[
  {
    "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, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0]\n[0, 0, 7, 1, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 5, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0]\n[0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 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, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 4, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n[7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 7, 7, 7, 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, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0]\n[0, 0, 7, 1, 1, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 5, 5, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 5, 5, 7, 0, 0]\n[0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0]\n[0, 0, 7, 1, 1, 1, 1, 7, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 1, 1, 1, 1, 7, 7, 7, 1, 7, 0, 0, 0, 7, 5, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 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, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 4, 4, 7, 7, 7, 7, 4, 7, 0, 0, 0, 0, 0, 0]\n[7, 7, 7, 0, 0, 7, 4, 4, 7, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n[7, 4, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[7, 4, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 7, 4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 7, 7, 7, 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, 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, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 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, 7, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 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, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 7, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 1, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0]\n\n\nOUTPUT:\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 7, 4, 4, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 4, 4, 4, 7, 0, 0, 0, 0, 0, 7, 4, 4, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 4, 4, 4, 7, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 4, 7, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 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, 7, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 7, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 7, 7, 7, 7, 4, 7]\n[0, 0, 0, 0, 0, 7, 4, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 7, 0, 0, 7, 4, 4, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 7, 4, 4, 4, 4, 4, 4, 4, 7, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 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, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 0, 7, 1, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 7, 1, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 7, 4, 4, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 7, 4, 4, 7, 0, 7, 1, 7, 7, 7, 1, 7, 0, 0, 0, 0]\n[0, 0, 0, 7, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 7, 1, 1, 1, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0]\n[0, 0, 7, 1, 7, 7, 7, 7, 1, 1, 1, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0]\n[0, 0, 7, 7, 7, 0, 0, 7, 1, 1, 1, 7, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 7, 1, 1, 1, 7, 7, 7, 7, 1, 1, 1, 1, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 1, 1, 1, 1, 7, 0, 0, 0, 7, 1, 7, 0, 0, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7, 7, 7, 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]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 1, 7, 7, 7, 7, 7, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7, 7, 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, 7, 7, 7, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n\n\nMASKED OUTPUT HINT:\n[MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, 0, MASK, 0, 0, 0]\n[0, MASK, 0, 7, 7, 7, 7, 0, 0, 7, 7, MASK, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, MASK, 5, 7, 7, 7, 7, 5, 5, MASK, 0, 0, 7, 7, 7]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, MASK, 5, 5, MASK, 7, 7, MASK, 5, 7]\n[MASK, 0, 0, 0, 0, 7, 0, 0, 0, MASK, 7, 7, 7, 0, 0, MASK, 7, 7]\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, 7, 7, MASK, 0, 0, 7, MASK, MASK, 0, 7, 7, 7, 0, 0]\n[MASK, MASK, 0, 7, 5, 5, 7, 0, 0, 7, 1, 7, 7, MASK, 1, 7, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, MASK, 7, 0, 7, 7, 7, 0, 0]\n[0, MASK, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, MASK, 0, 0, MASK, 0]\n[0, 0, 0, MASK, 0, 0, 0, 0, MASK, 0, 0, 0, 0, 7, 7, 7, MASK, 0]\n[0, 0, 0, MASK, 0, 0, 0, 0, 0, MASK, MASK, 0, 0, 7, 2, 7, MASK, 0]\n[0, 0, 0, MASK, 0, MASK, MASK, 0, 7, 7, 7, 7, MASK, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 7, 2, 2, 7, MASK, 0, 7, 0, MASK, 0]\n[0, MASK, 7, 2, 2, 7, 0, 0, 7, MASK, 2, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 2, 2, 7, 7, 7, 7, 2, MASK, 7, MASK, 7, 2, 7, MASK, 0]\n[MASK, 0, 7, 7, MASK, 7, 0, 0, MASK, 2, 2, 7, MASK, MASK, 7, 7, MASK, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, MASK, 7, 0, 0, 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": "Okay, so I'm trying to solve this puzzle where I have to figure out the pattern that transforms the input into the output based on the training examples, and then apply that pattern to the test input. Let me start by carefully analyzing the training examples to understand what's going on.\n\nLooking at Example 0, the input and output are both 20x20 grids. I notice that in the output, some numbers have changed from the input. For instance, in the third row of the input, there's a 1, and in the output, the surrounding 7s have turned into 1s. Similarly, in the fifth row, a 5 appears, and in the output, the 7s around it become 5s. This makes me think that the transformation involves some kind of spread or infection where certain numbers \"take over\" adjacent cells.