[
  {
    "messages": [
      {
        "role": "user",
        "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]\n[0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 3, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 2, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 4, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 3, 3, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 2, 2, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 2, 2, 9, 0, 0]\n[0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 3, 3, 3, 3, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 3, 3, 3, 3, 9, 9, 9, 3, 9, 0, 0, 0, 9, 2, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 4, 4, 9, 9, 9, 9, 4, 9, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 9, 4, 4, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[9, 4, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 4, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 4, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 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]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 3, 9, 9, 9, 9, 9, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 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, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 2, 2, 9, 9, 9, 9, 2, 2, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 2, 2, 9, 9, 9, 9, 2, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 9, 2, 2, 9, 0, 0, 9, 3, 9, 9, 9, 3, 9, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 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, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 5, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 5, 5, 9, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 5, 5, 9, 0, 0, 9, 5, 5, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 5, 5, 9, 9, 9, 9, 5, 5, 9, 9, 9, 5, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 5, 5, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 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, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 3, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 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, MASK, 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, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, MASK, 0, 9, 4, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 9, 4, 4, 9, MASK, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, MASK, 9, 9, 9, 9, 9, 9, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, MASK, 0]\n[0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0]\n[0, 0, 0, 0, MASK, 9, 9, 9, 0, 0, 0, 0, MASK, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, MASK, 4, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, MASK, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, MASK, MASK, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 9, 9, 9, MASK, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 4, 4, 4, 4, 4, 4, 4, 9, 9, 9, MASK, 4, 4, 9, MASK, 9, 9, 4, 9]\n[0, 0, MASK, 0, 0, 9, 4, 9, 9, 9, 9, 4, 4, 4, 4, 4, MASK, 4, 9, MASK, 0, 9, 4, 4, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, MASK, 0, 9, 4, 4, 4, 4, 4, 4, 4, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, MASK, 0, MASK, 0, 0, 0, 9, 9, 9, 9, 9, MASK, 9, 9, 9, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, MASK, 3, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 3, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9, MASK, 9, 9, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 4, 4, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, MASK, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 4, 4, 9, 0, 9, 3, 9, 9, 9, 3, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, MASK, 0, 0, 9, 9, 9, MASK, 9, 0, 0, 9, 9, MASK, MASK, MASK, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 3, 3, 3, 9, 0, 0, 0, 0, MASK, 0, 0, 0, MASK, MASK, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 3, 9, 9, 9, 9, 3, 3, 3, 9, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, MASK, 9, 9, 9, 0, 0, 9, 3, 3, 3, MASK, MASK, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, MASK, 3, 3, 3, 9, 9, 9, 9, 3, 3, 3, 3, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 3, 3, 3, 3, 9, 9, 9, 9, 9, 3, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 3, 3, 3, 3, 9, 0, 0, 0, 9, 3, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 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"
      },
      {
        "role": "assistant",
        "content": "<think>\nOkay, let's try to figure out the pattern from the training examples and apply it to the test input. So, looking at the examples, I notice that in both Example 0 and Example 1, the output seems to be modifying the input in a specific way. \n\nIn Example 0, the input has some 9s and a 3 and 2. The output changes some 9s into 3s and 2s. For instance, in the third row of the input, there's a 3, and in the output, that 3 remains, but surrounding 9s become 3s as well. Similarly, in the fifth row, a 2 appears, and the output changes some 9s to 2s. It seems like whenever there's a number that's not 9 or 0, it's acting as a seed, and the surrounding 9s are being replaced with that number, possibly spreading outwards.\n\nIn Example 1, the same pattern holds. The input has a 2, 3, and 5. The output changes the surrounding 9s to these numbers, creating regions around each seed. So, it looks like the transformation is about replacing 9s with the nearest non-9 number, perhaps in a flood fill manner.\n\nNow, looking at the test input, the masked output hint shows some cells already filled. For example, in the third row, there's a 4, and the surrounding 9s are turned into 4s. Similarly, in other rows, 3s and 2s are present, and the 9s around them are being replaced. \n\nSo, the pattern seems to be that each non-9 number (like 2, 3, 4, 5) acts as a seed, and all connected 9s around it are replaced with that number, creating regions. The replacement propagates outward, and each region is defined by the closest seed.\n\nTo apply this to the test input, I need to identify all the non-9 numbers and then replace the 9s around them with those numbers, ensuring that each 9 is replaced by the closest seed. If a 9 is equidistant to multiple seeds, perhaps the smallest number takes precedence, or maybe the first encountered in some order.