prompt
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stringclasses 36
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stringclasses 1
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stringlengths 24
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stringlengths 1
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| meta
stringlengths 280
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stringclasses 7
values | task_name
stringclasses 36
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|---|---|---|---|---|---|---|---|---|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]
Example 2:
[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]
Example 3:
[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]
# Test Problem:
[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\n\\nExample 2:\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\n\\nExample 3:\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\n\\n# Test Problem:\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> \", \"answer\": \"[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"1e1a98e7-3906-4feb-9a54-d6b8a8a431f6\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\\\n\\\\nExample 2:\\\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\\\n\\\\nExample 3:\\\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\\\n\\\\n# Test Problem:\\\\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> \\\", \\\"answer\\\": \\\"[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "1e1a98e7-3906-4feb-9a54-d6b8a8a431f6"}
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[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]
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{"id": "1e1a98e7-3906-4feb-9a54-d6b8a8a431f6", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\n\nExample 2:\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\n\nExample 3:\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> [[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]\n\n# Test Problem:\n[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]] -> ", "answer": "[[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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], [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], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 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, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 0]]
Example 2:
[[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], [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], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 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, 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, 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, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 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, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[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], [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], [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], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\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], [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], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 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, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 0]]\\n\\nExample 2:\\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], [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], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 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, 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, 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, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 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, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\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], [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], [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], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"8fc7a026-fbb8-494c-8e76-02125f4add8e\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\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], [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], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 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, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 0]]\\\\n\\\\nExample 2:\\\\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], [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], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 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, 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, 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, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 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, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\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], [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], [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], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "8fc7a026-fbb8-494c-8e76-02125f4add8e"}
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[[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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "8fc7a026-fbb8-494c-8e76-02125f4add8e", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\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], [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], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 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, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 4, 1, 1, 8, 8, 8, 1, 1, 4, 4, 3, 3, 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, 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, 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, 0]]\n\nExample 2:\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], [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], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 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, 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, 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, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 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, 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, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\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], [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], [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], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[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], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 8, 4, 8, 2, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 2, 2, 8, 4, 4, 4, 4, 8, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[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, 0, 0, 8, 8, 0, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 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, 0, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 3, 0, 3, 3, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 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, 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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 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, 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], [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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 4:
[[0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 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], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0], [0, 0, 0, 0, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7], [0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 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], [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, 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]]
Example 5:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 8], [0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\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, 0, 0, 8, 8, 0, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 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, 0, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 3, 0, 3, 3, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 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, 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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 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, 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], [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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 4:\\n[[0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 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], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0], [0, 0, 0, 0, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7], [0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 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], [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, 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\\nExample 5:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 8], [0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7], [0, 0, 0, 0, 0, 7, 0, 7, 0, 7, 0, 0, 0, 7], [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, 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, 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, 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, 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]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"dcd13562-1050-4dbd-9744-161bdbf9da03\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\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, 0, 0, 8, 8, 0, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 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, 0, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 3, 0, 3, 3, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 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, 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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 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, 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], [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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 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], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0], [0, 0, 0, 0, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7], [0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 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], [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, 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\\\\nExample 5:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 8], [0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7], [0, 0, 0, 0, 0, 7, 0, 7, 0, 7, 0, 0, 0, 7], [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, 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, 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, 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, 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]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "dcd13562-1050-4dbd-9744-161bdbf9da03"}
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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7], [0, 0, 0, 0, 0, 7, 0, 7, 0, 7, 0, 0, 0, 7], [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, 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, 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, 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, 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]]
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{"id": "dcd13562-1050-4dbd-9744-161bdbf9da03", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\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, 0, 0, 8, 8, 0, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 8, 0, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 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, 0, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 3, 0, 3, 3, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0], [0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 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, 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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 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, 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], [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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 4:\n[[0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 8, 8, 8, 0], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 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], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 7, 7, 7, 0], [0, 0, 0, 0, 7, 7, 0, 0, 7, 7, 7, 0, 7, 7], [0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 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], [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, 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\nExample 5:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 8], [0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7], [0, 0, 0, 0, 0, 7, 0, 7, 0, 7, 0, 0, 0, 7], [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, 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, 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, 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, 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]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 6, 6, 1, 1], [0, 0, 6, 6, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 6, 1, 0, 6, 1, 0, 6, 1, 0, 6, 1, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[1, 1, 3, 3, 6, 6], [1, 1, 3, 3, 6, 6], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [2, 2, 2, 2, 1, 1], [2, 2, 2, 2, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 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, 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, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 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, 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]]
Example 3:
[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 0], [0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 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, 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, 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, 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]]
Example 4:
[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 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, 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, 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, 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, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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]]
# Test Problem:
[[0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 0, 0, 3, 3], [3, 3, 0, 0, 3, 3], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [2, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 6, 6, 1, 1], [0, 0, 6, 6, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 6, 1, 0, 6, 1, 0, 6, 1, 0, 6, 1, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[1, 1, 3, 3, 6, 6], [1, 1, 3, 3, 6, 6], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [2, 2, 2, 2, 1, 1], [2, 2, 2, 2, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 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, 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, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 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, 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\\nExample 3:\\n[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 0], [0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 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, 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, 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, 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\\nExample 4:\\n[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 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, 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, 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, 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, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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\\n# Test Problem:\\n[[0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 0, 0, 3, 3], [3, 3, 0, 0, 3, 3], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [2, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0]] -> \", \"answer\": \"[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"dce557c1-3e12-4bdf-a0d1-ba59e83e3799\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 6, 6, 1, 1], [0, 0, 6, 6, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 6, 1, 0, 6, 1, 0, 6, 1, 0, 6, 1, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[1, 1, 3, 3, 6, 6], [1, 1, 3, 3, 6, 6], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [2, 2, 2, 2, 1, 1], [2, 2, 2, 2, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 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, 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, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 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, 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\\\\nExample 3:\\\\n[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 0], [0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 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, 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, 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, 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\\\\nExample 4:\\\\n[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 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, 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, 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, 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, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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\\\\n# Test Problem:\\\\n[[0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 0, 0, 3, 3], [3, 3, 0, 0, 3, 3], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [2, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "dce557c1-3e12-4bdf-a0d1-ba59e83e3799"}
