| "content": "You are participating in a puzzle solving competition. You are an expert at solving puzzles.\n\nBelow is a list of input and output pairs with a pattern. Your goal is to identify the pattern or transformation in the training examples that maps the input to the output, then apply that pattern to the test input to give a final output.\n\nThe MASKED OUTPUT HINT for the test input contains some correctly revealed cells.\nYour final output must match all revealed (non-masked) cells.\n\nRespond in the format of the training output examples\n\n--Training Examples--\n--Example 0--\n\nINPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]\n\n\nOUTPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1]\n[0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0, 0, 0]\n[0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n[0, 0, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]\n\n\n--Example 1--\n\nINPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n[1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n\n\nOUTPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0]\n[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n[0, 0, 1, 3, 3, 3, 3, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 3, 1, 0, 0, 0, 1, 4, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0]\n[1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n[1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n\n\n--Example 2--\n\nINPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 3, 1, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n\n\nOUTPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 1]\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 1, 4, 4, 1, 0, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0]\n[0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 0, 1, 0, 0, 0]\n[0, 0, 1, 6, 6, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 6, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]\n\n\n\n--End of Training Examples--\n\n--Test Input--\n--Test Example--\n\nINPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 4, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 6, 1, 0]\n[0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n\n\nMASKED OUTPUT HINT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[MASK, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0]\n[0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 0]\n[0, 0, 1, 4, 4, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, MASK, 0, 0, 1, 4, 4, 4, 4, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, 0, 0, 1, 4, 4, 1, 1, 1, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 4, 4, 1, 0, 0]\n[0, 0, MASK, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]\n[0, 0, MASK, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, MASK, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, MASK, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 8, 8, 8, 1, 1, 1, 8, 8, MASK, 0, 0, 0, 0, 0]\n[0, 0, MASK, 0, 0, 0, 0, 0, 0, 1, 8, 1, 0, 0, 0, 1, 8, 8, MASK, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 1, 8, 1, 1, 1, 8, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, MASK, 0, 1, 6, 6, 1, 0]\n[0, 1, 1, 1, 0, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0]\n[0, 0, 0, 0, 0, 1, 1, 1, MASK, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, MASK, 6, 6, 1, 0]\n[MASK, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, MASK, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n[0, 0, 1, 6, 6, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 6, 6, 1, 0]\n[0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 1, MASK, 1, 6, 6, 1, 0]\n[0, 0, 1, 1, 1, 1, 0, 0, 1, MASK, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]\n\n\n\n--End of Test Input--\n\nWe have included a MASKED OUTPUT HINT, which is the answer to the Test Output where some cells are replaced \nwith MASK but all non-masked cells are correctly revealed from the final output. Notice that in the MASKED OUTPUT HINT, \nthe cells that are not masked (MASK) are exactly correct\u2014so you can rely on them to confirm your deductions.\n\nYour response:\n---------\n" |