\n\nLooking at the masked output hint, some cells are already filled, so I can use those as a guide. For example, in row 3, the 4 is present, and the surrounding 9s are 4s. In row 4, there's a 4, and the 9s around it are also 4s. Similarly, in row 13, there's a 4, and the surrounding cells are 4s. \n\nI need to ensure that all 9s adjacent to these seeds are replaced correctly, and that the regions don't overlap unless they're supposed to. Also, the seeds themselves remain unchanged.\n\nSo, the approach is to:\n\n1. Identify all non-9 numbers in the input.\n2. For each non-9 number, replace all connected 9s with that number, propagating outwards.\n3. Ensure that each 9 is replaced by the closest non-9 number, and if multiple seeds are equidistant, perhaps the smallest number is used, or the first one encountered.\n\nNow, applying this to the test input, I'll go through each row and column, check for non-9 numbers, and replace the surrounding 9s accordingly. I'll make sure that the masked output hint's revealed cells are matched, as they are correct.\n\nFor example, in row 3, the input has a 4, so the surrounding 9s become 4s. In row 4, the input has a 4, so the 9s around it become 4s. Similarly, in row 13, the 4 is present, and the surrounding 9s are 4s. \n\nI'll proceed row by row, checking for seeds and replacing the 9s with the appropriate numbers, ensuring that the regions don't conflict with the masked output hint.\n\nAfter applying this transformation, the output should match all the non-masked cells in the hint and correctly fill in the MASKed cells with the appropriate numbers based on the nearest seed.\n</think>\n\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, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 4, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 9, 4, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 4, 9, 9, 9, 9, 9, 9, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 4, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 4, 4, 9, 9, 9, 9, 4, 9]\n[0, 0, 0, 0, 0, 9, 4, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 9, 0, 0, 9, 4, 4, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 4, 4, 4, 4, 4, 4, 4, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 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, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 9, 3, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 3, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 4, 4, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 4, 4, 9, 0, 9, 3, 9, 9, 9, 3, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 3, 3, 3, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 3, 9, 9, 9, 9, 3, 3, 3, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 3, 3, 3, 9, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 3, 3, 3, 9, 9, 9, 9, 3, 3, 3, 3, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 3, 3, 3, 3, 9, 9, 9, 9, 9, 3, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 3, 3, 3, 3, 9, 0, 0, 0, 9, 3, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]"
      }
    ],
    "difficulty": 5,
    "problem_uid": "09c534e7_leave_1_out_of_3_idx00_0degI_augmented_PermuteColors_0943285167_permuted_5412_level5",
    "step": 1
  },
  {
    "messages": [
      {
        "role": "user",
        "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]\n[0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0]\n[0, 0, 5, 7, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 4, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0]\n[0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 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, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 2, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0]\n[5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0]\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 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, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0]\n[0, 0, 5, 7, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 4, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 4, 5, 0, 0]\n[0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0]\n[0, 0, 5, 7, 7, 7, 7, 5, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 7, 7, 7, 7, 5, 5, 5, 7, 5, 0, 0, 0, 5, 4, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 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, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 2, 2, 5, 5, 5, 5, 2, 5, 0, 0, 0, 0, 0, 0]\n[5, 5, 5, 0, 0, 5, 2, 2, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0]\n[5, 2, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[5, 2, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 5, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 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]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0]\n[0, 0, 0, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 7, 5, 5, 5, 5, 5, 0, 0]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 5, 5, 5, 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, 5, 5, 5, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 5, 0, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 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, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0]\n[0, 0, 0, 5, 4, 4, 5, 5, 5, 5, 4, 4, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 4, 4, 5, 5, 5, 5, 4, 5]\n[0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 0, 5, 4, 4, 5, 0, 0, 5, 7, 5, 5, 5, 7, 5, 0, 0]\n[0, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5, 0, 5, 5, 5, 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, 5, 5, 5, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 3, 5, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 5, 3, 3, 5, 0, 0, 5, 0, 0, 0]\n[0, 0, 5, 3, 3, 5, 0, 0, 5, 3, 3, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 5, 3, 3, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 5, 0, 0]\n[0, 0, 5, 5, 5, 5, 0, 0, 5, 3, 3, 5, 0, 5, 5, 5, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, 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, 5, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 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, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 5, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 7, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 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, MASK, 0]\n[0, 0, MASK, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, MASK, 0]\n[0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 2, 2, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 2, 2, 2, 5, 0, 0, 0, 0, 0, 5, 2, 2, 5, 0, 0, MASK, 0]\n[0, 0, 0, 0, 0, 5, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, MASK, 2, 2, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, MASK, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0]\n[0, 0, MASK, 0, 0, 5, 5, 5, 0, 0, 0, MASK, 0, MASK, 5, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 2, 5, 0, 0, MASK, 0, 0, 0, 5, MASK, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 5, MASK, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, MASK, 0, 5, 5, 5]\n[0, MASK, MASK, 0, 0, 5, 5, 5, 0, 0, 5, 2, 2, 2, 2, MASK, 2, 2, 5, 5, 5, 5, 2, 2, 5, 5, 5, 5, 2, 5]\n[0, 0, 0, 0, 0, 5, 2, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 5, 0, 0, 5, 2, 2, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 5, 2, 2, 2, 2, 2, MASK, 2, 5, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, MASK]\n[0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, MASK, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, MASK, 0, MASK, MASK, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 5, 7, 5, 0, 0, MASK, 0, 5, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0]\n[0, 0, 5, 7, 5, 0, 0, 0, 5, 5, MASK, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, MASK, 0, 5, 2, 2, 5, 0, 5, 5, 5, 0, 5, MASK, 5, MASK, 0, 0, MASK]\n[0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 2, 2, 5, 0, 5, 7, 5, 5, 5, 7, 5, 0, 0, 0, 0]\n[0, MASK, 0, 5, 0, 0, 0, 5, 5, 5, MASK, 5, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 5, 7, 7, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 5, 7, MASK, 5, 5, 5, 7, 7, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 5, 7, 7, 7, 5, 0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 0, MASK, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 5, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 7, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 5, 7, 7, 7, 7, 5, 0, 0, 0, 5, 7, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 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"
      },
      {
        "role": "assistant",
        "content": "<think>\nOkay, so I've got this puzzle to solve, and I'm a bit new to this, but I'll try to figure it out step by step. Let's see what the problem is asking.\n\nFrom what I understand, there are some training examples provided, each with an input and an output. My task is to find the pattern or transformation that maps the input to the output. Then, I need to apply that same pattern to the test input and provide the correct output, making sure it matches the non-masked parts of the given hint.\n\nLooking at the training examples, both have inputs and outputs that are 2D arrays of numbers. The numbers seem to be in a grid, maybe representing some kind of map or image. The outputs are transformations of the inputs, but I need to figure out exactly how.\n\nLet me look at Example 0 first. The input is a 20x20 grid, and the output is another 20x20 grid. Comparing the two, I notice that in the output, certain cells have changed from the input. For instance, in the third row of the input, there's a 7 in the middle, and in the output, it's surrounded by 7s. Similarly, in the fifth row, there's a 5 that becomes a 4 in the output. Hmm, maybe it's something to do with neighboring cells.\n\nWait, looking closer, in Example 0, the output seems to have some cells changed based on their neighbors. For example, in the third row, the 7 is in the middle, and the surrounding cells become 7s. Maybe it's a kind of flood fill or something where certain numbers spread to adjacent cells.\n\nWait, no, maybe it's more like a cellular automaton rule. Let me think. In the input, certain cells are higher numbers, and in the output, their neighbors take on the same value. Or perhaps it's about the maximum value in the neighborhood.\n\nLooking at the first example, in the third row, the input has 5,7,5,5. The output changes the 7 to 7s around it. Wait, no, the output has 5,7,7,5. So the 7 in the input causes the adjacent cells to become 7s. Similarly, in the fifth row, the 5 becomes 4s around it. Wait, that doesn't fit. Alternatively, maybe it's about the minimum or maximum in the neighborhood.\n\nWait, perhaps it's about the number of surrounding cells. Let me think differently. Maybe each cell in the output is the maximum value in its Moore neighborhood (the surrounding 8 cells) from the input. Let's test this.\n\nIn Example 0, the third row input is [0,0,5,7,5,5,0,0,0,0,0,0,0,0,5,5,4,5,0,0]. The output is [0,0,5,7,7,5,0,0,0,0,0,0,0,0,5,4,4,5,0,0]. So, the 7 in the input is at position 3. Looking at its neighbors in the input: the cells around it are 5,5,5,5, etc. So the maximum around 7 is 7, so it stays 7. The cell to the right of 7 is 5, but in the output, it becomes 7. So perhaps the rule is that each cell takes the maximum value of its neighborhood, including itself.\n\nWait, let's check another point. In the fifth row of Example 0, the input has 0,0,0,0,5,0,0,0,0,0,0,0,0,0,5,5,5,5,0,0. The output is [0,0,0,0,5,0,0,0,0,0,0,0,0,0,5,5,5,5,0,0]. Hmm, that doesn't change much. Wait, maybe I'm looking at the wrong rows.\n\nWait, perhaps it's better to look at a specific cell. Let's take the cell at row 2, column 3 in Example 0. Input is 5, output is 5. The cell at row 2, column 4 is 7 in input, and in output, it's 7, but the cells around it become 7s. So maybe the rule is that if a cell has a higher value than its neighbors, it spreads that value to the adjacent cells.\n\nAlternatively, maybe it's a kind of dilation where each cell's value is the maximum in its 3x3 neighborhood. Let's test that.\n\nIn Example 0, the third row input is [0,0,5,7,5,5,0,0,0,0,0,0,0,0,5,5,4,5,0,0]. The output is [0,0,5,7,7,5,0,0,0,0,0,0,0,0,5,4,4,5,0,0]. So for the cell at position 4 (value 7), its neighborhood includes 5,7,5,5, etc. The maximum is 7, so it stays 7. The cell to the right of 7 (position 5) was 5, but in the output, it's 7. So that suggests that the cell takes the maximum of its neighborhood, including itself. So position 5 in input is 5, but its neighborhood includes 7, so the maximum is 7, hence it becomes 7 in output.\n\nSimilarly, in the fifth row, the input has 5 in position 4, and the output has 5. The cell to the right is 0, but in the output, it's 5. Wait, no, the fifth row input is [0,0,0,0,5,0,0,0,0,0,0,0,0,0,5,5,5,5,0,0]. The output is [0,0,0,0,5,0,0,0,0,0,0,0,0,0,5,5,5,5,0,0]. So the 5 in position 4 remains 5, and the cells to the right are 0, but in the output, they remain 0. Hmm, that doesn't fit the dilation idea because the 5's neighborhood includes 0s, but the output doesn't change. So maybe the rule is different.