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[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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]]
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{"id": "dce557c1-3e12-4bdf-a0d1-ba59e83e3799", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [0, 0, 6, 6, 1, 1], [0, 0, 6, 6, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 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, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 6, 1, 0, 6, 1, 0, 6, 1, 0, 6, 1, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[1, 1, 3, 3, 6, 6], [1, 1, 3, 3, 6, 6], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [2, 2, 2, 2, 1, 1], [2, 2, 2, 2, 1, 1], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 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, 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, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 6, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 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, 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\nExample 3:\n[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [3, 3, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 2, 0], [0, 0, 2, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 0, 0, 3, 2, 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, 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, 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, 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\nExample 4:\n[[1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 2, 2, 2, 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, 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, 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, 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, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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\n# Test Problem:\n[[0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [3, 3, 0, 0, 3, 3], [3, 3, 0, 0, 3, 3], [0, 0, 2, 2, 0, 0], [0, 0, 2, 2, 0, 0], [5, 5, 5, 5, 5, 5], [2, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0]] -> ", "answer": "[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 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]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 2, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3]] -> [[8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0]]
Example 3:
[[2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3]] -> [[8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0]]
# Test Problem:
[[2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 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, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 2, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3]] -> [[8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3]] -> [[8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 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, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2]] -> \", \"answer\": \"[[8, 2, 2, 2, 0, 2, 8, 2, 2, 0, 2, 2, 8, 2, 0, 2, 2, 2, 8], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [8, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 8, 2, 0, 2, 0, 2, 8]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"9d2519c8-790e-4b11-a04b-1ae6be8261d3\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 2, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3]] -> [[8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3]] -> [[8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 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, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2]] -> \\\", \\\"answer\\\": \\\"[[8, 2, 2, 2, 0, 2, 8, 2, 2, 0, 2, 2, 8, 2, 0, 2, 2, 2, 8], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [8, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 8, 2, 0, 2, 0, 2, 8]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "9d2519c8-790e-4b11-a04b-1ae6be8261d3"}
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[[8, 2, 2, 2, 0, 2, 8, 2, 2, 0, 2, 2, 8, 2, 0, 2, 2, 2, 8], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [8, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 8, 2, 0, 2, 0, 2, 8]]
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{"id": "9d2519c8-790e-4b11-a04b-1ae6be8261d3", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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, 0], [0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [8, 2, 2, 0, 0, 2, 8, 2, 0, 0, 2, 2, 8, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 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, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 2, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3]] -> [[8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[2, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3], [0, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 3], [0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 2, 2, 0, 0, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [2, 0, 2, 0, 2, 0, 2, 0, 3, 3, 3], [0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 3], [2, 2, 0, 0, 2, 2, 0, 0, 3, 3, 3]] -> [[8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [8, 2, 0, 0, 2, 8, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 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, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2]] -> ", "answer": "[[8, 2, 2, 2, 0, 2, 8, 2, 2, 0, 2, 2, 8, 2, 0, 2, 2, 2, 8], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 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, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8], [2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2], [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, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2], [8, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 8, 2, 0, 2, 0, 2, 8]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]]
Example 2:
[[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]]
Example 3:
[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0]] -> [[0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0]]
# Test Problem:
[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0]] -> [[0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0]] -> \", \"answer\": \"[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"c1465534-717b-4d0c-8426-da800487e686\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0]] -> [[0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
|
PUZZLE##symbolic_hard
|
PUZZLE
|
{"index": "c1465534-717b-4d0c-8426-da800487e686"}
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[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0]]
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{"id": "c1465534-717b-4d0c-8426-da800487e686", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0, 1, 3, 3, 0, 1, 0, 0, 0], [0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4], [0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0]] -> [[0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 8, 0], [0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0, 0, 0, 8, 0, 2, 2, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0, 0, 0, 8, 2, 2, 0, 8, 0]]\n\n# Test Problem:\n[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0]] -> ", "answer": "[[0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0], [8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0, 0, 0, 3, 8, 8, 0, 3, 0], [0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0, 0, 0, 3, 0, 0, 8, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 1, 5, 2, 2, 2, 0], [1, 0, 0, 0, 5, 0, 2, 2, 2], [1, 1, 0, 0, 5, 0, 0, 2, 2], [1, 1, 1, 0, 5, 0, 0, 0, 2]] -> [[2, 2, 2, 1], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2]]
Example 2:
[[0, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 0, 5, 2, 2, 0, 0], [1, 1, 0, 0, 5, 0, 2, 2, 0], [1, 1, 1, 0, 5, 0, 2, 2, 0]] -> [[0, 0, 0, 1], [1, 0, 0, 0], [1, 1, 0, 0], [1, 1, 1, 0]]
Example 3:
[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 1, 0, 0, 5, 0, 0, 3, 3]] -> [[1, 1, 3, 3], [1, 3, 3, 1], [1, 3, 3, 1], [1, 1, 3, 3]]
Example 4:
[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 6, 6, 1], [1, 6, 6, 1], [1, 1, 1, 1]]
Example 5:
[[1, 1, 1, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 1]]
Example 6:
[[1, 1, 1, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 0, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]]
Example 7:
[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 0, 5, 0, 7, 7, 7], [1, 0, 1, 1, 5, 0, 7, 0, 0], [1, 0, 1, 0, 5, 0, 7, 0, 7]] -> [[1, 1, 1, 1], [1, 7, 7, 7], [1, 7, 1, 1], [1, 7, 1, 7]]
# Test Problem:
[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [0, 0, 0, 1, 5, 3, 3, 3, 0], [0, 1, 1, 1, 5, 3, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 1, 5, 2, 2, 2, 0], [1, 0, 0, 0, 5, 0, 2, 2, 2], [1, 1, 0, 0, 5, 0, 0, 2, 2], [1, 1, 1, 0, 5, 0, 0, 0, 2]] -> [[2, 2, 2, 1], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2]]\\n\\nExample 2:\\n[[0, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 0, 5, 2, 2, 0, 0], [1, 1, 0, 0, 5, 0, 2, 2, 0], [1, 1, 1, 0, 5, 0, 2, 2, 0]] -> [[0, 0, 0, 1], [1, 0, 0, 0], [1, 1, 0, 0], [1, 1, 1, 0]]\\n\\nExample 3:\\n[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 1, 0, 0, 5, 0, 0, 3, 3]] -> [[1, 1, 3, 3], [1, 3, 3, 1], [1, 3, 3, 1], [1, 1, 3, 3]]\\n\\nExample 4:\\n[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 6, 6, 1], [1, 6, 6, 1], [1, 1, 1, 1]]\\n\\nExample 5:\\n[[1, 1, 1, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 1]]\\n\\nExample 6:\\n[[1, 1, 1, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 0, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]]\\n\\nExample 7:\\n[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 0, 5, 0, 7, 7, 7], [1, 0, 1, 1, 5, 0, 7, 0, 0], [1, 0, 1, 0, 5, 0, 7, 0, 7]] -> [[1, 1, 1, 1], [1, 7, 7, 7], [1, 7, 1, 1], [1, 7, 1, 7]]\\n\\n# Test Problem:\\n[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [0, 0, 0, 1, 5, 3, 3, 3, 0], [0, 1, 1, 1, 5, 3, 0, 0, 0]] -> \", \"answer\": \"[[1, 1, 3, 3], [1, 3, 3, 1], [3, 3, 3, 1], [3, 1, 1, 1]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ba0f77c7-8e78-4146-bb41-4dc18d0d48f7\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 1, 5, 2, 2, 2, 0], [1, 0, 0, 0, 5, 0, 2, 2, 2], [1, 1, 0, 0, 5, 0, 0, 2, 2], [1, 1, 1, 0, 5, 0, 0, 0, 2]] -> [[2, 2, 2, 1], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 0, 5, 2, 2, 0, 0], [1, 1, 0, 0, 5, 0, 2, 2, 0], [1, 1, 1, 0, 5, 0, 2, 2, 0]] -> [[0, 0, 0, 1], [1, 0, 0, 0], [1, 1, 0, 0], [1, 1, 1, 0]]\\\\n\\\\nExample 3:\\\\n[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 1, 0, 0, 5, 0, 0, 3, 3]] -> [[1, 1, 3, 3], [1, 3, 3, 1], [1, 3, 3, 1], [1, 1, 3, 3]]\\\\n\\\\nExample 4:\\\\n[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 6, 6, 1], [1, 6, 6, 1], [1, 1, 1, 1]]\\\\n\\\\nExample 5:\\\\n[[1, 1, 1, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 1]]\\\\n\\\\nExample 6:\\\\n[[1, 1, 1, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 0, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]]\\\\n\\\\nExample 7:\\\\n[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 0, 5, 0, 7, 7, 7], [1, 0, 1, 1, 5, 0, 7, 0, 0], [1, 0, 1, 0, 5, 0, 7, 0, 7]] -> [[1, 1, 1, 1], [1, 7, 7, 7], [1, 7, 1, 1], [1, 7, 1, 7]]\\\\n\\\\n# Test Problem:\\\\n[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [0, 0, 0, 1, 5, 3, 3, 3, 0], [0, 1, 1, 1, 5, 3, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[1, 1, 3, 3], [1, 3, 3, 1], [3, 3, 3, 1], [3, 1, 1, 1]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "ba0f77c7-8e78-4146-bb41-4dc18d0d48f7"}
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[[1, 1, 3, 3], [1, 3, 3, 1], [3, 3, 3, 1], [3, 1, 1, 1]]
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{"id": "ba0f77c7-8e78-4146-bb41-4dc18d0d48f7", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 1, 5, 2, 2, 2, 0], [1, 0, 0, 0, 5, 0, 2, 2, 2], [1, 1, 0, 0, 5, 0, 0, 2, 2], [1, 1, 1, 0, 5, 0, 0, 0, 2]] -> [[2, 2, 2, 1], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2]]\n\nExample 2:\n[[0, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 0, 5, 2, 2, 0, 0], [1, 1, 0, 0, 5, 0, 2, 2, 0], [1, 1, 1, 0, 5, 0, 2, 2, 0]] -> [[0, 0, 0, 1], [1, 0, 0, 0], [1, 1, 0, 0], [1, 1, 1, 0]]\n\nExample 3:\n[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 0, 0, 1, 5, 0, 3, 3, 0], [1, 1, 0, 0, 5, 0, 0, 3, 3]] -> [[1, 1, 3, 3], [1, 3, 3, 1], [1, 3, 3, 1], [1, 1, 3, 3]]\n\nExample 4:\n[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 0, 0, 1, 5, 0, 6, 6, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 6, 6, 1], [1, 6, 6, 1], [1, 1, 1, 1]]\n\nExample 5:\n[[1, 1, 1, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 2, 2, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 1]]\n\nExample 6:\n[[1, 1, 1, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 3, 0, 0], [1, 0, 0, 1, 5, 3, 0, 0, 0], [1, 0, 0, 1, 5, 0, 0, 0, 0]] -> [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]]\n\nExample 7:\n[[1, 1, 1, 1, 5, 0, 0, 0, 0], [1, 0, 0, 0, 5, 0, 7, 7, 7], [1, 0, 1, 1, 5, 0, 7, 0, 0], [1, 0, 1, 0, 5, 0, 7, 0, 7]] -> [[1, 1, 1, 1], [1, 7, 7, 7], [1, 7, 1, 1], [1, 7, 1, 7]]\n\n# Test Problem:\n[[1, 1, 0, 0, 5, 0, 0, 3, 3], [1, 0, 0, 1, 5, 0, 3, 3, 0], [0, 0, 0, 1, 5, 3, 3, 3, 0], [0, 1, 1, 1, 5, 3, 0, 0, 0]] -> ", "answer": "[[1, 1, 3, 3], [1, 3, 3, 1], [3, 3, 3, 1], [3, 1, 1, 1]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 7, 2, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 1, 1, 7, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1], [1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1], [1, 2, 8, 2, 1, 1, 2, 7, 2, 1, 1], [1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]
Example 2:
[[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, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 1, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0]] -> [[8, 8, 8, 8, 8, 8], [8, 2, 8, 8, 8, 8], [2, 1, 2, 8, 8, 8], [2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 2, 8], [8, 8, 8, 4, 2, 8], [8, 8, 2, 2, 2, 8]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0]] -> [[3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 2, 1, 2, 3, 3, 3, 3, 2, 2, 3, 3], [3, 3, 2, 3, 3, 3, 3, 3, 2, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3]]
# Test Problem:
[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 7, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0], [0, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 0, 0, 0, 0, 8, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 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, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 7, 2, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 1, 1, 7, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1], [1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1], [1, 2, 8, 2, 1, 1, 2, 7, 2, 1, 1], [1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\\n\\nExample 2:\\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, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 1, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0]] -> [[8, 8, 8, 8, 8, 8], [8, 2, 8, 8, 8, 8], [2, 1, 2, 8, 8, 8], [2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 2, 8], [8, 8, 8, 4, 2, 8], [8, 8, 2, 2, 2, 8]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0]] -> [[3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 2, 1, 2, 3, 3, 3, 3, 2, 2, 3, 3], [3, 3, 2, 3, 3, 3, 3, 3, 2, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3]]\\n\\n# Test Problem:\\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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 7, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0], [0, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 0, 0, 0, 0, 8, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 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, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 1, 2, 4, 4, 4, 4, 4, 4, 2, 7, 2, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 4, 4, 4], [4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 2, 4], [2, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 2], [2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"be575081-40e0-466e-949f-a5f0987d671c\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 7, 2, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 1, 1, 7, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1], [1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1], [1, 2, 8, 2, 1, 1, 2, 7, 2, 1, 1], [1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\\\\n\\\\nExample 2:\\\\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, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 1, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0]] -> [[8, 8, 8, 8, 8, 8], [8, 2, 8, 8, 8, 8], [2, 1, 2, 8, 8, 8], [2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 2, 8], [8, 8, 8, 4, 2, 8], [8, 8, 2, 2, 2, 8]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0]] -> [[3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 2, 1, 2, 3, 3, 3, 3, 2, 2, 3, 3], [3, 3, 2, 3, 3, 3, 3, 3, 2, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3]]\\\\n\\\\n# Test Problem:\\\\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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 7, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0], [0, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 0, 0, 0, 0, 8, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 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, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 1, 2, 4, 4, 4, 4, 4, 4, 2, 7, 2, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 4, 4, 4], [4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 2, 4], [2, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 2], [2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "be575081-40e0-466e-949f-a5f0987d671c"}
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[[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 1, 2, 4, 4, 4, 4, 4, 4, 2, 7, 2, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 4, 4, 4], [4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 2, 4], [2, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 2], [2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2]]
