\"\\n arr = np.array(grid)\\n return np.rot90(arr, k=-1).tolist()\\n```\\n\\nExample 3 - Object detection:\\n```python\\nimport numpy as np\\n\\ndef transform(grid: list[list[int]]) -> list[list[int]]:\\n \\\"\\\"\\\"Keep only the largest connected component of non-zero cells.\\\"\\\"\\\"\\n from scipy import ndimage\\n arr = np.array(grid)\\n labeled, num_features = ndimage.label(arr > 0)\\n if num_features == 0:\\n return grid\\n sizes = ndimage.sum(arr > 0, labeled, range(1, num_features + 1))\\n largest = np.argmax(sizes) + 1\\n result = np.where(labeled == largest, arr, 0)\\n return result.tolist()\\n```\\n\\n**Important:**\\n- Find the SIMPLEST rule that works - avoid memorizing examples\\n- Your code must handle grids of any valid size\\n- Do not include `if __name__ == \\\"__main__\\\"` blocks\"\n },\n {\n \"role\": \"user\",\n \"content\": \"Please solve this ARC-AGI problem:\\n\\nTrain Example 1:\\n\\nInput:\\n000022\\n053322\\n553311\\n773311\\n664660\\n660460\\n\\nOutput:\\n010000070\\n852030621\\n070000080\\n000000040\\n070030915\\n000000030\\n000000000\\n060040060\\n000000000\\n\\nTrain Example 2:\\n\\nInput:\\n000000\\n903350\\n992240\\n992240\\n044910\\n409400\\n\\nOutput:\\n000000010\\n090030852\\n000000070\\n000070000\\n090621040\\n000080000\\n000000040\\n040090915\\n000000030\\n\\nTrain Example 3:\\n\\nInput:\\n990000\\n110950\\n113352\\n113352\\n072222\\n072222\\n\\nOutput:\\n000000010\\n090090852\\n000000070\\n040000010\\n915030852\\n030000070\\n000070070\\n070621621\\n000080080\\n\\nTrain Example 4:\\n\\nInput:\\n000000\\n406610\\n142255\\n112255\\n101110\\n011110\\n\\nOutput:\\n000000040\\n040060915\\n000000030\\n040070010\\n915621852\\n030080070\\n040040040\\n915915915\\n030030030\\n\\nTrain Example 5:\\n\\nInput:\\n000022\\n101122\\n167156\\n061156\\n555330\\n775530\\n\\nOutput:\\n040040070\\n915915621\\n030030080\\n000040000\\n060915060\\n000030000\\n000010000\\n070852030\\n000070000\\n\\n\\n\\nTest Input:\\n000055\\n776355\\n222220\\n882260\\n560710\\n567710\\n\\n\\n\"\n }\n ]\n}"},"train":{"kind":"list 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Consider these transformation types:\\n - **Color Transformations:** Replacing colors based on adjacency, frequency, or position\\n - **Object Manipulation:** Moving, rotating, reflecting, or resizing objects\\n - **Spatial Operations:** Rotating, reflecting, or resizing the entire grid\\n - **Pattern Generation:** Replicating or extending existing patterns\\n3. **Find the Rule:** Identify a *single, consistent transformation rule* that generalizes across ALL examples.\\n\\n**Part 2: Code Requirements**\\n\\n- Function signature: `def transform(grid: list[list[int]]) -> list[list[int]]:`\\n- Input `grid` is a 2D list of integers (0-9 representing colors: 0=black, 1=blue, 2=red, 3=green, 4=yellow, 5=gray, 6=magenta, 7=orange, 8=cyan, 9=brown)\\n- Return a 2D list representing the output grid\\n- Wrap code in: ```python ... ```\\n- Available imports: numpy, scipy, torch, itertools, collections\\n- Write modular code with clear variable names\\n\\n**Part 3: Response Format**\\n\\nBefore your code, provide 3 sentences of reasoning explaining:\\n- What pattern you identified\\n- Why this rule works for all examples\\n\\n**Code Examples:**\\n\\nExample 1 - Color replacement:\\n```python\\nimport numpy as np\\n\\ndef transform(grid: list[list[int]]) -> list[list[int]]:\\n \\\"\\\"\\\"Replace all 0s with 1s.\\\"\\\"\\\"\\n arr = np.array(grid)\\n return np.where(arr == 0, 1, arr).tolist()\\n```\\n\\nExample 2 - Spatial operation:\\n```python\\nimport numpy as np\\n\\ndef transform(grid: list[list[int]]) -> list[list[int]]:\\n \\\"\\\"\\\"Rotate grid 90 degrees clockwise.\\\"\\\"\\\"\\n arr = np.array(grid)\\n return np.rot90(arr, k=-1).tolist()\\n```\\n\\nExample 3 - Object detection:\\n```python\\nimport numpy as np\\n\\ndef transform(grid: list[list[int]]) -> list[list[int]]:\\n \\\"\\\"\\\"Keep only the largest connected component of non-zero cells.\\\"\\\"\\\"\\n from scipy import ndimage\\n arr = np.array(grid)\\n labeled, num_features = ndimage.label(arr > 0)\\n if num_features == 0:\\n return grid\\n sizes = ndimage.sum(arr > 0, labeled, range(1, num_features + 1))\\n largest = np.argmax(sizes) + 1\\n result = np.where(labeled == largest, arr, 0)\\n return result.tolist()\\n```\\n\\n**Important:**\\n- Find the SIMPLEST rule that works - avoid memorizing examples\\n- Your code must handle grids of any valid size\\n- Do not include `if __name__ == \\\"__main__\\\"` blocks\"\n },\n {\n \"role\": \"user\",\n \"content\": \"Please solve this ARC-AGI problem:\\n\\nTrain Example 1:\\n\\nInput:\\n000000\\n000000\\n000000\\n000000\\n000000\\n000000\\n444444\\n063596\\n500000\\n800000\\n700000\\n600000\\n900000\\n200000\\n800000\\n600000\\n600000\\n800000\\n444444\\n051275\\n200000\\n600000\\n700000\\n200000\\n700000\\n100000\\n800000\\n500000\\n500000\\n200000\\n\\nOutput:\\n00500\\n00000\\n00070\\n60206\\n00090\\n01000\\n00000\\n60006\\n60006\\n00200\\n\\nTrain Example 2:\\n\\nInput:\\n000000\\n000000\\n000000\\n000000\\n000000\\n000000\\n000000\\n000000\\n444444\\n029592\\n300000\\n300000\\n800000\\n600000\\n500000\\n100000\\n200000\\n700000\\n200000\\n444444\\n075513\\n500000\\n800000\\n600000\\n500000\\n500000\\n100000\\n300000\\n200000\\n700000\\n\\nOutput:\\n05500\\n00000\\n00000\\n05500\\n05500\\n00010\\n20002\\n00000\\n20002\\n\\nTrain Example 3:\\n\\nInput:\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n0000000\\n4444444\\n0532636\\n5000000\\n2000000\\n3000000\\n4444444\\n0273695\\n2000000\\n3000000\\n7000000\\n\\nOutput:\\n500000\\n002000\\n030030\\n\\nTrain Example 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