\n\nWait, perhaps it's not dilation but something else. Let me look at another example. In Example 1, the input has a 4 in the third row, and the output changes the surrounding cells to 4s. Similarly, a 7 in the input causes surrounding cells to become 7s. So maybe the rule is that each cell's value is the maximum of its own value and the values of its immediate neighbors.\n\nWait, let's test that. For Example 0, the third row, position 4 is 7. Its neighbors are 5,5,5,5, etc. So the maximum is 7, so it remains 7. The cell to the right (position 5) was 5, but its neighbors include 7, so the maximum is 7, so it becomes 7. That fits. Similarly, in the fifth row, the 5 in position 4 has neighbors 0,0,0,5, etc. The maximum is 5, so it remains 5. The cell to the right is 0, but its neighbors include 5, so it becomes 5? Wait, but in the output, the fifth row's cell 5 is 0. Hmm, that contradicts.\n\nWait, no, in Example 0's fifth row, the input is [0,0,0,0,5,0,0,0,0,0,0,0,0,0,5,5,5,5,0,0]. The output is [0,0,0,0,5,0,0,0,0,0,0,0,0,0,5,5,5,5,0,0]. So the cell at position 5 is 0 in both input and output. But according to the dilation idea, it should be 5 because it's adjacent to 5. So maybe the rule isn't dilation.\n\nAlternatively, perhaps it's about the number of surrounding cells with a certain value. Or maybe it's about the corners or edges.\n\nWait, looking at the test input's masked output hint, I see that some cells are MASK, but others are revealed. For example, in the third row, the output has 5,5,5,5,5,5,5,0,0,0,0,0,5,2,2,5,0,0,0,0. So the 2s are in the middle. That suggests that perhaps the 2 is spreading from somewhere.\n\nWait, maybe the rule is that each cell's value is the minimum of its neighborhood. Let's test that. In Example 0, the third row input has 5,7,5,5. The output has 5,7,7,5. If it's the minimum, then the 7 would stay 7, but the 5s would remain 5. That doesn't fit because the output has 7s where the input had 5s.\n\nAlternatively, perhaps it's the maximum of the cell and its immediate neighbors. Let's see. For the cell at position 5 in the third row of Example 0, the input is 5. Its neighbors are 7 (left), 5 (right), and others. The maximum is 7, so it becomes 7. That fits. Similarly, in the fifth row, the cell at position 5 is 0. Its neighbors include 5 (left), so the maximum is 5, but in the output, it's 0. That contradicts. Hmm.\n\nWait, maybe the rule is that each cell's value is the maximum of its own value and the values of its four immediate neighbors (up, down, left, right), not including diagonals. Let's test that.\n\nIn Example 0, third row, position 5 is 5. Its left neighbor is 7, so the maximum is 7, so it becomes 7. That fits. For the fifth row, position 5 is 0. Its left neighbor is 5, so the maximum is 5, but in the output, it's 0. That doesn't fit. So maybe it's not that.\n\nAlternatively, perhaps it's the maximum of the cell and its diagonal neighbors. Let me think. In the third row, position 5 is 5. Its top-left neighbor is 5, top is 0, top-right is 0, etc. So the maximum would still be 5, but in the output, it's 7. So that doesn't fit.\n\nWait, maybe it's the maximum of the cell and its Moore neighborhood (all 8 surrounding cells). Let's try that. For the third row, position 5 is 5. Its Moore neighborhood includes 7 (left), so the maximum is 7, so it becomes 7. That fits. For the fifth row, position 5 is 0. Its Moore neighborhood includes 5 (left), so the maximum is 5, but in the output, it's 0. That doesn't fit. Hmm.\n\nWait, maybe the rule is applied only to certain cells, like non-zero cells. Or perhaps it's applied in a way that only certain values spread. Alternatively, maybe it's about the number of surrounding cells with a higher value.\n\nWait, looking at the test input's masked output hint, I see that in row 12, column 13, the output is 2. The input for that cell is 5. So perhaps the 2 is spreading from somewhere. Maybe the rule is that certain values replace others based on their neighborhood.\n\nAlternatively, perhaps it's a matter of the cell's value being the maximum in its row or column. But that seems less likely.\n\nWait, perhaps the rule is that each cell's value is the maximum value in its row up to that point. Let me check Example 0. In the third row, the input is 5,7,5,5. The output is 5,7,7,5. So the maximum up to each point would be 5,7,7,7, which doesn't fit because the last cell is 5 in output. So that's not it.\n\nAlternatively, maybe it's the maximum in the column. Let's see. In Example 0, the third column in the input has 5,5,5,5,0,5,5,5,5,0,0,0,0,0,5,5,5,5,0,0. The output for that column is 5,5,5,5,0,5,5,5,5,0,0,0,0,0,5,5,5,5,0,0. So no change, which suggests that's not the case.\n\nHmm, maybe I'm approaching this wrong. Let's think about the test input's masked output hint. The hint shows that in row 3, column 13, the output is 2. The input for that cell is 5. So how does 5 become 2? That suggests that the value decreases, which is the opposite of dilation. So maybe it's erosion, where the cell's value is the minimum of its neighborhood.\n\nWait, let's test that. In Example 0, the third row, position 4 is 7. If it's erosion, the cell would take the minimum of its neighborhood. The neighborhood includes 5s and 7. The minimum is 5, but in the output, it's 7</think>\n\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, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 2, 2, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 2, 2, 2, 5, 0, 0, 0, 0, 0, 5, 2, 2, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 2, 2, 2, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 2, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, 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, 5, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 5, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 2, 2, 5, 5, 5, 5, 2, 5]\n[0, 0, 0, 0, 0, 5, 2, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 5, 0, 0, 5, 2, 2, 5, 0, 0, 5, 5, 5]\n[0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 5, 2, 2, 2, 2, 2, 2, 2, 5, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 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, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 5, 7, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 7, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 2, 2, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 2, 2, 5, 0, 5, 7, 5, 5, 5, 7, 5, 0, 0, 0, 0]\n[0, 0, 0, 5, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 5, 7, 7, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 5, 7, 5, 5, 5, 5, 7, 7, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 5, 5, 5, 0, 0, 5, 7, 7, 7, 5, 0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 5, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 7, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 7, 7, 7, 7, 5, 0, 0, 0, 5, 7, 5, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0]"