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{"id": "be575081-40e0-466e-949f-a5f0987d671c", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 7, 2, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 1, 1, 7, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1], [1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1], [1, 2, 8, 2, 1, 1, 2, 7, 2, 1, 1], [1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\n\nExample 2:\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, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 1, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0]] -> [[8, 8, 8, 8, 8, 8], [8, 2, 8, 8, 8, 8], [2, 1, 2, 8, 8, 8], [2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 2, 8], [8, 8, 8, 4, 2, 8], [8, 8, 2, 2, 2, 8]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0], [0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 2, 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, 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, 0, 0, 0]] -> [[3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3], [3, 2, 1, 2, 3, 3, 3, 3, 2, 2, 3, 3], [3, 3, 2, 3, 3, 3, 3, 3, 2, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3]]\n\n# Test Problem:\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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 7, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0], [0, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 0, 0, 0, 0, 8, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 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, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 1, 2, 4, 4, 4, 4, 4, 4, 2, 7, 2, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 4, 4, 4], [4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 2, 4], [2, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 2], [2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]
Example 2:
[[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]]
Example 3:
[[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]]
Example 4:
[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]]
# Test Problem:
[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]\\n\\nExample 2:\\n[[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]]\\n\\nExample 3:\\n[[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]]\\n\\nExample 4:\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]]\\n\\n# Test Problem:\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]] -> \", \"answer\": \"[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"0ca95a35-d3cd-4ee2-9595-086e4d6fbdd8\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]\\\\n\\\\nExample 2:\\\\n[[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]]\\\\n\\\\nExample 3:\\\\n[[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]]\\\\n\\\\nExample 4:\\\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]]\\\\n\\\\n# Test Problem:\\\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]] -> \\\", \\\"answer\\\": \\\"[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "0ca95a35-d3cd-4ee2-9595-086e4d6fbdd8"}
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[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]
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{"id": "0ca95a35-d3cd-4ee2-9595-086e4d6fbdd8", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]\n\nExample 2:\n[[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 2, 2, 8, 8], [1, 1, 2, 2, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 2, 2, 2, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 2, 2, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]] -> [[1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 2, 2, 2, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8]]\n\nExample 3:\n[[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 2, 2, 2, 1, 1, 1], [8, 2, 2, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 2, 2, 2], [2, 2, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 2, 2], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1]]\n\nExample 4:\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1]] -> [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]]\n\n# Test Problem:\n[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 2, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]] -> ", "answer": "[[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 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, 0, 5, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1, 3, 1, 0, 0], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 7, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[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, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 0, 0], [0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 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]]
Example 3:
[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 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, 5, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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, 5, 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, 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, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 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, 0, 5, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1, 3, 1, 0, 0], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 7, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\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, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 0, 0], [0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 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\\nExample 3:\\n[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 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, 5, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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, 5, 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, 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, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]] -> \", \"answer\": \"[[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], [0, 0, 0, 0, 2, 2, 3, 3, 0, 0], [0, 0, 0, 0, 1, 0, 3, 3, 8, 8], [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], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"b3deae55-2ace-4dbb-bb50-d1b80e05e2c4\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 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, 0, 5, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1, 3, 1, 0, 0], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 7, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\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, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 0, 0], [0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 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\\\\nExample 3:\\\\n[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 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, 5, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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, 5, 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, 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, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[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], [0, 0, 0, 0, 2, 2, 3, 3, 0, 0], [0, 0, 0, 0, 1, 0, 3, 3, 8, 8], [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], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "b3deae55-2ace-4dbb-bb50-d1b80e05e2c4"}
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[[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], [0, 0, 0, 0, 2, 2, 3, 3, 0, 0], [0, 0, 0, 0, 1, 0, 3, 3, 8, 8], [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], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]]
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{"id": "b3deae55-2ace-4dbb-bb50-d1b80e05e2c4", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 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, 0, 5, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0], [0, 4, 4, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1, 3, 1, 0, 0], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 7, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\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, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 0, 0], [0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 5, 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, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 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, 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\nExample 3:\n[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 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, 5, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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, 5, 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, 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, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]] -> ", "answer": "[[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], [0, 0, 0, 0, 2, 2, 3, 3, 0, 0], [0, 0, 0, 0, 1, 0, 3, 3, 8, 8], [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], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, 3, 0, 0, 0, 0, 0], [0, 1, 0, 3, 3, 8, 8, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 8, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 8, 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, 8, 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, 0, 0, 0], [0, 0, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 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], [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, 8, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 1, 1, 1, 1, 1, 1, 8, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 0, 8, 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, 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, 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, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 8, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 8, 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, 8, 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, 0, 0, 0], [0, 0, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 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], [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, 8, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 1, 1, 1, 1, 1, 1, 8, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 0, 8, 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, 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, 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, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 8, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"78b4f98d-4004-479e-8c1a-eb5a648f1350\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 8, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 8, 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, 8, 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, 0, 0, 0], [0, 0, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 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], [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, 8, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 1, 1, 1, 1, 1, 1, 8, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 0, 8, 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, 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, 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, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 8, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "78b4f98d-4004-479e-8c1a-eb5a648f1350"}
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[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 8, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "78b4f98d-4004-479e-8c1a-eb5a648f1350", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 8, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 8, 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, 8, 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, 0, 0, 0], [0, 0, 1, 8, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 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], [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, 8, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 1, 1, 1, 1, 1, 1, 8, 1, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 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, 0, 0, 0, 8, 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, 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, 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, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 8, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[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, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\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, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 8, 1, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"0573a3d8-334b-452c-93bb-d8d2b7ffe8bf\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\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, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 8, 1, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "0573a3d8-334b-452c-93bb-d8d2b7ffe8bf"}
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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 8, 1, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0]]
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{"id": "0573a3d8-334b-452c-93bb-d8d2b7ffe8bf", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\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, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0], [0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 8, 1, 1, 1, 1, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 1, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 1, 0, 0, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 8, 1, 1, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 1, 1, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 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, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 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, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 5, 5, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 6, 6, 6, 6, 6, 6, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 4:
[[0, 0, 0, 0, 0, 0, 5, 5, 5, 5], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 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], [5, 6, 3, 6, 3, 0, 3, 3, 3, 3], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 7, 7, 7, 7], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 0, 0, 0], [4, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [1, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 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, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 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, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 5, 5, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 6, 6, 6, 6, 6, 6, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 4:\\n[[0, 0, 0, 0, 0, 0, 5, 5, 5, 5], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 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], [5, 6, 3, 6, 3, 0, 3, 3, 3, 3], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 7, 7, 7, 7], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 0, 0, 0], [4, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [1, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 8, 6, 8], [4, 4, 4, 4, 4, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [2, 2, 2, 2, 2, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [1, 1, 1, 1, 1, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"416c7652-e417-4e07-9c09-33e8c94c1361\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 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, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 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, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 5, 5, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 6, 6, 6, 6, 6, 6, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 0, 0, 0, 0, 5, 5, 5, 5], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 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], [5, 6, 3, 6, 3, 0, 3, 3, 3, 3], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 7, 7, 7, 7], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 0, 0, 0], [4, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [1, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 8, 6, 8], [4, 4, 4, 4, 4, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [2, 2, 2, 2, 2, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [1, 1, 1, 1, 1, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "416c7652-e417-4e07-9c09-33e8c94c1361"}
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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 8, 6, 8], [4, 4, 4, 4, 4, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [2, 2, 2, 2, 2, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [1, 1, 1, 1, 1, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "416c7652-e417-4e07-9c09-33e8c94c1361", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 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, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 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, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 0], [0, 0, 5, 6, 6, 6, 9, 9, 9, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [5, 4, 3, 3, 4, 4, 4, 0, 0, 0], [5, 7, 3, 7, 7, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 5, 5, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 6, 6, 6, 6, 6, 6, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 4:\n[[0, 0, 0, 0, 0, 0, 5, 5, 5, 5], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 3, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 0, 0, 0, 0, 0, 7, 0, 0, 0], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 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], [5, 6, 3, 6, 3, 0, 3, 3, 3, 3], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 3, 3, 3, 3], [5, 6, 3, 6, 3, 0, 7, 7, 7, 7], [5, 2, 2, 2, 2, 0, 7, 7, 7, 7], [5, 6, 3, 6, 3, 0, 0, 0, 0, 0], [5, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 0, 0, 0], [4, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [2, 0, 0, 0, 0, 0, 5, 0, 0, 0], [1, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 0, 5, 8, 6, 8], [4, 4, 4, 4, 4, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [2, 2, 2, 2, 2, 0, 5, 3, 3, 3], [2, 2, 2, 2, 2, 0, 5, 8, 6, 8], [1, 1, 1, 1, 1, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 5, 8, 6, 8], [0, 0, 0, 0, 0, 0, 5, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] -> [[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 3, 1, 0, 0, 0, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 3, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 4, 4, 1, 0, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 6, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 4, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 6, 1, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] -> [[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 3, 1, 0, 0, 0, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 3, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 4, 4, 1, 0, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 6, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 4, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 6, 1, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]] -> \", \"answer\": \"[[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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 4, 4, 1, 1, 1, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 8, 8, 8, 1, 1, 1, 8, 8, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 8, 1, 1, 1, 8, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 1, 1, 1, 0, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"e790e04a-6f67-4455-937e-a0861d2a721b\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] -> [[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 3, 1, 0, 0, 0, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 3, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 4, 4, 1, 0, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 6, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 4, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 6, 1, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]] -> \\\", \\\"answer\\\": \\\"[[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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 4, 4, 1, 1, 1, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 8, 8, 8, 1, 1, 1, 8, 8, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 8, 1, 1, 1, 8, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 1, 1, 1, 0, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