| "content": "Okay, so I'm trying to figure out the pattern or transformation that's happening here. Let's look at the training examples and see what's going on. \n\nIn Example 0, the input and output are both 2D arrays. I notice that in the output, certain cells have higher numbers where the input had 1s. For instance, in row 2, column 12, the input had a 1 and the output has a 2. Similarly, in row 3, column 12, the output has a 2. It looks like some kind of expansion or spread of numbers. Maybe it's a flood fill or something similar.\n\nLooking at Example 1, the input has a 4 in the middle, and the output spreads it out. The 4 becomes a cluster of 4s and 3s around it. It seems like numbers are growing or filling in neighboring cells. The 3 in the input becomes a 3 in the output, but maybe it's not changing as much. \n\nIn Example 2, the input has a 6, and the output has 6s and 5s around it. It looks like the higher numbers are causing some kind of region to expand. Maybe each number propagates its value to neighboring cells, but higher numbers take precedence or override lower ones.\n\nSo, the pattern seems to involve propagating the numbers outward, with higher numbers possibly overwriting lower ones. It might be similar to a BFS (Breadth-First Search) where each number's value spreads to adjacent cells, but higher numbers spread more or take over areas where lower numbers would have spread.\n\nLooking at the Test Input's MASKED OUTPUT HINT, I see that some cells are already filled with numbers, and some are MASKed. The goal is to figure out how the numbers spread based on the input.\n\nLet me try to break it down step by step. The input grid has certain numbers, and the output is a transformation where each number influences its neighbors. For example, in the Test Input, there's an 8 in row 14, column 16. That 8 is a high number, so it might spread outward, possibly turning surrounding cells into 8s or lower numbers, depending on the rules.\n\nWait, in Example 2, the 6 in the input becomes a 6 in the output, but also some surrounding cells become 6s as well. So, maybe each number propagates outward, and the higher numbers override the lower ones in their vicinity.\n\nLet's think about how the numbers spread. If a cell has a number, it might set its value and then all adjacent cells (up, down, left, right) get the same number, but if a cell is already set by a higher number, it doesn't change. So, the process might be that each number's area expands, and higher numbers take over regions where their spread overlaps with lower numbers.\n\nAnother possibility is that the numbers represent regions, and each region expands until it meets another region's boundary. The regions with higher numbers might take precedence, so when two regions meet, the higher number's region continues expanding while the lower one stops.\n\nLooking back at Example 0, there's a 2 in the output where the input had 1s. That suggests that the 2 is a result of some kind of interaction between 1s. Maybe it's a count of how many 1s are adjacent or something, but that doesn't quite fit because in Example 1, the 4 in the input leads to 4s and 3s around it, which doesn't seem like a simple count.\n\nWait, in Example 0, the 2 is in the middle of a cluster of 1s. Maybe it's the maximum value in the cluster. Or perhaps it's the sum of adjacent 1s. But that doesn't add up because the 2 is in a sea of 1s, but the sum would be higher.\n\nAlternatively, perhaps it's a kind of cellular automaton where each cell's value is determined by the number of neighbors with 1s. But in the output, some cells have 2s and 3s, which might suggest that the count is being used, but the initial input has 1s, so that might not explain the higher numbers.\n\nWait, looking again at Example 0's output, the 2 appears where the input had 1s, but it's in a specific position. Maybe it's related to the distance from the edge or some other feature.\n\nAlternatively, perhaps the numbers are being used to create regions where each number is the identifier, and the regions expand until they meet each other. The higher numbers might take over the regions where multiple numbers would otherwise spread.\n\nIn the Test Input, the MASKED OUTPUT HINT shows that some cells are already filled with certain numbers. For example, in row 2, the output has 4s, which suggests that the input's 4 is causing those cells to be 4. Similarly, the 8 in the input is leading to 8s in the output and maybe some surrounding cells.\n\nI think the key is that each number in the input represents a seed for a region. These regions expand outward, and when two regions meet, the higher number takes over. So, the process is similar to a multi-source BFS where each source has a priority (the number), and higher numbers overwrite lower ones in their area.