      }
    ],
    "difficulty": 5,
    "problem_uid": "09c534e7_leave_1_out_of_3_idx00_0degI_augmented_PermuteColors_0527483961_permuted_56620_level5",
    "step": 1
  },
  {
    "messages": [
      {
        "role": "user",
        "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]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 4, 9, 9, 9, 9, 9, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 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, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 6, 6, 9, 9, 9, 9, 6, 6, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 6, 6, 9, 9, 9, 9, 6, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 9, 6, 6, 9, 0, 0, 9, 4, 9, 9, 9, 4, 9, 0, 0]\n[0, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 9, 9, 9, 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, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 5, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 5, 5, 9, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 5, 5, 9, 0, 0, 9, 5, 5, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 5, 5, 9, 9, 9, 9, 5, 5, 9, 9, 9, 5, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 9, 5, 5, 9, 0, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 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, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 4, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 6, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 1, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 4, 4, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 6, 6, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 6, 6, 9, 0, 0]\n[0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0]\n[0, 0, 9, 4, 4, 4, 4, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0]\n[0, 0, 9, 4, 4, 4, 4, 9, 9, 9, 4, 9, 0, 0, 0, 9, 6, 9, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 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, 9, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 1, 1, 9, 9, 9, 9, 1, 9, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 9, 1, 1, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0]\n[9, 1, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 1, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 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, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 4, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n\n\nMASKED OUTPUT HINT:\n[0, 0, 0, 0, MASK, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 1, 1, 9, 0, 0, MASK, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 1, 1, 1, 9, 0, 0, 0, 0, 0, 9, 1, 1, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 9, 9, 9, MASK, 9, 9, 9, 1, 1, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 1, 1, 1, 9, 0, 0, 0, 0, 0, 9, 9, 9, MASK, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 0, MASK, 0, 0, 0, 9, 9, 9, 9, 9, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, MASK, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 1, 9, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 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, MASK, 0, 0, 0, 0, 9, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 9, 9, 9, 9, 9, MASK, 9, 9, 0, 0, MASK, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 1, 1, 9, MASK, 9, 9, 1, 9]\n[0, MASK, 0, 0, 0, 9, 1, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 9, 1, 1, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 1, MASK, 1, MASK, 1, 1, 1, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, MASK, 0, MASK, 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, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, MASK, 0, 0, 0, MASK, 0, 0, 0, 0, 0, MASK, 0, MASK, 0, 0, 0, MASK, MASK, 0]\n[0, 0, 9, 9, MASK, 0, 0, 0, 9, 4, 9, 0, 0, 0, 0, MASK, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, MASK, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9, MASK, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 1, 1, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, MASK, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 1, 1, 9, 0, 9, 4, 9, 9, 9, 4, 9, 0, 0, MASK, MASK]\n[0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 4, 9, 9, 9, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, MASK, 4, 4, 9, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 9, MASK, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 4, 4, 4, 9, 9, 9, 9, 4, 4, 4, 4, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 4, MASK, 4, 4, 9, 9, 9, 9, 9, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 9, 4, 4, 4, 4, 9, 0, 0, 0, 9, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, MASK, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 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"
      },
      {
        "role": "assistant",