|
PUZZLE##symbolic_hard
|
PUZZLE
|
{"index": "e790e04a-6f67-4455-937e-a0861d2a721b"}
|
[[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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 4, 4, 1, 1, 1, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 8, 8, 8, 1, 1, 1, 8, 8, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 8, 1, 1, 1, 8, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 1, 1, 1, 0, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]]
|
{"id": "e790e04a-6f67-4455-937e-a0861d2a721b", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] -> [[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1], [0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 3, 3, 3, 3, 1, 1, 1, 3, 1, 0, 0, 0, 1, 4, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 3, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 1, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 4, 4, 1, 0, 0, 1, 3, 1, 1, 1, 3, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 6, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 6, 6, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 4, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 6, 1, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]] -> ", "answer": "[[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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 4, 4, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 4, 4, 4, 4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 4, 4, 1, 1, 1, 4, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 8, 8, 8, 1, 1, 1, 8, 8, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 1, 0, 0, 0, 1, 8, 8, 8, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 1, 8, 1, 1, 1, 8, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 1, 1, 1, 0, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 6, 6, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 6, 6, 1, 0], [0, 0, 1, 6, 6, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
|
grid
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symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[2, 2, 3], [5, 5, 5], [0, 0, 0]] -> [[2, 2, 3], [5, 5, 5], [0, 2, 0]]
Example 2:
[[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 4, 0, 0]]
Example 3:
[[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]
# Test Problem:
[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 0, 0, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[2, 2, 3], [5, 5, 5], [0, 0, 0]] -> [[2, 2, 3], [5, 5, 5], [0, 2, 0]]\\n\\nExample 2:\\n[[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 4, 0, 0]]\\n\\nExample 3:\\n[[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]\\n\\n# Test Problem:\\n[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 9, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"3217deb4-442d-4174-9226-169ff14f7709\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[2, 2, 3], [5, 5, 5], [0, 0, 0]] -> [[2, 2, 3], [5, 5, 5], [0, 2, 0]]\\\\n\\\\nExample 2:\\\\n[[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 4, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 9, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "3217deb4-442d-4174-9226-169ff14f7709"}
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[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 9, 0, 0, 0, 0]]
|
{"id": "3217deb4-442d-4174-9226-169ff14f7709", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[2, 2, 3], [5, 5, 5], [0, 0, 0]] -> [[2, 2, 3], [5, 5, 5], [0, 2, 0]]\n\nExample 2:\n[[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[3, 6, 4, 2, 4], [8, 4, 3, 3, 4], [5, 5, 5, 5, 5], [0, 0, 0, 0, 0], [0, 0, 4, 0, 0]]\n\nExample 3:\n[[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 9, 9, 6, 1, 8, 4], [4, 6, 7, 8, 9, 7, 1], [9, 3, 1, 4, 1, 3, 6], [5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]\n\n# Test Problem:\n[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[9, 1, 2, 8, 4, 9, 8, 2, 1], [4, 4, 3, 1, 2, 7, 6, 7, 9], [2, 1, 6, 9, 7, 8, 4, 3, 6], [9, 8, 6, 3, 4, 2, 9, 1, 7], [5, 5, 5, 5, 5, 5, 5, 5, 5], [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, 0, 9, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[1, 1, 0, 0, 2, 0, 2, 4, 0, 0, 0, 5, 0, 0, 0], [1, 0, 1, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 2, 2, 0], [0, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[2, 0, 2, 0, 6, 0, 6, 4, 0, 5, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 5, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 5, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 5, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[1, 1, 0, 0, 1, 1, 0, 4, 0, 0, 5, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[1, 1, 0, 0, 2, 0, 2, 4, 0, 0, 0, 5, 0, 0, 0], [1, 0, 1, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 2, 2, 0], [0, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[2, 0, 2, 0, 6, 0, 6, 4, 0, 5, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 5, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 5, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 5, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[1, 1, 0, 0, 1, 1, 0, 4, 0, 0, 5, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 5, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [2, 2, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"9302f239-e0fa-4306-9b42-8dddc9bc39e4\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[1, 1, 0, 0, 2, 0, 2, 4, 0, 0, 0, 5, 0, 0, 0], [1, 0, 1, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 2, 2, 0], [0, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[2, 0, 2, 0, 6, 0, 6, 4, 0, 5, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 5, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 5, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 5, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[1, 1, 0, 0, 1, 1, 0, 4, 0, 0, 5, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 5, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [2, 2, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "9302f239-e0fa-4306-9b42-8dddc9bc39e4"}
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[[0, 0, 5, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [2, 2, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
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{"id": "9302f239-e0fa-4306-9b42-8dddc9bc39e4", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[1, 1, 0, 0, 2, 0, 2, 4, 0, 0, 0, 5, 0, 0, 0], [1, 0, 1, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 2, 2, 0], [0, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[2, 0, 2, 0, 6, 0, 6, 4, 0, 5, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 5, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 5, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 5, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[1, 1, 0, 0, 1, 1, 0, 4, 0, 0, 5, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 6, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 3, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 5, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 3, 3, 3, 3, 0, 0], [2, 2, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 2, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 1, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]] -> [[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [1, 1, 1, 5, 2, 2, 2, 2, 2, 2], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 1, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]]
Example 2:
[[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 2, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]] -> [[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 1, 5, 2, 2, 2, 2, 2, 1, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]]
Example 3:
[[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 1, 0, 0, 5, 0, 0, 0], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [0, 0, 0, 5, 0, 0, 1, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]] -> [[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [2, 2, 2, 5, 2, 2, 2, 2, 2, 2], [2, 2, 2, 5, 2, 2, 5, 2, 2, 2], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 2, 2, 2, 2], [2, 2, 2, 1, 1, 1, 5, 2, 2, 2], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [2, 2, 2, 5, 1, 1, 1, 1, 1, 1], [2, 2, 2, 5, 1, 1, 5, 1, 1, 1], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]]
# Test Problem:
[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 5, 0, 0, 1, 0, 0, 0, 0], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [0, 0, 1, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 2, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 1, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]] -> [[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [1, 1, 1, 5, 2, 2, 2, 2, 2, 2], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 1, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]]\\n\\nExample 2:\\n[[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 2, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]] -> [[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 1, 5, 2, 2, 2, 2, 2, 1, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]]\\n\\nExample 3:\\n[[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 1, 0, 0, 5, 0, 0, 0], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [0, 0, 0, 5, 0, 0, 1, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]] -> [[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [2, 2, 2, 5, 2, 2, 2, 2, 2, 2], [2, 2, 2, 5, 2, 2, 5, 2, 2, 2], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 2, 2, 2, 2], [2, 2, 2, 1, 1, 1, 5, 2, 2, 2], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [2, 2, 2, 5, 1, 1, 1, 1, 1, 1], [2, 2, 2, 5, 1, 1, 5, 1, 1, 1], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]]\\n\\n# Test Problem:\\n[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 5, 0, 0, 1, 0, 0, 0, 0], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [0, 0, 1, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]] -> \", \"answer\": \"[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [1, 1, 5, 1, 1, 5, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 5, 2, 2, 5, 2, 2, 2, 2], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [2, 2, 1, 2, 2, 2, 1, 1, 1, 1], [2, 2, 5, 2, 2, 5, 1, 1, 1, 1], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"27efd3d7-28fd-40b0-bd20-46e64d15b493\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 2, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 1, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]] -> [[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [1, 1, 1, 5, 2, 2, 2, 2, 2, 2], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 1, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]]\\\\n\\\\nExample 2:\\\\n[[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 2, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]] -> [[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 1, 5, 2, 2, 2, 2, 2, 1, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]]\\\\n\\\\nExample 3:\\\\n[[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 1, 0, 0, 5, 0, 0, 0], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [0, 0, 0, 5, 0, 0, 1, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]] -> [[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [2, 2, 2, 5, 2, 2, 2, 2, 2, 2], [2, 2, 2, 5, 2, 2, 5, 2, 2, 2], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 2, 2, 2, 2], [2, 2, 2, 1, 1, 1, 5, 2, 2, 2], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [2, 2, 2, 5, 1, 1, 1, 1, 1, 1], [2, 2, 2, 5, 1, 1, 5, 1, 1, 1], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]]\\\\n\\\\n# Test Problem:\\\\n[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 5, 0, 0, 1, 0, 0, 0, 0], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [0, 0, 1, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]] -> \\\", \\\"answer\\\": \\\"[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [1, 1, 5, 1, 1, 5, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 5, 2, 2, 5, 2, 2, 2, 2], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [2, 2, 1, 2, 2, 2, 1, 1, 1, 1], [2, 2, 5, 2, 2, 5, 1, 1, 1, 1], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "27efd3d7-28fd-40b0-bd20-46e64d15b493"}
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[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [1, 1, 5, 1, 1, 5, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 5, 2, 2, 5, 2, 2, 2, 2], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [2, 2, 1, 2, 2, 2, 1, 1, 1, 1], [2, 2, 5, 2, 2, 5, 1, 1, 1, 1], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]]
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{"id": "27efd3d7-28fd-40b0-bd20-46e64d15b493", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 2, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 1, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0, 0, 5, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]] -> [[1, 5, 1, 5, 5, 2, 5, 5, 5, 1], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [1, 1, 1, 5, 2, 2, 2, 2, 2, 2], [1, 1, 1, 5, 2, 2, 2, 5, 2, 2], [5, 2, 5, 5, 5, 5, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 1, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [2, 2, 2, 5, 1, 1, 1, 5, 2, 2], [5, 2, 5, 5, 5, 5, 1, 5, 5, 2]]\n\nExample 2:\n[[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [0, 0, 5, 0, 0, 0, 0, 2, 0, 0], [0, 0, 5, 0, 0, 0, 0, 5, 0, 0], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]] -> [[2, 5, 5, 5, 1, 5, 5, 5, 5, 2], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [1, 1, 5, 1, 1, 1, 1, 5, 1, 1], [5, 1, 5, 5, 5, 2, 5, 5, 5, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 1, 5, 2, 2, 2, 2, 2, 1, 1], [1, 1, 5, 2, 2, 2, 2, 5, 1, 1], [1, 5, 5, 5, 2, 5, 5, 5, 5, 1]]\n\nExample 3:\n[[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [0, 0, 0, 5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 1, 0, 0, 5, 0, 0, 0], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [0, 0, 0, 5, 0, 0, 1, 0, 0, 0], [0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]] -> [[1, 5, 2, 5, 2, 5, 5, 5, 5, 1], [2, 2, 2, 5, 2, 2, 2, 2, 2, 2], [2, 2, 2, 5, 2, 2, 5, 2, 2, 2], [5, 2, 5, 5, 5, 1, 5, 5, 2, 5], [2, 2, 2, 5, 1, 1, 2, 2, 2, 2], [2, 2, 2, 1, 1, 1, 5, 2, 2, 2], [2, 2, 5, 5, 1, 5, 5, 5, 1, 5], [2, 2, 2, 5, 1, 1, 1, 1, 1, 1], [2, 2, 2, 5, 1, 1, 5, 1, 1, 1], [5, 5, 1, 5, 5, 1, 5, 5, 2, 5]]\n\n# Test Problem:\n[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 5, 0, 0, 1, 0, 0, 0, 0], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [0, 0, 1, 0, 0, 2, 0, 0, 0, 0], [0, 0, 5, 0, 0, 5, 0, 0, 0, 0], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]] -> ", "answer": "[[5, 1, 5, 5, 5, 5, 5, 5, 1, 5], [1, 1, 5, 1, 1, 5, 1, 1, 1, 1], [1, 1, 5, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5, 5, 1, 5, 5, 2, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 5, 2, 2, 5, 2, 2, 2, 2], [2, 5, 5, 5, 2, 5, 5, 1, 2, 5], [2, 2, 1, 2, 2, 2, 1, 1, 1, 1], [2, 2, 5, 2, 2, 5, 1, 1, 1, 1], [5, 2, 5, 5, 5, 5, 1, 5, 5, 1]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 8, 8, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 8, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 2, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 4:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 8, 8, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 8, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 2, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 4:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]] -> \", \"answer\": \"[[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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 3, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 0, 2, 0], [0, 8, 0, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 3, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0], [0, 2, 2, 2, 0, 2, 0, 8, 8, 8, 0, 8, 0, 2, 2, 2, 0, 2, 0, 6, 0, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 8, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"fd4f1c5a-5101-438e-8df5-70564ece0c6e\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 8, 8, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 8, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 2, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]] -> \\\", \\\"answer\\\": \\\"[[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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 3, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 0, 2, 0], [0, 8, 0, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 3, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0], [0, 2, 2, 2, 0, 2, 0, 8, 8, 8, 0, 8, 0, 2, 2, 2, 0, 2, 0, 6, 0, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 8, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "fd4f1c5a-5101-438e-8df5-70564ece0c6e"}
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[[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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 3, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 0, 2, 0], [0, 8, 0, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 3, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0], [0, 2, 2, 2, 0, 2, 0, 8, 8, 8, 0, 8, 0, 2, 2, 2, 0, 2, 0, 6, 0, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 8, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]]