\n\nSo, the algorithm would be something like:\n\n1. Identify all the non-zero cells in the input as seeds with their respective values.\n2. Perform a BFS starting from all these seeds simultaneously.\n3. Each cell's value is determined by the highest number that reaches it first.\n4. If multiple numbers reach a cell, the highest one stays.\n\nThis would explain why in the training examples, higher numbers like 4, 6, and 8 spread outward and overwrite lower numbers around them.\n\nLooking at the Test Input, the 8 is a high number, so it would spread outward, possibly turning surrounding cells into 8s. The 6 is also a high number but lower than 8, so where the 6's spread would have been, the 8's spread would take precedence.\n\nSo, applying this to the Test Input:\n\n- The 8 in row 14, column 16 would spread to the surrounding cells, turning them into 8s.\n- The 6 in row 29, column 27 would spread, but where it meets the 8's spread, it would be overwritten.\n- Other numbers like 4 and 1 would spread, but their areas would be limited by higher numbers.\n\nThe MASKED OUTPUT HINT already shows some cells as 8s, so I can use that to confirm. For example, in row 25, the 8s are already present, so that aligns with the idea that 8 spreads outward.\n\nTherefore, the transformation is that each non-zero number in the input is a seed for a region, and these regions expand, with higher numbers taking precedence over lower ones in overlapping areas.\n\nNow, to apply this to the Test Input, I need to:\n\n1. Identify all the seeds (non-zero cells) and their values.\n2. Perform a BFS, assigning each cell the highest value that reaches it first.\n3. Replace the masked cells with the appropriate numbers based on this rule.\n\nGiven the MASKED OUTPUT HINT, I can see that some cells are already filled, so I need to ensure that the final output matches those non-masked cells.\n\nFor example, in row 2, the output has 4s, which means that the 4 in the input has spread to those cells, and no higher number has overwritten them yet.\n\nIn row 14, the 8 is present, and it's spreading outward, so the cells around it in the output should be 8s or higher, but since 8 is the highest, they should be 8s.\n\nSimilarly, the 6 in the input will spread, but only to areas not already taken by 8s or higher numbers.\n\nSo, the final output will have regions of 8, 6, 4, and 1, with 8 being the dominant region wherever it spreads.\n</think>\n[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]\n[0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0]\n[0,0,1,1,1,1,0,0,1,4,4,4,1,0,0,1,1,1,1,1,1,0,0,1,4,4,4,4,1,0]\n[0,0,1,4,4,1,1,1,1,4,4,4,1,1,1,1,4,4,4,4,1,1,1,1,4,4,4,4,1,0]\n[0,0,1,4,4,1,0,0,1,4,4,4,1,0,0,1,4,4,4,4,1,0,0,1,4,4,4,4,1,0]\n[0,0,1,1,1,1,0,0,1,4,4,4,1,0,0,1,1,1,1,1,1,0,0,1,4,4,4,4,1,0]\n[0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,1,1,1,1,1,0]\n[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]\n[0,0,0,0,1,1,1,1,0,1,1,1,0,0,0,0,1,4,4,1,0,0,0,0,1,1,1,1,0,0]\n[0,0,0,0,1,4,4,1,1,1,4,1,0,0,0,0,1,1,1,1,0,0,0,0,1,4,4,1,0,0]\n[0,0,0,0,1,1,1,1,0,1,4,1,0,0,0,0,0,0,0,0,0,0,0,0,1,4,4,1,0,0]\n[0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0]\n[0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]\n[0,0,0,0,1,4,1,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]\n[0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,8,8,8,1,0,1,1,1,1,0,0,0,0,0]\n[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,8,8,8,1,1,1,8,8,1,0,0,0,0,0]\n[0,0,0,0,0,0,0,0,0,1,8,1,0,0,0,1,8,8,8,1,0,1,1,1,1,0,0,0,0,0]\n[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]\n[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]\n[0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]\n[0,1,1,1,0,1,1,1,0,1,8,8,8,8,8,8,8,8,8,8,1,0,0,0,0,1,1,1,1,0]\n[0,1,8,1,1,1,8,1,0,1,8,8,8,8,8,8,8,8,8,8,1,0,0,0,0,1,6,6,1,0]\n[0,1,1,1,0,1,8,1,1,1,8,8,8,8,8,8,8,8,8,8,1,0,0,0,0,1,6,6,1,0]\n[0,0,0,0,0,1,1,1,0,1,8,8,8,8,8,8,8,8,8,8,1,0,0,0,0,1,6,6,1,0]\n[0,0,0,0,0,0,0,0,0,1,8,8,8,8,8,8,8,8,8,8,1,0,0,0,0,1,1,1,1,0]\n[0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]\n[0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0]\n[0,0,1,6,6,1,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,6,6,1,0]\n[0,0,1,6,6,1,1,1,1,6,6,1,1,1,1,1,6,6,1,1,1,1,1,1,1,1,6,6,1,0]\n[0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0]\n" |