        "content": "<think>\nAlright, let's try to figure out the pattern here. I'm looking at the training examples to understand how the input is transformed into the output. \n\nIn Example 0, the input has a lot of 9s and some 6s and 4s. The output seems to replace certain 9s with 6s or 4s in specific positions. For instance, in the third row of the input, there's a 6, and in the output, the surrounding 9s are replaced with 6s. Similarly, in the eighth row, a 4 is present, and the output replaces some 9s with 4s around it.\n\nLooking at Example 1, the same pattern seems to apply. The input has 4s and 6s, and the output replaces nearby 9s with these numbers, creating a sort of spread or influence from the original numbers.\n\nSo, the pattern might be that any 9 in the input that is adjacent (maybe including diagonally) to a number like 4, 5, or 6 is replaced by that number in the output. This seems to create a kind of flood fill effect where the numbers spread to neighboring 9s.\n\nNow, looking at the test input, the masked output hint shows some cells already filled. For example, in the third row, there's a 1, and the output has 1s spreading out. Similarly, in other rows, numbers like 4 and 9 are present, and the output seems to be replacing surrounding 9s with these numbers.\n\nI need to apply this pattern to the test input. So, wherever there's a number like 1, 4, or 6 in the input, the surrounding 9s in the output should be replaced by that number. The MASKED OUTPUT HINT already shows some of these replacements, so I need to ensure that the final output matches those revealed cells.\n\nI'll go through each row and column, checking for numbers that are not 9 or 0. For each such number, I'll replace the adjacent 9s with that number, propagating outwards as per the examples. This should give me the correct output that matches the MASKED HINT.\n</think>\n\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, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 1, 1, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 1, 1, 1, 9, 0, 0, 0, 0, 0, 9, 1, 1, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 1, 1, 1, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 1, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 9, 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, 9, 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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 1, 9]\n[0, 0, 0, 0, 0, 9, 1, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 9, 1, 1, 9, 0, 0, 9, 9, 9]\n[0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 9, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 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, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 9, 4, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 4, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 1, 1, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 1, 1, 9, 0, 9, 4, 9, 9, 9, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 9, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 4, 9, 9, 9, 9, 4, 4, 4, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 9, 9, 9, 0, 0, 9, 4, 4, 4, 9, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 4, 4, 4, 9, 9, 9, 9, 4, 4, 4, 4, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 9, 4, 4, 4, 4, 9, 9, 9, 9, 9, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 4, 4, 4, 4, 9, 0, 0, 0, 9, 4, 9, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0]"
      }
    ],
    "difficulty": 5,
    "problem_uid": "09c534e7_leave_1_out_of_3_idx00_0degI_augmented_PermuteColors_0914625783_permuted_7938_level5",
    "step": 1
  },
  {
    "messages": [
      {
        "role": "user",
        "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]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 9, 2, 2, 2, 2, 2, 0, 0]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 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, 2, 2, 2, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 3, 3, 2, 2, 2, 2, 3, 2]\n[0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 0, 2, 3, 3, 2, 0, 0, 2, 9, 2, 2, 2, 9, 2, 0, 0]\n[0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 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, 2, 2, 2, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 2, 6, 6, 2, 0, 0, 2, 0, 0, 0]\n[0, 0, 2, 6, 6, 2, 0, 0, 2, 6, 6, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 6, 6, 2, 2, 2, 2, 6, 6, 2, 2, 2, 6, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 2, 6, 6, 2, 0, 2, 2, 2, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 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, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0]\n[0, 0, 2, 9, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0]\n[0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 8, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0]\n[2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0]\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 2, 2, 2, 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, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0]\n[0, 0, 2, 9, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 2, 0, 0]\n[0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]\n[0, 0, 2, 9, 9, 9, 9, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0]\n[0, 0, 2, 9, 9, 9, 9, 2, 2, 2, 9, 2, 0, 0, 0, 2, 3, 2, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 8, 8, 2, 2, 2, 2, 8, 2, 0, 0, 0, 0, 0, 0]\n[2, 2, 2, 0, 0, 2, 8, 8, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0]\n[2, 8, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[2, 8, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 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, 2, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 9, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 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, MASK, 0, 0, 0, MASK, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 8, 8, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, MASK, 0, 2, 8, 8, 8, 2, 0, 0, 0, 0, 0, 2, 8, 8, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 8, 2, 2, 2, 2, 2, 2, 8, 8, 8, MASK, 2, 2, 2, 2, 2, 2, 8, 8, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 8, 8, 8, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, MASK, 0]\n[0, 0, MASK, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 8, 2, 0, MASK, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, MASK, 0, 0]\n[0, 0, 0, 0, MASK, 0, MASK, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, MASK, MASK, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, MASK, 2, 2, 2, 0, 0, 2, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 8, 2]\n[0, 0, 0, 0, 0, 2, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 2, 0, 0, 2, 8, 8, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 8, MASK, 8, 8, 8, 8, 8, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, MASK, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, MASK, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 0, MASK, 9, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0]\n[0, 0, 2, 9, 2, 0, 0, 0, 2, MASK, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0]\n[0, 0, 2, MASK, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 8, 2, 0, 2, 2, 2, 0, MASK, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, MASK, 2, 8, 8, 2, 0, 2, 9, 2, 2, 2, 9, 2, 0, 0, 0, 0]\n[0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, MASK, 0, 2, 2, 2, 0, 0, MASK, 0]\n[0, 0, 2, 2, MASK, 0, 0, 2, 9, 9, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, MASK, 0, 0]\n[MASK, 0, 2, MASK, 2, 2, 2, MASK, 9, 9, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, MASK, 0, 0, MASK]\n[0, 0, 2, 2, 2, 0, 0, 2, 9, 9, 9, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, MASK, MASK, 2, 9, 9, 9, 2, 2, 2, 2, 9, 9, 9, 9, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, MASK]\n[0, 0, 0, 0, 0, 0, 0, 2, MASK, 2, 2, 2, 0, 0, 2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 9, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, MASK, 9, 9, 9, 9, 2, 0, 0, 0, 2, 9, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 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"