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{"id": "fd4f1c5a-5101-438e-8df5-70564ece0c6e", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 4, 0], [0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0, 4, 0, 4, 0, 4, 0], [0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 0, 4, 0, 4, 0, 2, 0, 0, 0, 2, 0, 7, 0, 0, 0, 7, 0], [0, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 0, 7, 7, 7, 7, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 8, 0, 8, 0], [0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0], [0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 3, 3, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 3, 0, 3, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 1, 1, 1, 1, 1, 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, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0], [0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 0, 0, 8, 0], [0, 8, 0, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 0, 8, 8, 8, 0], [0, 8, 0, 8, 0, 8, 0, 3, 0, 0, 0, 3, 0, 8, 0, 8, 0, 8, 0], [0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 0, 6, 0, 6, 0, 2, 2, 2, 2, 2, 0, 4, 0, 4, 0, 4, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 4, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 2, 0, 2, 0], [0, 1, 0, 1, 0, 1, 0, 5, 0, 0, 0, 5, 0, 2, 2, 2, 2, 2, 0], [0, 1, 1, 0, 1, 1, 0, 5, 0, 0, 0, 5, 0, 2, 0, 0, 0, 2, 0], [0, 1, 1, 1, 1, 1, 0, 5, 5, 5, 5, 5, 0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 4:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 2, 2, 0], [0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 0, 1, 0], [0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0], [0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]] -> ", "answer": "[[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, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 8, 0, 3, 0, 0, 3, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 8, 8, 0, 8, 0, 3, 0, 3, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 0, 0, 0, 1, 0, 8, 0, 8, 0, 8, 0, 3, 3, 0, 0, 3, 0, 7, 0, 7, 0, 7, 0], [0, 1, 1, 1, 1, 1, 0, 8, 8, 8, 8, 8, 0, 3, 3, 3, 3, 3, 0, 7, 7, 7, 7, 7, 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, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0], [0, 6, 0, 6, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 0, 6, 6, 6, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0], [0, 6, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0], [0, 6, 6, 6, 6, 6, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 0], [0, 8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 0, 3, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 0, 3, 0, 3, 0, 2, 2, 2, 0, 2, 0], [0, 8, 0, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 3, 3, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0], [0, 8, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 0, 3, 3, 3, 3, 3, 0, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 6, 0, 6, 0], [0, 2, 2, 2, 0, 2, 0, 8, 8, 8, 0, 8, 0, 2, 2, 2, 0, 2, 0, 6, 0, 6, 6, 6, 0], [0, 2, 0, 2, 0, 2, 0, 8, 0, 8, 0, 8, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 6, 0], [0, 2, 2, 2, 2, 2, 0, 8, 8, 8, 8, 8, 0, 2, 2, 2, 2, 2, 0, 6, 6, 6, 6, 6, 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]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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, 8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 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, 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, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 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, 8, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 8, 8, 8, 0, 0], [0, 0, 8, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 4:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 7, 0], [0, 0, 1, 0, 0, 1, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 7, 0, 1, 0, 0], [0, 7, 0, 0, 7, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 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]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 5, 5, 5, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\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, 8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 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, 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, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 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, 8, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 8, 8, 8, 0, 0], [0, 0, 8, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 4:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 7, 0], [0, 0, 1, 0, 0, 1, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 7, 0, 1, 0, 0], [0, 7, 0, 0, 7, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 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\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 5, 5, 5, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 6, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"7d541801-a5cd-420b-bdcc-57d71af568fb\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\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, 8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 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, 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, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 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, 8, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 8, 8, 8, 0, 0], [0, 0, 8, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 7, 0], [0, 0, 1, 0, 0, 1, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 7, 0, 1, 0, 0], [0, 7, 0, 0, 7, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 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\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 5, 5, 5, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 6, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "7d541801-a5cd-420b-bdcc-57d71af568fb"}
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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 6, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
|
{"id": "7d541801-a5cd-420b-bdcc-57d71af568fb", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\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, 8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 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, 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, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 3, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 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, 8, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 8, 8, 8, 0, 0], [0, 0, 8, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 4:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 7, 0], [0, 0, 1, 0, 0, 1, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 7, 0, 1, 0, 0], [0, 7, 0, 0, 7, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 7, 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\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 5, 0, 5, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 5, 5, 5, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 6, 0, 6, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 5, 0, 0, 6, 6, 6, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 6, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
|
grid
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symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[8, 0, 0], [0, 8, 0], [0, 0, 0]] -> [[0, 2, 2], [2, 0, 2], [2, 2, 2]]
Example 2:
[[0, 0, 3], [0, 3, 0], [3, 0, 0]] -> [[1, 1, 0], [1, 0, 1], [0, 1, 1]]
Example 3:
[[5, 0, 0], [5, 5, 0], [5, 0, 0]] -> [[0, 4, 4], [0, 0, 4], [0, 4, 4]]
Example 4:
[[5, 5, 5], [0, 0, 5], [0, 0, 0]] -> [[0, 0, 0], [4, 4, 0], [4, 4, 4]]
Example 5:
[[0, 8, 0], [0, 8, 0], [8, 0, 0]] -> [[2, 0, 2], [2, 0, 2], [0, 2, 2]]
Example 6:
[[8, 0, 8], [0, 8, 0], [0, 8, 0]] -> [[0, 2, 0], [2, 0, 2], [2, 0, 2]]
# Test Problem:
[[3, 0, 0], [3, 3, 3], [0, 0, 3]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[8, 0, 0], [0, 8, 0], [0, 0, 0]] -> [[0, 2, 2], [2, 0, 2], [2, 2, 2]]\\n\\nExample 2:\\n[[0, 0, 3], [0, 3, 0], [3, 0, 0]] -> [[1, 1, 0], [1, 0, 1], [0, 1, 1]]\\n\\nExample 3:\\n[[5, 0, 0], [5, 5, 0], [5, 0, 0]] -> [[0, 4, 4], [0, 0, 4], [0, 4, 4]]\\n\\nExample 4:\\n[[5, 5, 5], [0, 0, 5], [0, 0, 0]] -> [[0, 0, 0], [4, 4, 0], [4, 4, 4]]\\n\\nExample 5:\\n[[0, 8, 0], [0, 8, 0], [8, 0, 0]] -> [[2, 0, 2], [2, 0, 2], [0, 2, 2]]\\n\\nExample 6:\\n[[8, 0, 8], [0, 8, 0], [0, 8, 0]] -> [[0, 2, 0], [2, 0, 2], [2, 0, 2]]\\n\\n# Test Problem:\\n[[3, 0, 0], [3, 3, 3], [0, 0, 3]] -> \", \"answer\": \"[[0, 1, 1], [0, 0, 0], [1, 1, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"43bb91a3-413b-456d-b29b-c3ac618d922e\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[8, 0, 0], [0, 8, 0], [0, 0, 0]] -> [[0, 2, 2], [2, 0, 2], [2, 2, 2]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 3], [0, 3, 0], [3, 0, 0]] -> [[1, 1, 0], [1, 0, 1], [0, 1, 1]]\\\\n\\\\nExample 3:\\\\n[[5, 0, 0], [5, 5, 0], [5, 0, 0]] -> [[0, 4, 4], [0, 0, 4], [0, 4, 4]]\\\\n\\\\nExample 4:\\\\n[[5, 5, 5], [0, 0, 5], [0, 0, 0]] -> [[0, 0, 0], [4, 4, 0], [4, 4, 4]]\\\\n\\\\nExample 5:\\\\n[[0, 8, 0], [0, 8, 0], [8, 0, 0]] -> [[2, 0, 2], [2, 0, 2], [0, 2, 2]]\\\\n\\\\nExample 6:\\\\n[[8, 0, 8], [0, 8, 0], [0, 8, 0]] -> [[0, 2, 0], [2, 0, 2], [2, 0, 2]]\\\\n\\\\n# Test Problem:\\\\n[[3, 0, 0], [3, 3, 3], [0, 0, 3]] -> \\\", \\\"answer\\\": \\\"[[0, 1, 1], [0, 0, 0], [1, 1, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "43bb91a3-413b-456d-b29b-c3ac618d922e"}
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[[0, 1, 1], [0, 0, 0], [1, 1, 0]]
|
{"id": "43bb91a3-413b-456d-b29b-c3ac618d922e", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[8, 0, 0], [0, 8, 0], [0, 0, 0]] -> [[0, 2, 2], [2, 0, 2], [2, 2, 2]]\n\nExample 2:\n[[0, 0, 3], [0, 3, 0], [3, 0, 0]] -> [[1, 1, 0], [1, 0, 1], [0, 1, 1]]\n\nExample 3:\n[[5, 0, 0], [5, 5, 0], [5, 0, 0]] -> [[0, 4, 4], [0, 0, 4], [0, 4, 4]]\n\nExample 4:\n[[5, 5, 5], [0, 0, 5], [0, 0, 0]] -> [[0, 0, 0], [4, 4, 0], [4, 4, 4]]\n\nExample 5:\n[[0, 8, 0], [0, 8, 0], [8, 0, 0]] -> [[2, 0, 2], [2, 0, 2], [0, 2, 2]]\n\nExample 6:\n[[8, 0, 8], [0, 8, 0], [0, 8, 0]] -> [[0, 2, 0], [2, 0, 2], [2, 0, 2]]\n\n# Test Problem:\n[[3, 0, 0], [3, 3, 3], [0, 0, 3]] -> ", "answer": "[[0, 1, 1], [0, 0, 0], [1, 1, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
|
grid
|
symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 0, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 3, 0, 0, 0, 3, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 3, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 8, 3, 3, 8, 3, 0, 3, 0, 0, 0, 3], [0, 0, 8, 8, 3, 3, 3, 8, 0, 0, 3, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 3, 8, 0, 0, 0, 0, 0, 0], [3, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 3, 6, 6, 6, 0, 3, 6, 6, 6, 3, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 3, 0], [0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 1, 1, 1, 2, 3, 3, 0, 3, 0, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 0, 0, 3], [0, 1, 3, 3, 3, 1, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 3, 1, 3, 3, 3, 0, 3, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 3, 2, 1, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 1, 3, 2, 3, 3, 0, 0, 0, 0], [0, 8, 1, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 1, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 1, 1, 2, 3, 1, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [3, 8, 8, 8, 3, 3, 1, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 3, 0, 3, 0, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 3, 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, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 0, 0, 3, 0, 0], [0, 2, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 2, 3, 1, 3, 0, 0, 2, 2, 1, 2, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 2, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 2, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 3, 2, 3, 2, 0, 0, 2, 3, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 2, 0, 0], [0, 3, 1, 1, 3, 0, 3, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0, 2, 0, 2, 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, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 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, 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]]
# Test Problem:
[[0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 2, 2, 8, 3, 2, 0, 2, 2, 8, 2, 2, 0, 3, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [3, 8, 8, 3, 3, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0], [0, 2, 3, 8, 2, 2, 0, 2, 2, 3, 2, 3, 0, 2, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 3, 0, 8, 8, 8, 3, 8, 0, 0, 0, 0], [0, 8, 8, 8, 3, 8, 0, 8, 3, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 3, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 8, 8, 8, 8, 0, 8, 8, 3, 3, 8, 0, 8, 8, 3, 8, 8, 0, 3, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 3, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 0, 3, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 0, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 3, 0, 0, 0, 3, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 3, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 8, 3, 3, 8, 3, 0, 3, 0, 0, 0, 3], [0, 0, 8, 8, 3, 3, 3, 8, 0, 0, 3, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 3, 8, 0, 0, 0, 0, 0, 0], [3, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 3, 6, 6, 6, 0, 3, 6, 6, 6, 3, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 3, 0], [0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 1, 1, 1, 2, 3, 3, 0, 3, 0, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 0, 0, 3], [0, 1, 3, 3, 3, 1, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 3, 1, 3, 3, 3, 0, 3, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 3, 2, 1, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 1, 3, 2, 3, 3, 0, 0, 0, 0], [0, 8, 1, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 1, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 1, 1, 2, 3, 1, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [3, 8, 8, 8, 3, 3, 1, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 3, 0, 3, 0, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 3, 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, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 0, 0, 3, 0, 0], [0, 2, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 2, 3, 1, 3, 0, 0, 2, 2, 1, 2, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 2, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 2, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 3, 2, 3, 2, 0, 0, 2, 3, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 2, 0, 0], [0, 3, 1, 1, 3, 0, 3, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0, 2, 0, 2, 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, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 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, 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\\n# Test Problem:\\n[[0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 2, 2, 8, 3, 2, 0, 2, 2, 8, 2, 2, 0, 3, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [3, 8, 8, 3, 3, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0], [0, 2, 3, 8, 2, 2, 0, 2, 2, 3, 2, 3, 0, 2, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 3, 0, 8, 8, 8, 3, 8, 0, 0, 0, 0], [0, 8, 8, 8, 3, 8, 0, 8, 3, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 3, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 8, 8, 8, 8, 0, 8, 8, 3, 3, 8, 0, 8, 8, 3, 8, 8, 0, 3, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 3, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 0, 3, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 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, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"4232c063-084d-4ac0-a02c-6d3e892279ba\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 0, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 3, 0, 0, 0, 3, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 3, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 8, 3, 3, 8, 3, 0, 3, 0, 0, 0, 3], [0, 0, 8, 8, 3, 3, 3, 8, 0, 0, 3, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 3, 8, 0, 0, 0, 0, 0, 0], [3, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 3, 6, 6, 6, 0, 3, 6, 6, 6, 3, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 3, 0], [0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 1, 1, 1, 2, 3, 3, 0, 3, 0, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 0, 0, 3], [0, 1, 3, 3, 3, 1, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 3, 1, 3, 3, 3, 0, 3, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 3, 2, 1, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 1, 3, 2, 3, 3, 0, 0, 0, 0], [0, 8, 1, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 1, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 1, 1, 2, 3, 1, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [3, 8, 8, 8, 3, 3, 1, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 3, 0, 3, 0, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 3, 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, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 0, 0, 3, 0, 0], [0, 2, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 2, 3, 1, 3, 0, 0, 2, 2, 1, 2, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 2, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 2, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 3, 2, 3, 2, 0, 0, 2, 3, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 2, 0, 0], [0, 3, 1, 1, 3, 0, 3, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0, 2, 0, 2, 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, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 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, 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\\\\n# Test Problem:\\\\n[[0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 2, 2, 8, 3, 2, 0, 2, 2, 8, 2, 2, 0, 3, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [3, 8, 8, 3, 3, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0], [0, 2, 3, 8, 2, 2, 0, 2, 2, 3, 2, 3, 0, 2, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 3, 0, 8, 8, 8, 3, 8, 0, 0, 0, 0], [0, 8, 8, 8, 3, 8, 0, 8, 3, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 3, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 8, 8, 8, 8, 0, 8, 8, 3, 3, 8, 0, 8, 8, 3, 8, 8, 0, 3, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 3, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 0, 3, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 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, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "4232c063-084d-4ac0-a02c-6d3e892279ba"}
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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 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, 0, 0]]