\n\nIn Example 1, the input is a 30x30 grid. The output shows similar changes. For example, a 4 in the input causes surrounding 7s to become 4s, and a 1 does the same. It seems like the numbers 1, 4, 5 are acting as seeds that convert adjacent 7s into themselves. The 2 in the input also affects the output, turning some 7s into 2s. So, the pattern might be that each number (except 0 and 7) is spreading to adjacent 7s, replacing them with the same number.\n\nNow, looking at the test input, I need to apply this pattern. The input is an 18x18 grid. The masked output hint shows some cells as MASK, but others are revealed. My task is to fill in the MASKed cells correctly without changing the revealed ones.\n\nLet me go through the test input row by row and see where the numbers other than 0 and 7 are, as those are the seeds.\n\nIn row 2, there's a 5. So, the 7s around it should become 5s. Looking at the output hint, the third cell is MASK, but the fifth is 5, and the eleventh is 5. That makes sense because the 5 in the input would spread to its neighbors.\n\nIn row 7, there's a 1. The output hint shows 1s in some positions, so the 1 is spreading to adjacent 7s.\n\nIn row 15, there's a 2. So, the 7s around it should become 2s. The output hint shows 2s in some places, which aligns with this.\n\nI also notice that in the training examples, the spread seems to happen in all directions\u2014up, down, left, right, and diagonally. So, each seed number affects all adjacent cells, not just the four cardinal directions.\n\nNow, I'll go through each cell in the test input and determine if it should be changed based on the nearest seed. For each cell that's a 7 in the input, I'll check all eight surrounding cells. If any of them is a number other than 0 or 7, that number will spread to this cell. If multiple seeds are adjacent, the cell takes the value of the seed that appears first or is the strongest? Wait, in the training examples, it seems that the seed with the highest value takes precedence. For example, in Example 0, the 5 is surrounded by 7s, and they become 5s, but if there's a 1 and a 5 adjacent, the 5 would override the 1. Or maybe it's the other way around. Hmm, I need to clarify.\n\nLooking back at Example 0, in row 2, the input has a 1, and the output turns the surrounding 7s into 1s. But in row 3, the 7s around the 5 become 5s. So, it seems that each seed affects its own area, and if a cell is adjacent to multiple seeds, it takes the value of the seed that is numerically higher. Wait, no, in row 2, the 1 is lower than 5, but the 7s around 1 become 1s, and those around 5 become 5s. So, perhaps each seed independently spreads, and if a cell is adjacent to multiple seeds, it takes the value of the seed that is closest or the one that appears first. Alternatively, maybe the seeds with higher values override lower ones.\n\nWait, in Example 0, the 5 is in row 2, column 14 (if we start counting from 0). The 7s around it become 5s, and the 1 is in row 2, column 3, so the 7s around it become 1s. So, the 5 and 1 are separate, and their areas don't overlap. So, perhaps each seed spreads as far as it can without overlapping with another seed's area. So, the transformation is that each number (1,2,4,5) in the input causes all adjacent 7s (including diagonally) to become that number, and this spreads until it hits another number or the edge.\n\nSo, the process is:\n\n1. Identify all the seed numbers (1,2,4,5) in the input.\n2. For each seed, spread its value to all adjacent 7s, including diagonally.\n3. The spreading continues until all possible 7s are converted, but if a cell is reachable by multiple seeds, the seed with the highest value takes precedence. Or maybe the first seed encountered in a certain order.\n\nWait, in Example 0, the 5 is in row 2, column 14, and the 1 is in row 2, column 3. The 5's area doesn't overlap with the 1's area because they are on opposite sides. So, perhaps the spreading is done in a way that each seed's area is exclusive, and the highest value seed takes precedence if there's an overlap.\n\nAlternatively, maybe the seeds are processed in a certain order, like highest to lowest, so that higher seeds override lower ones in case of overlap.\n\nLooking at Example 1, the 4 is in row 13, column 5, and the 1 is in row 20, column 19. The 4 spreads to its area, and the 1 spreads to its own. So, again, no overlap.\n\nIn the test input, the seeds are 5, 1, and 2. So, 5 is higher than 2, which is higher than 1. So, if a cell is adjacent to both 5 and 2, it should become 5. If it's adjacent to 2 and 1, it becomes 2.\n\nSo, the approach is:\n\n- For each cell in the grid, if it's a 7 in the input, check all eight surrounding cells.\n- If any of those cells is a seed (1,2,4,5), the cell takes the value of the seed with the highest value among them.\n- If multiple seeds are adjacent, the highest value seed determines the cell's value.\n- If no seeds are adjacent, the cell remains 7.\n\nWait, but in the training examples, sometimes the seeds are not directly adjacent but several steps away. For example, in Example 0, the 5 is in row 2, and the 7s in row 3, columns 14-17 become 5s. So, it's not just direct adjacency but a flood fill from the seed, converting all reachable 7s into the seed's value, until another seed's area is encountered.\n\nSo, the correct approach is:\n\n- Perform a flood fill from each seed, converting all connected 7s into the seed's value.