      },
      {
        "role": "assistant",
        "content": "<think>\nAlright, let's tackle this problem step by step. So, the task is to figure out the pattern or transformation that maps the input grids to the output grids in the training examples and then apply it to the test input, making sure the output matches the non-masked cells in the provided hint.\n\nFirst, looking at the training examples. Let's start with Example 0. The input and output grids are both 18x18. Comparing them, I notice that in the input, there are certain numbers, like 3 and 9, and in the output, those numbers seem to have expanded or influenced their neighboring cells. For example, in the third row of Example 0's input, there's a 3. In the output, this 3 is surrounded by 3s. Similarly, the 9 in the input's seventh row is surrounded by 9s in the output. It looks like each number (other than 0 and 2) is causing some kind of spread to adjacent cells, replacing 2s with the same number.\n\nWait, but in the output, the 3s and 9s are not just in their original positions but also in neighboring cells. So maybe the rule is that any cell with a number higher than 2 (like 3, 6, 9) propagates that number to all adjacent cells (including diagonally adjacent ones?), replacing the 2s with that number. Let me check this.\n\nIn Example 0, the input has a 3 at position (2,4) (assuming rows and columns start at 0). In the output, this becomes a 3 in that cell and all surrounding cells. Similarly, the 9 in the input's row 7, column 10 is surrounded by 9s in the output. So it seems like each such number \"infects\" all adjacent cells, turning them into the same number.\n\nLooking at Example 1, the input has a 9 and an 8. The output shows that the 9 has spread to its neighbors, turning them into 9s, and the 8 has done the same, turning adjacent 2s into 8s. So the pattern is consistent: any cell with a number greater than 2 causes all adjacent cells (including diagonally) to take that number, replacing 2s.\n\nSo the transformation rule seems to be:\n\n- For each cell in the input grid:\n  - If the cell's value is greater than 2, it remains the same.\n  - All 2s adjacent (including diagonally) to a cell with a value greater than 2 are changed to that value.\n  - Other cells (0s and 2s not adjacent to any higher numbers) remain as they are.\n\nWait, but in the output grids, some 2s are replaced, but others remain. For example, in Example 0's output, there are still 2s in some areas. So the rule is that only 2s adjacent to higher numbers are changed. So the process is:\n\n1. Identify all cells with values >2. These are the \"sources.\"\n2. For each source, change all adjacent cells (including diagonally) that are 2s to the source's value.\n3. The 0s remain unchanged unless they are adjacent to a source, but in the examples, 0s don't change. Wait, no, in the output, 0s are only where the input had 0s, except when a 2 was adjacent to a source and becomes the source's value. So 0s stay 0s unless they are 2s adjacent to a source.\n\nWait, no, in the output, the 0s are the same as the input. So the process is:\n\n- For each cell in the input:\n  - If the cell is 0, it remains 0.\n  - If the cell is 2, check all eight surrounding cells. If any of them has a value >2, then this 2 becomes that value. If multiple sources are adjacent, which one takes precedence? It seems that the highest value might take precedence, but in the examples, it's not clear. Alternatively, perhaps each 2 is replaced by the first source it encounters, but that's unclear.\n\nWait, in Example 0, the 3 is at (2,4). The surrounding 2s become 3s. Similarly, the 9 at (7,10) in the input becomes 9s around it. So each 2 adjacent to any source (value >2) is replaced by the source's value. If a 2 is adjacent to multiple sources, which value does it take? For example, if a 2 is next to both a 3 and a 9, which one does it become? The examples don't show this, so perhaps the rule is that the 2 takes the value of the first source it encounters, but I'm not sure. Alternatively, perhaps the highest value among the adjacent sources is taken.\n\nBut looking at the test input's masked output, I see that some cells are already filled, so I can use those to deduce the rule.\n\nWait, in the test input's masked output, for example, in row 2, column 12, the value is 2, but in the output hint, it's 8. So the 2 was replaced by 8 because it was adjacent to an 8. Similarly, in row 3, column 12, it's 8, and in the output, it's 8, so that makes sense.\n\nSo the rule is: for each 2 in the input, if it is adjacent (including diagonally) to any cell with a value >2, it becomes that value. If multiple such cells are adjacent, perhaps the highest value is taken, or maybe the first one encountered. But in the examples, it seems that the value is taken from the source, and if a 2 is adjacent to multiple sources, perhaps the highest value is used. Alternatively, maybe the 2 is replaced by the value of the nearest source, but that's more complex.\n\nWait, in Example 0, the 3 is at (2,4). The surrounding 2s become 3s. The 9 is at (7,10), and the surrounding 2s become 9s. So each 2 is replaced by the value of any adjacent source. But if a 2 is adjacent to multiple sources, which one takes precedence? For example, if a 2 is next to a 3 and a 9, does it become 3 or 9? The examples don't show this, so perhaps the rule is that the 2 takes the value of the first source it encounters, but that's unclear. Alternatively, perhaps the 2 takes the maximum value among adjacent sources.\n\nBut in the test input's output hint, I see that some cells are already filled, so perhaps the rule is that each 2 is replaced by the value of the first source it encounters when scanning the grid in a certain order, perhaps row-wise from top-left to bottom-right.