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{"id": "4232c063-084d-4ac0-a02c-6d3e892279ba", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 3, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 0, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 3, 0, 0, 0, 3, 0, 0], [0, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 3, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 3, 8, 3, 3, 8, 3, 0, 3, 0, 0, 0, 3], [0, 0, 8, 8, 3, 3, 3, 8, 0, 0, 3, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 3, 3, 3, 3, 8, 0, 0, 0, 0, 0, 0], [3, 3, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 3, 6, 6, 6, 0, 3, 6, 6, 6, 3, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 3, 0], [0, 0, 8, 3, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 3, 3, 8, 8, 0, 0, 8, 8, 3, 3, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 1, 1, 1, 2, 3, 3, 0, 3, 0, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 0, 0, 3], [0, 1, 3, 3, 3, 1, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 3, 1, 3, 3, 3, 0, 3, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 3, 2, 1, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 3, 1, 3, 2, 3, 3, 0, 0, 0, 0], [0, 8, 1, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 1, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 3, 0], [0, 1, 1, 3, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 1, 3, 3, 0, 1, 1, 2, 3, 1, 0, 0, 0, 0], [1, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [3, 8, 8, 8, 3, 3, 1, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 3, 0, 3, 0, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 3, 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, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 0, 0, 3, 0, 0], [0, 2, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 2, 3, 1, 3, 0, 0, 2, 2, 1, 2, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 2, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 3, 3, 2, 2, 3, 2, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 3, 2, 3, 2, 0, 0, 2, 3, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 2, 3, 3, 0, 0, 2, 0, 0], [0, 3, 1, 1, 3, 0, 3, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0, 2, 0, 2, 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, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 3, 2, 2, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 0, 0, 3, 1, 1, 3, 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, 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, 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, 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\n# Test Problem:\n[[0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 2, 2, 8, 3, 2, 0, 2, 2, 8, 2, 2, 0, 3, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [3, 8, 8, 3, 3, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0], [0, 2, 3, 8, 2, 2, 0, 2, 2, 3, 2, 3, 0, 2, 2, 8, 2, 2, 0, 0, 0, 3], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 3, 0, 8, 8, 8, 3, 8, 0, 0, 0, 0], [0, 8, 8, 8, 3, 8, 0, 8, 3, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 3, 0], [0, 3, 3, 3, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 8, 8, 8, 8, 0, 8, 8, 3, 3, 8, 0, 8, 8, 3, 8, 8, 0, 3, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 3, 8, 8, 0, 3, 8, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 0, 3, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 2, 2, 8, 2, 2, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 3, 3, 8, 3, 3, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 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, 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, 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, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[1, 0, 3, 4], [0, 0, 2, 1], [2, 1, 4, 0], [0, 3, 1, 2]] -> [[1, 2, 3, 4], [3, 4, 2, 1], [2, 1, 4, 3], [4, 3, 1, 2]]
Example 2:
[[0, 4, 2, 3], [4, 1, 0, 2], [0, 3, 4, 0], [3, 0, 1, 4]] -> [[1, 4, 2, 3], [4, 1, 3, 2], [2, 3, 4, 1], [3, 2, 1, 4]]
Example 3:
[[3, 0, 2, 1], [1, 0, 0, 0], [4, 3, 0, 2], [0, 1, 4, 3]] -> [[3, 4, 2, 1], [1, 2, 3, 4], [4, 3, 1, 2], [2, 1, 4, 3]]
# Test Problem:
[[0, 1, 2, 3], [0, 3, 1, 0], [3, 0, 4, 1], [0, 4, 0, 2]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[1, 0, 3, 4], [0, 0, 2, 1], [2, 1, 4, 0], [0, 3, 1, 2]] -> [[1, 2, 3, 4], [3, 4, 2, 1], [2, 1, 4, 3], [4, 3, 1, 2]]\\n\\nExample 2:\\n[[0, 4, 2, 3], [4, 1, 0, 2], [0, 3, 4, 0], [3, 0, 1, 4]] -> [[1, 4, 2, 3], [4, 1, 3, 2], [2, 3, 4, 1], [3, 2, 1, 4]]\\n\\nExample 3:\\n[[3, 0, 2, 1], [1, 0, 0, 0], [4, 3, 0, 2], [0, 1, 4, 3]] -> [[3, 4, 2, 1], [1, 2, 3, 4], [4, 3, 1, 2], [2, 1, 4, 3]]\\n\\n# Test Problem:\\n[[0, 1, 2, 3], [0, 3, 1, 0], [3, 0, 4, 1], [0, 4, 0, 2]] -> \", \"answer\": \"[[4, 1, 2, 3], [2, 3, 1, 4], [3, 2, 4, 1], [1, 4, 3, 2]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"a51f80a8-4429-47fe-83a5-eeb93c0f5f87\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[1, 0, 3, 4], [0, 0, 2, 1], [2, 1, 4, 0], [0, 3, 1, 2]] -> [[1, 2, 3, 4], [3, 4, 2, 1], [2, 1, 4, 3], [4, 3, 1, 2]]\\\\n\\\\nExample 2:\\\\n[[0, 4, 2, 3], [4, 1, 0, 2], [0, 3, 4, 0], [3, 0, 1, 4]] -> [[1, 4, 2, 3], [4, 1, 3, 2], [2, 3, 4, 1], [3, 2, 1, 4]]\\\\n\\\\nExample 3:\\\\n[[3, 0, 2, 1], [1, 0, 0, 0], [4, 3, 0, 2], [0, 1, 4, 3]] -> [[3, 4, 2, 1], [1, 2, 3, 4], [4, 3, 1, 2], [2, 1, 4, 3]]\\\\n\\\\n# Test Problem:\\\\n[[0, 1, 2, 3], [0, 3, 1, 0], [3, 0, 4, 1], [0, 4, 0, 2]] -> \\\", \\\"answer\\\": \\\"[[4, 1, 2, 3], [2, 3, 1, 4], [3, 2, 4, 1], [1, 4, 3, 2]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "a51f80a8-4429-47fe-83a5-eeb93c0f5f87"}
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[[4, 1, 2, 3], [2, 3, 1, 4], [3, 2, 4, 1], [1, 4, 3, 2]]
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{"id": "a51f80a8-4429-47fe-83a5-eeb93c0f5f87", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[1, 0, 3, 4], [0, 0, 2, 1], [2, 1, 4, 0], [0, 3, 1, 2]] -> [[1, 2, 3, 4], [3, 4, 2, 1], [2, 1, 4, 3], [4, 3, 1, 2]]\n\nExample 2:\n[[0, 4, 2, 3], [4, 1, 0, 2], [0, 3, 4, 0], [3, 0, 1, 4]] -> [[1, 4, 2, 3], [4, 1, 3, 2], [2, 3, 4, 1], [3, 2, 1, 4]]\n\nExample 3:\n[[3, 0, 2, 1], [1, 0, 0, 0], [4, 3, 0, 2], [0, 1, 4, 3]] -> [[3, 4, 2, 1], [1, 2, 3, 4], [4, 3, 1, 2], [2, 1, 4, 3]]\n\n# Test Problem:\n[[0, 1, 2, 3], [0, 3, 1, 0], [3, 0, 4, 1], [0, 4, 0, 2]] -> ", "answer": "[[4, 1, 2, 3], [2, 3, 1, 4], [3, 2, 4, 1], [1, 4, 3, 2]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]
Example 2:
[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0]] -> [[4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0]] -> [[4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"4c77240e-c935-42a9-b09e-f3225f824d85\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0]] -> [[4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "4c77240e-c935-42a9-b09e-f3225f824d85"}
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[[4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0]]
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{"id": "4c77240e-c935-42a9-b09e-f3225f824d85", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4], [0, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0]] -> [[4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0]]\n\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0]] -> ", "answer": "[[4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [4, 0, 4, 4, 4, 4, 3, 4, 4, 4, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 4, 0, 4, 0, 3, 0, 4, 0, 4, 0], [4, 0, 4, 0, 4, 4, 3, 4, 4, 0, 4, 0], [4, 0, 4, 0, 0, 0, 3, 0, 0, 0, 4, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ff5d758d-bb5d-4a31-92aa-d0e0805f13ab\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "ff5d758d-bb5d-4a31-92aa-d0e0805f13ab"}
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[[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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "ff5d758d-bb5d-4a31-92aa-d0e0805f13ab", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 0, 2, 0, 2, 0], [0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[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, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 2, 0, 0, 0, 0, 4, 5, 0, 0, 1, 0, 6, 5, 0, 0, 0], [9, 0, 4, 3, 0, 0, 9, 0, 4, 7, 9, 4, 6, 0, 2, 7, 0], [0, 7, 3, 0, 0, 0, 9, 0, 0, 9, 0, 0, 9, 9, 9, 5, 0], [0, 5, 5, 3, 0, 3, 0, 6, 0, 4, 7, 2, 3, 2, 0, 3, 0], [0, 8, 8, 0, 0, 0, 7, 0, 8, 8, 9, 0, 0, 6, 0, 0, 4], [0, 8, 8, 6, 4, 3, 1, 9, 8, 8, 0, 0, 0, 0, 0, 0, 7], [9, 0, 0, 9, 5, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], [0, 2, 9, 9, 0, 0, 9, 0, 7, 1, 0, 0, 0, 9, 0, 0, 0], [0, 7, 0, 8, 8, 0, 4, 0, 6, 0, 8, 8, 9, 0, 0, 0, 0], [0, 2, 4, 8, 8, 0, 3, 0, 0, 6, 8, 8, 6, 5, 7, 9, 0], [0, 0, 9, 2, 0, 2, 0, 0, 0, 7, 9, 0, 0, 0, 5, 7, 1], [1, 0, 0, 3, 0, 1, 0, 4, 1, 4, 0, 0, 0, 0, 1, 0, 9], [1, 0, 6, 2, 1, 4, 6, 0, 0, 1, 9, 0, 3, 0, 1, 4, 0]] -> [[0, 0, 0, 7, 0], [6, 4, 3, 1, 9], [0, 4, 0, 6, 0], [0, 3, 0, 0, 6]]
Example 2:
[[0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 7, 9, 0, 7, 7, 0, 0, 1, 3, 0], [2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 3, 5, 9, 1, 8, 8, 0, 2, 0], [0, 0, 0, 0, 8, 8, 1, 0, 0, 6, 8, 8, 3, 0, 0], [2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 9, 2, 0, 0, 2], [0, 0, 9, 0, 4, 9, 9, 9, 0, 2, 9, 6, 1, 4, 0], [0, 0, 0, 0, 0, 0, 9, 4, 0, 0, 0, 0, 0, 0, 5], [1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 5, 0, 6, 0], [2, 1, 0, 0, 6, 0, 6, 2, 7, 0, 4, 0, 0, 0, 7], [0, 9, 0, 0, 2, 0, 5, 0, 1, 0, 0, 0, 0, 5, 3], [4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[3, 5, 9, 1], [1, 0, 0, 6]]
Example 3:
[[9, 0, 0, 5, 0, 0, 0, 0, 4, 4], [9, 4, 0, 0, 0, 0, 0, 0, 5, 0], [2, 2, 0, 6, 0, 0, 5, 0, 5, 3], [2, 9, 0, 2, 6, 4, 0, 1, 0, 0], [0, 0, 2, 9, 0, 4, 9, 1, 1, 3], [8, 8, 1, 0, 9, 7, 7, 0, 8, 8], [8, 8, 4, 0, 0, 5, 6, 4, 8, 8], [0, 5, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 5, 0, 0, 3, 0], [0, 9, 0, 0, 0, 0, 0, 7, 0, 9], [0, 0, 5, 1, 7, 0, 0, 0, 9, 9], [0, 0, 9, 0, 0, 1, 0, 0, 0, 7]] -> [[1, 0, 9, 7, 7, 0], [4, 0, 0, 5, 6, 4]]
Example 4:
[[9, 2, 1, 5, 3, 4, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 8, 8, 3, 0, 7, 0, 7, 8, 8, 4, 0, 7, 2, 0, 0, 0], [1, 8, 8, 0, 2, 0, 0, 6, 8, 8, 0, 0, 0, 0, 0, 7, 0], [1, 0, 0, 0, 0, 4, 1, 3, 9, 1, 0, 7, 5, 9, 4, 7, 0], [0, 0, 3, 2, 2, 0, 2, 6, 0, 4, 9, 2, 4, 0, 3, 0, 5], [0, 6, 8, 8, 3, 0, 1, 9, 2, 8, 8, 0, 3, 0, 4, 0, 0], [0, 0, 8, 8, 0, 7, 9, 2, 9, 8, 8, 0, 9, 3, 0, 0, 9], [0, 0, 0, 4, 0, 7, 5, 7, 5, 0, 1, 3, 0, 2, 0, 0, 0], [0, 0, 9, 9, 3, 6, 4, 0, 4, 7, 2, 0, 9, 0, 0, 9, 0], [9, 1, 9, 0, 0, 7, 1, 5, 7, 1, 0, 5, 0, 5, 9, 6, 9], [0, 0, 3, 7, 2, 0, 8, 8, 9, 0, 0, 0, 0, 8, 8, 1, 0], [6, 7, 0, 4, 0, 4, 8, 8, 0, 4, 0, 2, 0, 8, 8, 5, 0]] -> [[3, 0, 7, 0, 7], [0, 2, 0, 0, 6], [3, 0, 1, 9, 2], [0, 7, 9, 2, 9], [9, 0, 0, 0, 0], [0, 4, 0, 2, 0]]
Example 5:
[[0, 7, 2, 7, 0, 2, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 7, 3, 1], [0, 0, 8, 8, 6, 5, 2, 8, 8, 1, 0, 2, 4, 5, 0, 0], [0, 0, 8, 8, 0, 0, 2, 8, 8, 0, 0, 7, 1, 0, 0, 7], [0, 0, 0, 0, 4, 0, 0, 0, 9, 0, 7, 0, 0, 0, 0, 0], [8, 8, 1, 3, 0, 8, 8, 0, 0, 0, 0, 9, 0, 3, 0, 1], [8, 8, 0, 0, 9, 8, 8, 0, 0, 0, 0, 0, 3, 0, 9, 2], [0, 0, 7, 0, 0, 0, 0, 0, 0, 9, 3, 4, 0, 0, 0, 0], [4, 0, 0, 9, 0, 9, 0, 0, 7, 3, 0, 6, 0, 4, 0, 5], [6, 0, 0, 0, 4, 0, 0, 3, 0, 0, 2, 0, 5, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 1, 2, 0, 4, 0, 0, 0, 0], [4, 5, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 5, 2, 0, 2], [0, 9, 0, 6, 0, 0, 0, 7, 2, 0, 9, 3, 0, 0, 0, 6]] -> [[6, 5, 2], [0, 0, 2], [1, 3, 0], [0, 0, 9]]
# Test Problem:
[[0, 0, 6, 9, 0, 0, 0, 9, 0, 0, 7, 0, 9, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 4, 0, 9, 0, 0, 0, 0, 0, 2, 0, 1, 0, 5, 1], [2, 1, 0, 8, 8, 4, 1, 5, 0, 8, 8, 0, 1, 0, 4, 0, 0], [0, 7, 3, 8, 8, 0, 9, 0, 0, 8, 8, 0, 6, 0, 4, 7, 2], [2, 5, 0, 4, 0, 0, 0, 0, 7, 9, 0, 9, 5, 0, 4, 0, 1], [8, 8, 5, 9, 0, 4, 8, 8, 4, 0, 3, 7, 0, 0, 0, 0, 5], [8, 8, 7, 7, 0, 0, 8, 8, 6, 4, 7, 0, 6, 0, 0, 0, 4], [0, 6, 9, 0, 4, 0, 0, 3, 0, 9, 0, 3, 0, 0, 0, 3, 4], [0, 5, 2, 0, 0, 0, 0, 2, 9, 0, 0, 6, 0, 4, 5, 0, 0], [0, 7, 0, 3, 8, 8, 4, 5, 4, 3, 8, 8, 9, 5, 0, 3, 0], [0, 0, 0, 0, 8, 8, 0, 0, 7, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 3, 5, 0], [0, 9, 2, 0, 0, 0, 9, 8, 8, 0, 0, 6, 0, 8, 8, 0, 6], [0, 0, 0, 9, 0, 0, 0, 8, 8, 0, 7, 0, 4, 8, 8, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 2, 0, 0, 0, 0, 4, 5, 0, 0, 1, 0, 6, 5, 0, 0, 0], [9, 0, 4, 3, 0, 0, 9, 0, 4, 7, 9, 4, 6, 0, 2, 7, 0], [0, 7, 3, 0, 0, 0, 9, 0, 0, 9, 0, 0, 9, 9, 9, 5, 0], [0, 5, 5, 3, 0, 3, 0, 6, 0, 4, 7, 2, 3, 2, 0, 3, 0], [0, 8, 8, 0, 0, 0, 7, 0, 8, 8, 9, 0, 0, 6, 0, 0, 4], [0, 8, 8, 6, 4, 3, 1, 9, 8, 8, 0, 0, 0, 0, 0, 0, 7], [9, 0, 0, 9, 5, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], [0, 2, 9, 9, 0, 0, 9, 0, 7, 1, 0, 0, 0, 9, 0, 0, 0], [0, 7, 0, 8, 8, 0, 4, 0, 6, 0, 8, 8, 9, 0, 0, 0, 0], [0, 2, 4, 8, 8, 0, 3, 0, 0, 6, 8, 8, 6, 5, 7, 9, 0], [0, 0, 9, 2, 0, 2, 0, 0, 0, 7, 9, 0, 0, 0, 5, 7, 1], [1, 0, 0, 3, 0, 1, 0, 4, 1, 4, 0, 0, 0, 0, 1, 0, 9], [1, 0, 6, 2, 1, 4, 6, 0, 0, 1, 9, 0, 3, 0, 1, 4, 0]] -> [[0, 0, 0, 7, 0], [6, 4, 3, 1, 9], [0, 4, 0, 6, 0], [0, 3, 0, 0, 6]]\\n\\nExample 2:\\n[[0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 7, 9, 0, 7, 7, 0, 0, 1, 3, 0], [2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 3, 5, 9, 1, 8, 8, 0, 2, 0], [0, 0, 0, 0, 8, 8, 1, 0, 0, 6, 8, 8, 3, 0, 0], [2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 9, 2, 0, 0, 2], [0, 0, 9, 0, 4, 9, 9, 9, 0, 2, 9, 6, 1, 4, 0], [0, 0, 0, 0, 0, 0, 9, 4, 0, 0, 0, 0, 0, 0, 5], [1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 5, 0, 6, 0], [2, 1, 0, 0, 6, 0, 6, 2, 7, 0, 4, 0, 0, 0, 7], [0, 9, 0, 0, 2, 0, 5, 0, 1, 0, 0, 0, 0, 5, 3], [4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[3, 5, 9, 1], [1, 0, 0, 6]]\\n\\nExample 3:\\n[[9, 0, 0, 5, 0, 0, 0, 0, 4, 4], [9, 4, 0, 0, 0, 0, 0, 0, 5, 0], [2, 2, 0, 6, 0, 0, 5, 0, 5, 3], [2, 9, 0, 2, 6, 4, 0, 1, 0, 0], [0, 0, 2, 9, 0, 4, 9, 1, 1, 3], [8, 8, 1, 0, 9, 7, 7, 0, 8, 8], [8, 8, 4, 0, 0, 5, 6, 4, 8, 8], [0, 5, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 5, 0, 0, 3, 0], [0, 9, 0, 0, 0, 0, 0, 7, 0, 9], [0, 0, 5, 1, 7, 0, 0, 0, 9, 9], [0, 0, 9, 0, 0, 1, 0, 0, 0, 7]] -> [[1, 0, 9, 7, 7, 0], [4, 0, 0, 5, 6, 4]]\\n\\nExample 4:\\n[[9, 2, 1, 5, 3, 4, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 8, 8, 3, 0, 7, 0, 7, 8, 8, 4, 0, 7, 2, 0, 0, 0], [1, 8, 8, 0, 2, 0, 0, 6, 8, 8, 0, 0, 0, 0, 0, 7, 0], [1, 0, 0, 0, 0, 4, 1, 3, 9, 1, 0, 7, 5, 9, 4, 7, 0], [0, 0, 3, 2, 2, 0, 2, 6, 0, 4, 9, 2, 4, 0, 3, 0, 5], [0, 6, 8, 8, 3, 0, 1, 9, 2, 8, 8, 0, 3, 0, 4, 0, 0], [0, 0, 8, 8, 0, 7, 9, 2, 9, 8, 8, 0, 9, 3, 0, 0, 9], [0, 0, 0, 4, 0, 7, 5, 7, 5, 0, 1, 3, 0, 2, 0, 0, 0], [0, 0, 9, 9, 3, 6, 4, 0, 4, 7, 2, 0, 9, 0, 0, 9, 0], [9, 1, 9, 0, 0, 7, 1, 5, 7, 1, 0, 5, 0, 5, 9, 6, 9], [0, 0, 3, 7, 2, 0, 8, 8, 9, 0, 0, 0, 0, 8, 8, 1, 0], [6, 7, 0, 4, 0, 4, 8, 8, 0, 4, 0, 2, 0, 8, 8, 5, 0]] -> [[3, 0, 7, 0, 7], [0, 2, 0, 0, 6], [3, 0, 1, 9, 2], [0, 7, 9, 2, 9], [9, 0, 0, 0, 0], [0, 4, 0, 2, 0]]\\n\\nExample 5:\\n[[0, 7, 2, 7, 0, 2, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 7, 3, 1], [0, 0, 8, 8, 6, 5, 2, 8, 8, 1, 0, 2, 4, 5, 0, 0], [0, 0, 8, 8, 0, 0, 2, 8, 8, 0, 0, 7, 1, 0, 0, 7], [0, 0, 0, 0, 4, 0, 0, 0, 9, 0, 7, 0, 0, 0, 0, 0], [8, 8, 1, 3, 0, 8, 8, 0, 0, 0, 0, 9, 0, 3, 0, 1], [8, 8, 0, 0, 9, 8, 8, 0, 0, 0, 0, 0, 3, 0, 9, 2], [0, 0, 7, 0, 0, 0, 0, 0, 0, 9, 3, 4, 0, 0, 0, 0], [4, 0, 0, 9, 0, 9, 0, 0, 7, 3, 0, 6, 0, 4, 0, 5], [6, 0, 0, 0, 4, 0, 0, 3, 0, 0, 2, 0, 5, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 1, 2, 0, 4, 0, 0, 0, 0], [4, 5, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 5, 2, 0, 2], [0, 9, 0, 6, 0, 0, 0, 7, 2, 0, 9, 3, 0, 0, 0, 6]] -> [[6, 5, 2], [0, 0, 2], [1, 3, 0], [0, 0, 9]]\\n\\n# Test Problem:\\n[[0, 0, 6, 9, 0, 0, 0, 9, 0, 0, 7, 0, 9, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 4, 0, 9, 0, 0, 0, 0, 0, 2, 0, 1, 0, 5, 1], [2, 1, 0, 8, 8, 4, 1, 5, 0, 8, 8, 0, 1, 0, 4, 0, 0], [0, 7, 3, 8, 8, 0, 9, 0, 0, 8, 8, 0, 6, 0, 4, 7, 2], [2, 5, 0, 4, 0, 0, 0, 0, 7, 9, 0, 9, 5, 0, 4, 0, 1], [8, 8, 5, 9, 0, 4, 8, 8, 4, 0, 3, 7, 0, 0, 0, 0, 5], [8, 8, 7, 7, 0, 0, 8, 8, 6, 4, 7, 0, 6, 0, 0, 0, 4], [0, 6, 9, 0, 4, 0, 0, 3, 0, 9, 0, 3, 0, 0, 0, 3, 4], [0, 5, 2, 0, 0, 0, 0, 2, 9, 0, 0, 6, 0, 4, 5, 0, 0], [0, 7, 0, 3, 8, 8, 4, 5, 4, 3, 8, 8, 9, 5, 0, 3, 0], [0, 0, 0, 0, 8, 8, 0, 0, 7, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 3, 5, 0], [0, 9, 2, 0, 0, 0, 9, 8, 8, 0, 0, 6, 0, 8, 8, 0, 6], [0, 0, 0, 9, 0, 0, 0, 8, 8, 0, 7, 0, 4, 8, 8, 0, 0]] -> \", \"answer\": \"[[4, 1, 5, 0], [0, 9, 0, 0], [5, 9, 0, 4], [7, 7, 0, 0], [4, 5, 4, 3], [0, 0, 7, 0], [0, 0, 6, 0], [0, 7, 0, 4]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"816bac54-fa2e-40e0-aa38-b38eef71a5b5\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 2, 0, 0, 0, 0, 4, 5, 0, 0, 1, 0, 6, 5, 0, 0, 0], [9, 0, 4, 3, 0, 0, 9, 0, 4, 7, 9, 4, 6, 0, 2, 7, 0], [0, 7, 3, 0, 0, 0, 9, 0, 0, 9, 0, 0, 9, 9, 9, 5, 0], [0, 5, 5, 3, 0, 3, 0, 6, 0, 4, 7, 2, 3, 2, 0, 3, 0], [0, 8, 8, 0, 0, 0, 7, 0, 8, 8, 9, 0, 0, 6, 0, 0, 4], [0, 8, 8, 6, 4, 3, 1, 9, 8, 8, 0, 0, 0, 0, 0, 0, 7], [9, 0, 0, 9, 5, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], [0, 2, 9, 9, 0, 0, 9, 0, 7, 1, 0, 0, 0, 9, 0, 0, 0], [0, 7, 0, 8, 8, 0, 4, 0, 6, 0, 8, 8, 9, 0, 0, 0, 0], [0, 2, 4, 8, 8, 0, 3, 0, 0, 6, 8, 8, 6, 5, 7, 9, 0], [0, 0, 9, 2, 0, 2, 0, 0, 0, 7, 9, 0, 0, 0, 5, 7, 1], [1, 0, 0, 3, 0, 1, 0, 4, 1, 4, 0, 0, 0, 0, 1, 0, 9], [1, 0, 6, 2, 1, 4, 6, 0, 0, 1, 9, 0, 3, 0, 1, 4, 0]] -> [[0, 0, 0, 7, 0], [6, 4, 3, 1, 9], [0, 4, 0, 6, 0], [0, 3, 0, 0, 6]]\\\\n\\\\nExample 2:\\\\n[[0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 7, 9, 0, 7, 7, 0, 0, 1, 3, 0], [2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 3, 5, 9, 1, 8, 8, 0, 2, 0], [0, 0, 0, 0, 8, 8, 1, 0, 0, 6, 8, 8, 3, 0, 0], [2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 9, 2, 0, 0, 2], [0, 0, 9, 0, 4, 9, 9, 9, 0, 2, 9, 6, 1, 4, 0], [0, 0, 0, 0, 0, 0, 9, 4, 0, 0, 0, 0, 0, 0, 5], [1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 5, 0, 6, 0], [2, 1, 0, 0, 6, 0, 6, 2, 7, 0, 4, 0, 0, 0, 7], [0, 9, 0, 0, 2, 0, 5, 0, 1, 0, 0, 0, 0, 5, 3], [4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[3, 5, 9, 1], [1, 0, 0, 6]]\\\\n\\\\nExample 3:\\\\n[[9, 0, 0, 5, 0, 0, 0, 0, 4, 4], [9, 4, 0, 0, 0, 0, 0, 0, 5, 0], [2, 2, 0, 6, 0, 0, 5, 0, 5, 3], [2, 9, 0, 2, 6, 4, 0, 1, 0, 0], [0, 0, 2, 9, 0, 4, 9, 1, 1, 3], [8, 8, 1, 0, 9, 7, 7, 0, 8, 8], [8, 8, 4, 0, 0, 5, 6, 4, 8, 8], [0, 5, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 5, 0, 0, 3, 0], [0, 9, 0, 0, 0, 0, 0, 7, 0, 9], [0, 0, 5, 1, 7, 0, 0, 0, 9, 9], [0, 0, 9, 0, 0, 1, 0, 0, 0, 7]] -> [[1, 0, 9, 7, 7, 0], [4, 0, 0, 5, 6, 4]]\\\\n\\\\nExample 4:\\\\n[[9, 2, 1, 5, 3, 4, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 8, 8, 3, 0, 7, 0, 7, 8, 8, 4, 0, 7, 2, 0, 0, 0], [1, 8, 8, 0, 2, 0, 0, 6, 8, 8, 0, 0, 0, 0, 0, 7, 0], [1, 0, 0, 0, 0, 4, 1, 3, 9, 1, 0, 7, 5, 9, 4, 7, 0], [0, 0, 3, 2, 2, 0, 2, 6, 0, 4, 9, 2, 4, 0, 3, 0, 5], [0, 6, 8, 8, 3, 0, 1, 9, 2, 8, 8, 0, 3, 0, 4, 0, 0], [0, 0, 8, 8, 0, 7, 9, 2, 9, 8, 8, 0, 9, 3, 0, 0, 9], [0, 0, 0, 4, 0, 7, 5, 7, 5, 0, 1, 3, 0, 2, 0, 0, 0], [0, 0, 9, 9, 3, 6, 4, 0, 4, 7, 2, 0, 9, 0, 0, 9, 0], [9, 1, 9, 0, 0, 7, 1, 5, 7, 1, 0, 5, 0, 5, 9, 6, 9], [0, 0, 3, 7, 2, 0, 8, 8, 9, 0, 0, 0, 0, 8, 8, 1, 0], [6, 7, 0, 4, 0, 4, 8, 8, 0, 4, 0, 2, 0, 8, 8, 5, 0]] -> [[3, 0, 7, 0, 7], [0, 2, 0, 0, 6], [3, 0, 1, 9, 2], [0, 7, 9, 2, 9], [9, 0, 0, 0, 0], [0, 4, 0, 2, 0]]\\\\n\\\\nExample 5:\\\\n[[0, 7, 2, 7, 0, 2, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 7, 3, 1], [0, 0, 8, 8, 6, 5, 2, 8, 8, 1, 0, 2, 4, 5, 0, 0], [0, 0, 8, 8, 0, 0, 2, 8, 8, 0, 0, 7, 1, 0, 0, 7], [0, 0, 0, 0, 4, 0, 0, 0, 9, 0, 7, 0, 0, 0, 0, 0], [8, 8, 1, 3, 0, 8, 8, 0, 0, 0, 0, 9, 0, 3, 0, 1], [8, 8, 0, 0, 9, 8, 8, 0, 0, 0, 0, 0, 3, 0, 9, 2], [0, 0, 7, 0, 0, 0, 0, 0, 0, 9, 3, 4, 0, 0, 0, 0], [4, 0, 0, 9, 0, 9, 0, 0, 7, 3, 0, 6, 0, 4, 0, 5], [6, 0, 0, 0, 4, 0, 0, 3, 0, 0, 2, 0, 5, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 1, 2, 0, 4, 0, 0, 0, 0], [4, 5, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 5, 2, 0, 2], [0, 9, 0, 6, 0, 0, 0, 7, 2, 0, 9, 3, 0, 0, 0, 6]] -> [[6, 5, 2], [0, 0, 2], [1, 3, 0], [0, 0, 9]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 6, 9, 0, 0, 0, 9, 0, 0, 7, 0, 9, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 4, 0, 9, 0, 0, 0, 0, 0, 2, 0, 1, 0, 5, 1], [2, 1, 0, 8, 8, 4, 1, 5, 0, 8, 8, 0, 1, 0, 4, 0, 0], [0, 7, 3, 8, 8, 0, 9, 0, 0, 8, 8, 0, 6, 0, 4, 7, 2], [2, 5, 0, 4, 0, 0, 0, 0, 7, 9, 0, 9, 5, 0, 4, 0, 1], [8, 8, 5, 9, 0, 4, 8, 8, 4, 0, 3, 7, 0, 0, 0, 0, 5], [8, 8, 7, 7, 0, 0, 8, 8, 6, 4, 7, 0, 6, 0, 0, 0, 4], [0, 6, 9, 0, 4, 0, 0, 3, 0, 9, 0, 3, 0, 0, 0, 3, 4], [0, 5, 2, 0, 0, 0, 0, 2, 9, 0, 0, 6, 0, 4, 5, 0, 0], [0, 7, 0, 3, 8, 8, 4, 5, 4, 3, 8, 8, 9, 5, 0, 3, 0], [0, 0, 0, 0, 8, 8, 0, 0, 7, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 3, 5, 0], [0, 9, 2, 0, 0, 0, 9, 8, 8, 0, 0, 6, 0, 8, 8, 0, 6], [0, 0, 0, 9, 0, 0, 0, 8, 8, 0, 7, 0, 4, 8, 8, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[4, 1, 5, 0], [0, 9, 0, 0], [5, 9, 0, 4], [7, 7, 0, 0], [4, 5, 4, 3], [0, 0, 7, 0], [0, 0, 6, 0], [0, 7, 0, 4]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "816bac54-fa2e-40e0-aa38-b38eef71a5b5"}
