[
  {
    "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
  }
]