\n\nAlternatively, perhaps the 2s are replaced by the value of the nearest source, but that would complicate things.\n\nWait, perhaps the correct approach is that each 2 is replaced by the value of any adjacent source, regardless of others. So if a 2 is adjacent to multiple sources, it could take any of their values, but in practice, the output seems to have the highest value in such cases. For example, in the test input, the 8 is a source, and the 2s around it become 8s. Similarly, the 9s spread as well.\n\nWait, in the test input's output hint, row 2, column 12 is 8, which was a 2 in the input. So the 2 was adjacent to an 8, hence became 8.\n\nSo, the transformation is:\n\nFor each cell in the input grid:\n\n- If the cell is 0, it remains 0.\n- If the cell is 2, check all eight surrounding cells. If any of them has a value >2, then this cell becomes that value. If multiple sources are present, the cell takes the maximum value among them.\n- If the cell is >2, it remains the same.\n\nWait, but in the training examples, when a 2 is adjacent to multiple sources, which value does it take? For example, if a 2 is next to both a 3 and a 9, does it become 9? Because 9 is higher than 3. So perhaps the rule is that the 2 takes the maximum value among all adjacent sources.\n\nLet me check Example 0. In row 7, column 10, the input has a 9. The surrounding 2s become 9s. In row 2, column 4, the 3 causes surrounding 2s to become 3s. So if a 2 is adjacent to both a 3 and a 9, it would become 9.\n\nIn the test input, looking at the output hint, in row 2, column 12, the value is 8, which is adjacent to an 8 in the input. So that makes sense.\n\nAnother example: in the test input's output hint, row 3, column 12 is 8, which was a 2 in the input. So it's adjacent to an 8.\n\nSo, the process is:\n\n1. For each cell in the input grid, if it's a 2, check all eight surrounding cells. If any of those cells have a value >2, then this cell becomes the maximum value among those sources. If no sources are adjacent, it remains 2.\n\nWait, but in the training examples, some 2s remain as 2s in the output. For example, in Example 0's output, the bottom rows have 2s that are not adjacent to any sources, so they remain 2s.\n\nSo, the algorithm is:\n\n- For each cell (i,j) in the grid:\n  - If input[i][j] is 0: output[i][j] = 0\n  - Else if input[i][j] > 2: output[i][j] = input[i][j]\n  - Else (input[i][j] is 2):\n    - Look at all eight surrounding cells (i-1,j-1 to i+1,j+1)\n    - Collect all values from those cells that are >2\n    - If any such values exist, output[i][j] is the maximum of those values\n    - Else, output[i][j] remains 2\n\nThis seems to fit the examples.\n\nNow, applying this to the test input.\n\nThe test input is a 29x30 grid. The output hint has some cells revealed as MASK, but others are filled. We need to fill in the MASKed cells according to the rule.\n\nLet's look at the test input's output hint. For example, in row 2, the output hint has [0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,0,0,0,0,0,2,8,8,2,0,0,0,0]. So, the 2s in the input at positions (2,12) to (2,16) are now 2,2,2,2,2, but in the output, they become 2,2,2,2,2,0,0,0,0,0,2,8,8,2,0,0,0,0. Wait, no, the output hint shows that in row 2, column 12 is 2, but in the output, it's 8. Wait, no, the output hint shows that in row 2, column 12 is 8, but the input had 2 there. So, according to the rule, this 2 must be adjacent to an 8.\n\nLooking at the test input's row 4, which is [0,0,0,0,0,2,2,2,2,2,2,2,2,2,8,2,2,2,2,2,2,2,2,2,2,0,0,0,0]. So, the 8 is at position (4,14). So, in the input, the cell at (2,12) is 2, and it's two rows above the 8 at (4,14). So, the distance is two rows down and two columns to the right. So, is (2,12) adjacent to (4,14)? No, because adjacency is only immediate neighbors. So, perhaps I'm misunderstanding the positions.\n\nWait, perhaps the rows and columns are 0-based. So, in the test input, the 8 is at row 4, column 14. The cell at row 2, column 12 is two rows above and two columns to the left. So, they are not adjacent. So why is the output hint showing 8 at (2,12)? That suggests that the 2 at (2,12) is adjacent to an 8 in the input.\n\nWait, perhaps I'm miscounting. Let me recount the rows and columns.\n\nIn the test input, the 8 is in row 4, column 14. The cell at row 2, column 12 is two rows above and two columns to the left. So, they are not adjacent. So, how does the 2 at (2,12) become 8 in the output? It must be because it's adjacent to another 8 elsewhere.\n\nWait, looking at the test input, perhaps there's another 8 elsewhere. Let me check the test input's row 12: [0,0,0,0,0,2,2,2,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,</think>\n\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, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 8, 8, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 8, 8, 8, 2, 0, 0, 0, 0, 0, 2, 8, 8, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 8, 2, 2, 2, 2, 2, 2, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 8, 8, 8, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 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, 2, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 8, 2]\n[0, 0, 0, 0, 0, 2, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 2, 0, 0, 2, 8, 8, 2, 0, 0, 2, 2, 2]\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 8, 8, 8, 8, 8, 8, 8, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 0, 2, 9, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 9, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 8, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 8, 2, 0, 2, 9, 2, 2, 2, 9, 2, 0, 0, 0, 0]\n[0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 2, 9, 9, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 2, 9, 2, 2, 2, 2, 9, 9, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 2, 2, 2, 0, 0, 2, 9, 9, 9, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 2, 9, 9, 9, 2, 2, 2, 2, 9, 9, 9, 9, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 9, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 9, 9, 9, 9, 2, 0, 0, 0, 2, 9, 2, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0]\n"
      }
    ],
    "difficulty": 5,
    "problem_uid": "09c534e7_leave_1_out_of_3_idx00_0degI_augmented_PermuteColors_0289346751_permuted_9389_level5",
    "step": 1
  }
]