\n- Seeds with higher values take precedence over lower ones. So, if a cell can be reached by multiple seeds, it takes the value of the highest seed.\n\nWait, but in Example 0, the 5 is in row 2, column 14, and the 1 is in row 2, column 3. The 5's area expands to the right, and the 1's area expands to the left. They don't overlap, so no conflict. But if they did, the higher seed (5) would take precedence.\n\nSo, the algorithm is:\n\n1. Identify all seeds (cells with values 1,2,4,5) in the input.\n2. Sort the seeds in descending order of their values.\n3. For each seed in this order, perform a flood fill (including diagonally) converting all adjacent 7s into the seed's value. This flood fill should not overwrite cells that have already been assigned a higher value.\n\nWait, but in the training examples, the flood fill seems to be done simultaneously, not in a specific order. Alternatively, perhaps each seed's area is determined by the closest seed, but that's more complex.\n\nAlternatively, perhaps each cell takes the value of the nearest seed, with higher seeds overriding lower ones if they are equally near.\n\nBut given the examples, it's more likely that the seeds are processed in order of their values, highest first, and their areas are filled without considering lower seeds.\n\nSo, the steps would be:\n\n- Create a copy of the input grid.\n- For each cell in the grid, if it's a seed (1,2,4,5), note its position and value.\n- Sort the seeds in descending order of their values.\n- For each seed in this order, perform a BFS or DFS to flood fill all connected 7s (including diagonally) with the seed's value. Mark these cells as filled so that lower seeds don't overwrite them.\n\nThis way, higher seeds take precedence.\n\nNow, applying this to the test input:\n\nFirst, identify all seeds:\n\n- Row 2, column 4: 5\n- Row 7, column 10: 1\n- Row 15, column 4: 2\n\nSort them by value: 5, 2, 1.\n\nStart with the 5 in row 2, column 4. Flood fill all connected 7s with 5, including diagonally. This will affect cells around it, expanding as far as possible without hitting another seed's area.\n\nNext, process the 2 in row 15, column 4. Flood fill its connected 7s with 2, but only where not already filled by 5.\n\nFinally, process the 1 in row 7, column 10. Flood fill its connected 7s with 1, but only where not filled by 5 or 2.\n\nLooking at the masked output hint, some cells are already filled. For example, in row 2, the fifth cell is 5, and the eleventh is 5. So, the 5 has spread to the right and left.\n\nIn row 7, the cell at position 10 is 1, and the surrounding cells are 1s. So, the 1 has spread to its area.\n\nIn row 15, the 2 has spread to some cells, but the output hint shows 2s in certain positions.\n\nNow, I'll go through each row of the test input and apply this logic, considering the masked output hint to guide me.\n\nFor example, in row 0, all are 0s, so output remains 0s.\n\nRow 1: The third cell is 7, but in the output hint, it's MASK. However, the fifth cell is 7, and the output hint shows 7. Wait, no, the output hint for row 1 is [0, MASK, 0, 7, 7, 7, 7, 0, 0, 7, 7, MASK, 7, 0, 0, 0, 0, 0]. So, the third cell is MASK, but the fifth is 7. So, perhaps the 7 in the input remains 7 because it's not adjacent to any seed.\n\nWait, but the 5 is in row 2, column 4. So, the cell in row 1, column 4 is adjacent to the 5 (diagonally). So, it should become 5. But in the output hint, row 1, column 4 is 7. Hmm, that's confusing. Maybe I'm misunderstanding the grid indices.\n\nWait, perhaps the rows and columns are 0-indexed. So, row 2, column 4 is the fifth cell in row 2. So, row 1, column 4 is directly above it, so it should be converted to 5. But in the output hint, row 1, column 4 is 7. That contradicts my earlier assumption.\n\nWait, maybe the spreading is only to orthogonally adjacent cells, not diagonally. Let me re-examine the training examples.\n\nIn Example 0, the 1 in row 2, column 3 causes the cell to the right (column 4) to become 1, which is orthogonal. Similarly, the 5 in row 2, column 14 causes the cell to the right (column 15) to become 5. So, perhaps the spreading is only orthogonal, not diagonal.\n\nWait, but in Example 1, the 4 in row 13, column 5 causes the cells around it to become 4, including diagonally. For example, in row 12, column 5 is 7, and in the output, it's 4. So, that's orthogonal. Wait, no, row 12 is above row 13, so it's orthogonal. But in row 14, column 5 is 7, and in the output, it's 4. So, orthogonal spreading.\n\nWait, perhaps the spreading is only orthogonal. Let me check Example 0 again. The 1 in row 2, column 3 causes the cell to the right (column 4) to become 1, which is orthogonal. The 5 in row 2, column 14 causes the cell to the right (column 15) to become 5. So, perhaps the spreading is only</think>\n\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 5, 5, 7, 7, 7, 7, 5, 7]\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7]\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 0, 7, 5, 5, 7, 0, 0, 7, 1, 7, 7, 7, 1, 7, 0, 0]\n[0, 0, 0, 7, 7, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7, 7, 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, 7, 7, 7, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 2, 7, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 7, 2, 2, 7, 0, 0, 7, 0, 0, 0]\n[0, 0, 7, 2, 2, 7, 0, 0, 7, 2, 2, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 7, 2, 2, 7, 7, 7, 7, 2, 2, 7, 7, 7, 2, 7, 0, 0]\n[0, 0, 7, 7, 7, 7, 0, 0, 7, 2, 2, 7, 0, 7, 7, 7, 0, 0]\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0]\n"
      }
    ],
    "difficulty": 15,
    "problem_uid": "09c534e7_leave_1_out_of_3_idx02_0degI_augmented_PermuteColors_0741532986_permuted_34510_level15",
    "step": 5
  }
]