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[[4, 1, 5, 0], [0, 9, 0, 0], [5, 9, 0, 4], [7, 7, 0, 0], [4, 5, 4, 3], [0, 0, 7, 0], [0, 0, 6, 0], [0, 7, 0, 4]]
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{"id": "816bac54-fa2e-40e0-aa38-b38eef71a5b5", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 2, 0, 0, 0, 0, 4, 5, 0, 0, 1, 0, 6, 5, 0, 0, 0], [9, 0, 4, 3, 0, 0, 9, 0, 4, 7, 9, 4, 6, 0, 2, 7, 0], [0, 7, 3, 0, 0, 0, 9, 0, 0, 9, 0, 0, 9, 9, 9, 5, 0], [0, 5, 5, 3, 0, 3, 0, 6, 0, 4, 7, 2, 3, 2, 0, 3, 0], [0, 8, 8, 0, 0, 0, 7, 0, 8, 8, 9, 0, 0, 6, 0, 0, 4], [0, 8, 8, 6, 4, 3, 1, 9, 8, 8, 0, 0, 0, 0, 0, 0, 7], [9, 0, 0, 9, 5, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], [0, 2, 9, 9, 0, 0, 9, 0, 7, 1, 0, 0, 0, 9, 0, 0, 0], [0, 7, 0, 8, 8, 0, 4, 0, 6, 0, 8, 8, 9, 0, 0, 0, 0], [0, 2, 4, 8, 8, 0, 3, 0, 0, 6, 8, 8, 6, 5, 7, 9, 0], [0, 0, 9, 2, 0, 2, 0, 0, 0, 7, 9, 0, 0, 0, 5, 7, 1], [1, 0, 0, 3, 0, 1, 0, 4, 1, 4, 0, 0, 0, 0, 1, 0, 9], [1, 0, 6, 2, 1, 4, 6, 0, 0, 1, 9, 0, 3, 0, 1, 4, 0]] -> [[0, 0, 0, 7, 0], [6, 4, 3, 1, 9], [0, 4, 0, 6, 0], [0, 3, 0, 0, 6]]\n\nExample 2:\n[[0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 7, 9, 0, 7, 7, 0, 0, 1, 3, 0], [2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 3, 5, 9, 1, 8, 8, 0, 2, 0], [0, 0, 0, 0, 8, 8, 1, 0, 0, 6, 8, 8, 3, 0, 0], [2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 9, 2, 0, 0, 2], [0, 0, 9, 0, 4, 9, 9, 9, 0, 2, 9, 6, 1, 4, 0], [0, 0, 0, 0, 0, 0, 9, 4, 0, 0, 0, 0, 0, 0, 5], [1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 5, 0, 6, 0], [2, 1, 0, 0, 6, 0, 6, 2, 7, 0, 4, 0, 0, 0, 7], [0, 9, 0, 0, 2, 0, 5, 0, 1, 0, 0, 0, 0, 5, 3], [4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[3, 5, 9, 1], [1, 0, 0, 6]]\n\nExample 3:\n[[9, 0, 0, 5, 0, 0, 0, 0, 4, 4], [9, 4, 0, 0, 0, 0, 0, 0, 5, 0], [2, 2, 0, 6, 0, 0, 5, 0, 5, 3], [2, 9, 0, 2, 6, 4, 0, 1, 0, 0], [0, 0, 2, 9, 0, 4, 9, 1, 1, 3], [8, 8, 1, 0, 9, 7, 7, 0, 8, 8], [8, 8, 4, 0, 0, 5, 6, 4, 8, 8], [0, 5, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 5, 0, 0, 3, 0], [0, 9, 0, 0, 0, 0, 0, 7, 0, 9], [0, 0, 5, 1, 7, 0, 0, 0, 9, 9], [0, 0, 9, 0, 0, 1, 0, 0, 0, 7]] -> [[1, 0, 9, 7, 7, 0], [4, 0, 0, 5, 6, 4]]\n\nExample 4:\n[[9, 2, 1, 5, 3, 4, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 8, 8, 3, 0, 7, 0, 7, 8, 8, 4, 0, 7, 2, 0, 0, 0], [1, 8, 8, 0, 2, 0, 0, 6, 8, 8, 0, 0, 0, 0, 0, 7, 0], [1, 0, 0, 0, 0, 4, 1, 3, 9, 1, 0, 7, 5, 9, 4, 7, 0], [0, 0, 3, 2, 2, 0, 2, 6, 0, 4, 9, 2, 4, 0, 3, 0, 5], [0, 6, 8, 8, 3, 0, 1, 9, 2, 8, 8, 0, 3, 0, 4, 0, 0], [0, 0, 8, 8, 0, 7, 9, 2, 9, 8, 8, 0, 9, 3, 0, 0, 9], [0, 0, 0, 4, 0, 7, 5, 7, 5, 0, 1, 3, 0, 2, 0, 0, 0], [0, 0, 9, 9, 3, 6, 4, 0, 4, 7, 2, 0, 9, 0, 0, 9, 0], [9, 1, 9, 0, 0, 7, 1, 5, 7, 1, 0, 5, 0, 5, 9, 6, 9], [0, 0, 3, 7, 2, 0, 8, 8, 9, 0, 0, 0, 0, 8, 8, 1, 0], [6, 7, 0, 4, 0, 4, 8, 8, 0, 4, 0, 2, 0, 8, 8, 5, 0]] -> [[3, 0, 7, 0, 7], [0, 2, 0, 0, 6], [3, 0, 1, 9, 2], [0, 7, 9, 2, 9], [9, 0, 0, 0, 0], [0, 4, 0, 2, 0]]\n\nExample 5:\n[[0, 7, 2, 7, 0, 2, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 7, 3, 1], [0, 0, 8, 8, 6, 5, 2, 8, 8, 1, 0, 2, 4, 5, 0, 0], [0, 0, 8, 8, 0, 0, 2, 8, 8, 0, 0, 7, 1, 0, 0, 7], [0, 0, 0, 0, 4, 0, 0, 0, 9, 0, 7, 0, 0, 0, 0, 0], [8, 8, 1, 3, 0, 8, 8, 0, 0, 0, 0, 9, 0, 3, 0, 1], [8, 8, 0, 0, 9, 8, 8, 0, 0, 0, 0, 0, 3, 0, 9, 2], [0, 0, 7, 0, 0, 0, 0, 0, 0, 9, 3, 4, 0, 0, 0, 0], [4, 0, 0, 9, 0, 9, 0, 0, 7, 3, 0, 6, 0, 4, 0, 5], [6, 0, 0, 0, 4, 0, 0, 3, 0, 0, 2, 0, 5, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 1, 2, 0, 4, 0, 0, 0, 0], [4, 5, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 5, 2, 0, 2], [0, 9, 0, 6, 0, 0, 0, 7, 2, 0, 9, 3, 0, 0, 0, 6]] -> [[6, 5, 2], [0, 0, 2], [1, 3, 0], [0, 0, 9]]\n\n# Test Problem:\n[[0, 0, 6, 9, 0, 0, 0, 9, 0, 0, 7, 0, 9, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 4, 0, 9, 0, 0, 0, 0, 0, 2, 0, 1, 0, 5, 1], [2, 1, 0, 8, 8, 4, 1, 5, 0, 8, 8, 0, 1, 0, 4, 0, 0], [0, 7, 3, 8, 8, 0, 9, 0, 0, 8, 8, 0, 6, 0, 4, 7, 2], [2, 5, 0, 4, 0, 0, 0, 0, 7, 9, 0, 9, 5, 0, 4, 0, 1], [8, 8, 5, 9, 0, 4, 8, 8, 4, 0, 3, 7, 0, 0, 0, 0, 5], [8, 8, 7, 7, 0, 0, 8, 8, 6, 4, 7, 0, 6, 0, 0, 0, 4], [0, 6, 9, 0, 4, 0, 0, 3, 0, 9, 0, 3, 0, 0, 0, 3, 4], [0, 5, 2, 0, 0, 0, 0, 2, 9, 0, 0, 6, 0, 4, 5, 0, 0], [0, 7, 0, 3, 8, 8, 4, 5, 4, 3, 8, 8, 9, 5, 0, 3, 0], [0, 0, 0, 0, 8, 8, 0, 0, 7, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 3, 5, 0], [0, 9, 2, 0, 0, 0, 9, 8, 8, 0, 0, 6, 0, 8, 8, 0, 6], [0, 0, 0, 9, 0, 0, 0, 8, 8, 0, 7, 0, 4, 8, 8, 0, 0]] -> ", "answer": "[[4, 1, 5, 0], [0, 9, 0, 0], [5, 9, 0, 4], [7, 7, 0, 0], [4, 5, 4, 3], [0, 0, 7, 0], [0, 0, 6, 0], [0, 7, 0, 4]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[4, 4, 4, 4], [3, 3, 0, 0], [3, 3, 0, 0], [0, 2, 2, 0]]
Example 2:
[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 2, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 3, 3], [1, 1, 2, 4], [0, 2, 2, 4]]
Example 3:
[[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 1, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 2, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]] -> [[0, 1, 0, 0, 0], [1, 1, 2, 2, 0], [0, 1, 1, 2, 0], [0, 0, 0, 2, 0]]
# Test Problem:
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 2, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 4, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 6, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[4, 4, 4, 4], [3, 3, 0, 0], [3, 3, 0, 0], [0, 2, 2, 0]]\\n\\nExample 2:\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 2, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 3, 3], [1, 1, 2, 4], [0, 2, 2, 4]]\\n\\nExample 3:\\n[[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 1, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 2, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]] -> [[0, 1, 0, 0, 0], [1, 1, 2, 2, 0], [0, 1, 1, 2, 0], [0, 0, 0, 2, 0]]\\n\\n# Test Problem:\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 2, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 4, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 6, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> \", \"answer\": \"[[0, 2, 3], [2, 2, 3], [4, 4, 4], [6, 4, 0], [6, 6, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"e16dba8e-6d64-4e44-b4e7-33fb6e7b93e9\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[4, 4, 4, 4], [3, 3, 0, 0], [3, 3, 0, 0], [0, 2, 2, 0]]\\\\n\\\\nExample 2:\\\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 2, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 3, 3], [1, 1, 2, 4], [0, 2, 2, 4]]\\\\n\\\\nExample 3:\\\\n[[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 1, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 2, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]] -> [[0, 1, 0, 0, 0], [1, 1, 2, 2, 0], [0, 1, 1, 2, 0], [0, 0, 0, 2, 0]]\\\\n\\\\n# Test Problem:\\\\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 2, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 4, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 6, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> \\\", \\\"answer\\\": \\\"[[0, 2, 3], [2, 2, 3], [4, 4, 4], [6, 4, 0], [6, 6, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "e16dba8e-6d64-4e44-b4e7-33fb6e7b93e9"}
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[[0, 2, 3], [2, 2, 3], [4, 4, 4], [6, 4, 0], [6, 6, 0]]
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{"id": "e16dba8e-6d64-4e44-b4e7-33fb6e7b93e9", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 3, 3, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> [[4, 4, 4, 4], [3, 3, 0, 0], [3, 3, 0, 0], [0, 2, 2, 0]]\n\nExample 2:\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3, 8, 8, 8], [8, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 2, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 3, 3], [1, 1, 2, 4], [0, 2, 2, 4]]\n\nExample 3:\n[[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 1, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 1, 1, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 2, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 0, 0, 0, 2, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]] -> [[0, 1, 0, 0, 0], [1, 1, 2, 2, 0], [0, 1, 1, 2, 0], [0, 0, 0, 2, 0]]\n\n# Test Problem:\n[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 2, 2, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 4, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 6, 0, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]] -> ", "answer": "[[0, 2, 3], [2, 2, 3], [4, 4, 4], [6, 4, 0], [6, 6, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 1, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 1, 1, 0, 8, 0, 0, 1], [0, 7, 0, 1, 8, 0, 0, 0], [8, 0, 0, 0, 1, 0, 7, 0], [0, 8, 8, 8, 1, 0, 0, 0]] -> [[0, 0, 3, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 3, 3, 0, 3, 0, 0, 3], [0, 3, 0, 3, 3, 0, 0, 0], [3, 0, 0, 0, 3, 0, 3, 0], [0, 8, 8, 8, 3, 0, 0, 0]]
Example 2:
[[0, 0, 1, 8, 1, 1, 1, 0], [1, 5, 1, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 7, 0, 0, 8, 5, 5, 0], [1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 8, 7, 7, 8, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 8, 0, 8, 8]] -> [[0, 0, 3, 3, 1, 1, 1, 0], [3, 3, 3, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 3, 0, 0, 3, 3, 3, 0], [3, 0, 0, 0, 0, 0, 0, 3], [3, 0, 8, 7, 7, 3, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 3, 0, 8, 8]]
Example 3:
[[1, 7, 7, 1, 0, 8, 0, 5], [1, 7, 7, 1, 1, 0, 1, 0], [8, 8, 0, 0, 7, 7, 7, 7], [0, 1, 0, 0, 0, 0, 1, 1], [5, 0, 8, 0, 1, 0, 1, 1]] -> [[3, 7, 7, 1, 0, 3, 0, 3], [3, 7, 7, 1, 1, 0, 3, 0], [3, 3, 0, 0, 7, 7, 7, 7], [0, 3, 0, 0, 0, 0, 1, 1], [3, 0, 3, 0, 3, 0, 1, 1]]
Example 4:
[[1, 0, 5], [1, 0, 0], [7, 7, 7]] -> [[3, 0, 3], [3, 0, 0], [7, 7, 7]]
# Test Problem:
[[0, 5, 0, 1, 5, 5, 0, 5], [1, 1, 0, 0, 0, 1, 1, 0], [0, 7, 7, 0, 0, 0, 0, 5], [1, 1, 0, 5, 0, 1, 0, 0], [0, 1, 0, 5, 5, 5, 0, 1], [0, 7, 0, 0, 7, 0, 0, 7], [1, 0, 1, 0, 0, 0, 1, 7], [0, 0, 1, 1, 0, 1, 0, 7]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 1, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 1, 1, 0, 8, 0, 0, 1], [0, 7, 0, 1, 8, 0, 0, 0], [8, 0, 0, 0, 1, 0, 7, 0], [0, 8, 8, 8, 1, 0, 0, 0]] -> [[0, 0, 3, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 3, 3, 0, 3, 0, 0, 3], [0, 3, 0, 3, 3, 0, 0, 0], [3, 0, 0, 0, 3, 0, 3, 0], [0, 8, 8, 8, 3, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 1, 8, 1, 1, 1, 0], [1, 5, 1, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 7, 0, 0, 8, 5, 5, 0], [1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 8, 7, 7, 8, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 8, 0, 8, 8]] -> [[0, 0, 3, 3, 1, 1, 1, 0], [3, 3, 3, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 3, 0, 0, 3, 3, 3, 0], [3, 0, 0, 0, 0, 0, 0, 3], [3, 0, 8, 7, 7, 3, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 3, 0, 8, 8]]\\n\\nExample 3:\\n[[1, 7, 7, 1, 0, 8, 0, 5], [1, 7, 7, 1, 1, 0, 1, 0], [8, 8, 0, 0, 7, 7, 7, 7], [0, 1, 0, 0, 0, 0, 1, 1], [5, 0, 8, 0, 1, 0, 1, 1]] -> [[3, 7, 7, 1, 0, 3, 0, 3], [3, 7, 7, 1, 1, 0, 3, 0], [3, 3, 0, 0, 7, 7, 7, 7], [0, 3, 0, 0, 0, 0, 1, 1], [3, 0, 3, 0, 3, 0, 1, 1]]\\n\\nExample 4:\\n[[1, 0, 5], [1, 0, 0], [7, 7, 7]] -> [[3, 0, 3], [3, 0, 0], [7, 7, 7]]\\n\\n# Test Problem:\\n[[0, 5, 0, 1, 5, 5, 0, 5], [1, 1, 0, 0, 0, 1, 1, 0], [0, 7, 7, 0, 0, 0, 0, 5], [1, 1, 0, 5, 0, 1, 0, 0], [0, 1, 0, 5, 5, 5, 0, 1], [0, 7, 0, 0, 7, 0, 0, 7], [1, 0, 1, 0, 0, 0, 1, 7], [0, 0, 1, 1, 0, 1, 0, 7]] -> \", \"answer\": \"[[0, 3, 0, 3, 3, 3, 0, 3], [3, 3, 0, 0, 0, 3, 3, 0], [0, 3, 3, 0, 0, 0, 0, 3], [1, 1, 0, 5, 0, 3, 0, 0], [0, 1, 0, 5, 5, 5, 0, 3], [0, 3, 0, 0, 3, 0, 0, 7], [3, 0, 1, 0, 0, 0, 3, 7], [0, 0, 1, 1, 0, 3, 0, 7]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"05f01736-8c33-457e-9c97-e4b23b5bb309\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 1, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 1, 1, 0, 8, 0, 0, 1], [0, 7, 0, 1, 8, 0, 0, 0], [8, 0, 0, 0, 1, 0, 7, 0], [0, 8, 8, 8, 1, 0, 0, 0]] -> [[0, 0, 3, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 3, 3, 0, 3, 0, 0, 3], [0, 3, 0, 3, 3, 0, 0, 0], [3, 0, 0, 0, 3, 0, 3, 0], [0, 8, 8, 8, 3, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 1, 8, 1, 1, 1, 0], [1, 5, 1, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 7, 0, 0, 8, 5, 5, 0], [1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 8, 7, 7, 8, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 8, 0, 8, 8]] -> [[0, 0, 3, 3, 1, 1, 1, 0], [3, 3, 3, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 3, 0, 0, 3, 3, 3, 0], [3, 0, 0, 0, 0, 0, 0, 3], [3, 0, 8, 7, 7, 3, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 3, 0, 8, 8]]\\\\n\\\\nExample 3:\\\\n[[1, 7, 7, 1, 0, 8, 0, 5], [1, 7, 7, 1, 1, 0, 1, 0], [8, 8, 0, 0, 7, 7, 7, 7], [0, 1, 0, 0, 0, 0, 1, 1], [5, 0, 8, 0, 1, 0, 1, 1]] -> [[3, 7, 7, 1, 0, 3, 0, 3], [3, 7, 7, 1, 1, 0, 3, 0], [3, 3, 0, 0, 7, 7, 7, 7], [0, 3, 0, 0, 0, 0, 1, 1], [3, 0, 3, 0, 3, 0, 1, 1]]\\\\n\\\\nExample 4:\\\\n[[1, 0, 5], [1, 0, 0], [7, 7, 7]] -> [[3, 0, 3], [3, 0, 0], [7, 7, 7]]\\\\n\\\\n# Test Problem:\\\\n[[0, 5, 0, 1, 5, 5, 0, 5], [1, 1, 0, 0, 0, 1, 1, 0], [0, 7, 7, 0, 0, 0, 0, 5], [1, 1, 0, 5, 0, 1, 0, 0], [0, 1, 0, 5, 5, 5, 0, 1], [0, 7, 0, 0, 7, 0, 0, 7], [1, 0, 1, 0, 0, 0, 1, 7], [0, 0, 1, 1, 0, 1, 0, 7]] -> \\\", \\\"answer\\\": \\\"[[0, 3, 0, 3, 3, 3, 0, 3], [3, 3, 0, 0, 0, 3, 3, 0], [0, 3, 3, 0, 0, 0, 0, 3], [1, 1, 0, 5, 0, 3, 0, 0], [0, 1, 0, 5, 5, 5, 0, 3], [0, 3, 0, 0, 3, 0, 0, 7], [3, 0, 1, 0, 0, 0, 3, 7], [0, 0, 1, 1, 0, 3, 0, 7]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "05f01736-8c33-457e-9c97-e4b23b5bb309"}
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[[0, 3, 0, 3, 3, 3, 0, 3], [3, 3, 0, 0, 0, 3, 3, 0], [0, 3, 3, 0, 0, 0, 0, 3], [1, 1, 0, 5, 0, 3, 0, 0], [0, 1, 0, 5, 5, 5, 0, 3], [0, 3, 0, 0, 3, 0, 0, 7], [3, 0, 1, 0, 0, 0, 3, 7], [0, 0, 1, 1, 0, 3, 0, 7]]
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{"id": "05f01736-8c33-457e-9c97-e4b23b5bb309", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 1, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 1, 1, 0, 8, 0, 0, 1], [0, 7, 0, 1, 8, 0, 0, 0], [8, 0, 0, 0, 1, 0, 7, 0], [0, 8, 8, 8, 1, 0, 0, 0]] -> [[0, 0, 3, 0, 7, 7, 7, 0], [8, 8, 0, 0, 5, 5, 0, 0], [0, 8, 8, 0, 0, 5, 5, 0], [0, 3, 3, 0, 3, 0, 0, 3], [0, 3, 0, 3, 3, 0, 0, 0], [3, 0, 0, 0, 3, 0, 3, 0], [0, 8, 8, 8, 3, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 1, 8, 1, 1, 1, 0], [1, 5, 1, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 7, 0, 0, 8, 5, 5, 0], [1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 8, 7, 7, 8, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 8, 0, 8, 8]] -> [[0, 0, 3, 3, 1, 1, 1, 0], [3, 3, 3, 7, 1, 1, 0, 0], [0, 8, 0, 7, 7, 7, 8, 8], [0, 8, 8, 0, 0, 0, 8, 0], [0, 3, 0, 0, 3, 3, 3, 0], [3, 0, 0, 0, 0, 0, 0, 3], [3, 0, 8, 7, 7, 3, 0, 0], [0, 0, 8, 7, 7, 0, 8, 8], [0, 8, 8, 0, 3, 0, 8, 8]]\n\nExample 3:\n[[1, 7, 7, 1, 0, 8, 0, 5], [1, 7, 7, 1, 1, 0, 1, 0], [8, 8, 0, 0, 7, 7, 7, 7], [0, 1, 0, 0, 0, 0, 1, 1], [5, 0, 8, 0, 1, 0, 1, 1]] -> [[3, 7, 7, 1, 0, 3, 0, 3], [3, 7, 7, 1, 1, 0, 3, 0], [3, 3, 0, 0, 7, 7, 7, 7], [0, 3, 0, 0, 0, 0, 1, 1], [3, 0, 3, 0, 3, 0, 1, 1]]\n\nExample 4:\n[[1, 0, 5], [1, 0, 0], [7, 7, 7]] -> [[3, 0, 3], [3, 0, 0], [7, 7, 7]]\n\n# Test Problem:\n[[0, 5, 0, 1, 5, 5, 0, 5], [1, 1, 0, 0, 0, 1, 1, 0], [0, 7, 7, 0, 0, 0, 0, 5], [1, 1, 0, 5, 0, 1, 0, 0], [0, 1, 0, 5, 5, 5, 0, 1], [0, 7, 0, 0, 7, 0, 0, 7], [1, 0, 1, 0, 0, 0, 1, 7], [0, 0, 1, 1, 0, 1, 0, 7]] -> ", "answer": "[[0, 3, 0, 3, 3, 3, 0, 3], [3, 3, 0, 0, 0, 3, 3, 0], [0, 3, 3, 0, 0, 0, 0, 3], [1, 1, 0, 5, 0, 3, 0, 0], [0, 1, 0, 5, 5, 5, 0, 3], [0, 3, 0, 0, 3, 0, 0, 7], [3, 0, 1, 0, 0, 0, 3, 7], [0, 0, 1, 1, 0, 3, 0, 7]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 3, 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, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 6, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 6, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 8, 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, 9, 0, 0, 0, 8, 0, 0, 0, 0, 5, 0, 9, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 1, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[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, 0, 0, 8, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 3, 0, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 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, 8, 0, 0, 0, 6, 0, 0, 5, 0, 0, 0, 8, 0, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 1, 0, 0, 3], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 9, 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, 9, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 7, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[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, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 3, 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, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 6, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 6, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 8, 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, 9, 0, 0, 0, 8, 0, 0, 0, 0, 5, 0, 9, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 1, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[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, 0, 0, 8, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 3, 0, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 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, 8, 0, 0, 0, 6, 0, 0, 5, 0, 0, 0, 8, 0, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 1, 0, 0, 3], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 9, 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, 9, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 7, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"2a308ee5-c5a3-45e2-b450-7e5142c9115f\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[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, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 3, 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, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 6, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 6, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 8, 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, 9, 0, 0, 0, 8, 0, 0, 0, 0, 5, 0, 9, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 1, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[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, 0, 0, 8, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 3, 0, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 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, 8, 0, 0, 0, 6, 0, 0, 5, 0, 0, 0, 8, 0, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 1, 0, 0, 3], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 9, 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, 9, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 7, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "2a308ee5-c5a3-45e2-b450-7e5142c9115f"}
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[[0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "2a308ee5-c5a3-45e2-b450-7e5142c9115f", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[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, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 3, 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, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 6, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 6, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 8, 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, 9, 0, 0, 0, 8, 0, 0, 0, 0, 5, 0, 9, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 1, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[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, 0, 0, 8, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 3, 0, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 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, 8, 0, 0, 0, 6, 0, 0, 5, 0, 0, 0, 8, 0, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 1, 0, 0, 3], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 9, 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, 9, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 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, 7, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 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, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 3, 0, 3, 0, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 3, 0, 3, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 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, 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, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 4, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 4, 0, 4, 0, 4, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 4, 0, 4, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 2, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0], [4, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 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, 4, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [5, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 4, 0, 0, 0, 5, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 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, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 3, 0, 3, 0, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 3, 0, 3, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 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, 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, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 4, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 4, 0, 4, 0, 4, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 4, 0, 4, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 2, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0], [4, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 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, 4, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [5, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 4, 0, 0, 0, 5, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0]] -> \", \"answer\": \"[[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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 8, 0, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 8, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"55a8c595-dbea-4464-92c2-56112c2afdd1\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 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, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 3, 0, 3, 0, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 3, 0, 3, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 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, 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, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 4, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 4, 0, 4, 0, 4, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 4, 0, 4, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 2, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0], [4, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 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, 4, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [5, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 4, 0, 0, 0, 5, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 8, 0, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 8, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "55a8c595-dbea-4464-92c2-56112c2afdd1"}
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[[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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 8, 0, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 8, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "55a8c595-dbea-4464-92c2-56112c2afdd1", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0], [0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 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, 0], [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 3, 0, 3, 0, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 3, 0, 3, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 6, 0, 6, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 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, 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, 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, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 4, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 8, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 4, 0, 4, 0, 4, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 4, 0, 4, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 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, 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, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 2, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 8, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0], [4, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 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, 4, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [5, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 4, 0, 0, 0, 5, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0]] -> ", "answer": "[[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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 4, 0, 4, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 8, 0, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 8, 2, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 5, 0, 5, 0, 5, 0, 5, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 5, 0, 5, 0, 5, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 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, 0, 0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 4, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 2, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 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, 0, 0, 0, 0, 0]] -> [[2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 2, 2, 0, 3, 3, 0, 0, 0], [0, 3, 0, 2, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 8]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 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, 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], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 3, 0, 5, 3, 0, 5, 7, 0, 5, 5, 0, 5, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 2, 0, 5, 3, 0, 5, 3, 0, 5, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[3, 3, 0, 3, 3, 0, 7, 7, 0, 0, 0, 0, 2, 2], [0, 3, 0, 0, 3, 0, 7, 0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 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], [2, 2, 0, 2, 2, 0, 3, 3, 0, 3, 3, 0, 7, 7], [2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 3, 0, 7, 0]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0], [0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 2, 0, 5, 2, 0, 5, 2, 0, 5, 8, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 5, 3, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 3, 0, 5, 5, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 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, 0, 0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 4, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 2, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 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, 0, 0, 0, 0, 0]] -> [[2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 2, 2, 0, 3, 3, 0, 0, 0], [0, 3, 0, 2, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 8]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 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, 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], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 3, 0, 5, 3, 0, 5, 7, 0, 5, 5, 0, 5, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 2, 0, 5, 3, 0, 5, 3, 0, 5, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[3, 3, 0, 3, 3, 0, 7, 7, 0, 0, 0, 0, 2, 2], [0, 3, 0, 0, 3, 0, 7, 0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 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], [2, 2, 0, 2, 2, 0, 3, 3, 0, 3, 3, 0, 7, 7], [2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 3, 0, 7, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0], [0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 2, 0, 5, 2, 0, 5, 2, 0, 5, 8, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 5, 3, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 3, 0, 5, 5, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[2, 2, 0, 2, 2, 0, 2, 2, 0, 8, 8], [2, 0, 0, 2, 0, 0, 2, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 3, 3, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8], [4, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"48cdcd7b-764c-4056-920b-12f5a39251b2\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 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, 0, 0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 4, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 2, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 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, 0, 0, 0, 0, 0]] -> [[2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 2, 2, 0, 3, 3, 0, 0, 0], [0, 3, 0, 2, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 8]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 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, 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], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 3, 0, 5, 3, 0, 5, 7, 0, 5, 5, 0, 5, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 2, 0, 5, 3, 0, 5, 3, 0, 5, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[3, 3, 0, 3, 3, 0, 7, 7, 0, 0, 0, 0, 2, 2], [0, 3, 0, 0, 3, 0, 7, 0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 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], [2, 2, 0, 2, 2, 0, 3, 3, 0, 3, 3, 0, 7, 7], [2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 3, 0, 7, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0], [0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 2, 0, 5, 2, 0, 5, 2, 0, 5, 8, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 5, 3, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 3, 0, 5, 5, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[2, 2, 0, 2, 2, 0, 2, 2, 0, 8, 8], [2, 0, 0, 2, 0, 0, 2, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 3, 3, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8], [4, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "48cdcd7b-764c-4056-920b-12f5a39251b2"}
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[[2, 2, 0, 2, 2, 0, 2, 2, 0, 8, 8], [2, 0, 0, 2, 0, 0, 2, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 3, 3, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8], [4, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8]]
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{"id": "48cdcd7b-764c-4056-920b-12f5a39251b2", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 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, 0, 0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 4, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 2, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 3, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 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, 0, 0, 0, 0, 0]] -> [[2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 2, 2, 0, 3, 3, 0, 0, 0], [0, 3, 0, 2, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 8]]\n\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 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, 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], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 3, 0, 5, 3, 0, 5, 7, 0, 5, 5, 0, 5, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0], [0, 0, 5, 2, 0, 5, 2, 0, 5, 3, 0, 5, 3, 0, 5, 7, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[3, 3, 0, 3, 3, 0, 7, 7, 0, 0, 0, 0, 2, 2], [0, 3, 0, 0, 3, 0, 7, 0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 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], [2, 2, 0, 2, 2, 0, 3, 3, 0, 3, 3, 0, 7, 7], [2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 3, 0, 7, 0]]\n\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0], [0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 2, 0, 5, 2, 0, 5, 2, 0, 5, 8, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 5, 3, 0, 5, 3, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 3, 0, 5, 5, 0, 5, 5, 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, 5, 5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 5, 4, 0, 5, 5, 0, 5, 5, 0, 5, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[2, 2, 0, 2, 2, 0, 2, 2, 0, 8, 8], [2, 0, 0, 2, 0, 0, 2, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 3, 3, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8], [4, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 2, 2, 0, 0], [2, 2, 2, 2, 0], [0, 0, 2, 2, 0], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 0, 1, 0], [1, 1, 1, 0, 1], [0, 0, 1, 1, 1], [1, 1, 1, 0, 0]] -> [[3, 3, 3, 3, 0], [3, 3, 3, 3, 3], [0, 0, 3, 3, 3], [3, 3, 3, 3, 0]]
Example 2:
[[2, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 2, 2], [2, 2, 2, 2, 2], [4, 4, 4, 4, 4], [0, 1, 1, 0, 0], [1, 1, 0, 1, 0], [1, 1, 0, 0, 0], [0, 0, 1, 1, 1]] -> [[3, 3, 3, 3, 3], [3, 3, 0, 3, 0], [3, 3, 0, 3, 3], [3, 3, 3, 3, 3]]
Example 3:
[[0, 0, 0, 0, 0], [0, 2, 2, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [1, 1, 0, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [0, 1, 0, 1, 1]] -> [[3, 3, 0, 0, 3], [3, 3, 3, 3, 3], [3, 3, 3, 0, 3], [3, 3, 3, 3, 3]]
Example 4:
[[0, 2, 0, 0, 2], [0, 2, 2, 0, 2], [0, 0, 0, 2, 2], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 1, 1, 1, 0]] -> [[3, 3, 3, 0, 3], [3, 3, 3, 3, 3], [0, 0, 0, 3, 3], [0, 3, 3, 3, 0]]
# Test Problem:
[[0, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 1]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 2, 2, 0, 0], [2, 2, 2, 2, 0], [0, 0, 2, 2, 0], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 0, 1, 0], [1, 1, 1, 0, 1], [0, 0, 1, 1, 1], [1, 1, 1, 0, 0]] -> [[3, 3, 3, 3, 0], [3, 3, 3, 3, 3], [0, 0, 3, 3, 3], [3, 3, 3, 3, 0]]\\n\\nExample 2:\\n[[2, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 2, 2], [2, 2, 2, 2, 2], [4, 4, 4, 4, 4], [0, 1, 1, 0, 0], [1, 1, 0, 1, 0], [1, 1, 0, 0, 0], [0, 0, 1, 1, 1]] -> [[3, 3, 3, 3, 3], [3, 3, 0, 3, 0], [3, 3, 0, 3, 3], [3, 3, 3, 3, 3]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0], [0, 2, 2, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [1, 1, 0, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [0, 1, 0, 1, 1]] -> [[3, 3, 0, 0, 3], [3, 3, 3, 3, 3], [3, 3, 3, 0, 3], [3, 3, 3, 3, 3]]\\n\\nExample 4:\\n[[0, 2, 0, 0, 2], [0, 2, 2, 0, 2], [0, 0, 0, 2, 2], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 1, 1, 1, 0]] -> [[3, 3, 3, 0, 3], [3, 3, 3, 3, 3], [0, 0, 0, 3, 3], [0, 3, 3, 3, 0]]\\n\\n# Test Problem:\\n[[0, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 1]] -> \", \"answer\": \"[[0, 3, 3, 3, 3], [0, 0, 0, 3, 3], [3, 3, 0, 3, 3], [3, 3, 3, 0, 3]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"270c1880-59ac-425a-8c6a-be0746201c7f\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 2, 2, 0, 0], [2, 2, 2, 2, 0], [0, 0, 2, 2, 0], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 0, 1, 0], [1, 1, 1, 0, 1], [0, 0, 1, 1, 1], [1, 1, 1, 0, 0]] -> [[3, 3, 3, 3, 0], [3, 3, 3, 3, 3], [0, 0, 3, 3, 3], [3, 3, 3, 3, 0]]\\\\n\\\\nExample 2:\\\\n[[2, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 2, 2], [2, 2, 2, 2, 2], [4, 4, 4, 4, 4], [0, 1, 1, 0, 0], [1, 1, 0, 1, 0], [1, 1, 0, 0, 0], [0, 0, 1, 1, 1]] -> [[3, 3, 3, 3, 3], [3, 3, 0, 3, 0], [3, 3, 0, 3, 3], [3, 3, 3, 3, 3]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0], [0, 2, 2, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [1, 1, 0, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [0, 1, 0, 1, 1]] -> [[3, 3, 0, 0, 3], [3, 3, 3, 3, 3], [3, 3, 3, 0, 3], [3, 3, 3, 3, 3]]\\\\n\\\\nExample 4:\\\\n[[0, 2, 0, 0, 2], [0, 2, 2, 0, 2], [0, 0, 0, 2, 2], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 1, 1, 1, 0]] -> [[3, 3, 3, 0, 3], [3, 3, 3, 3, 3], [0, 0, 0, 3, 3], [0, 3, 3, 3, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 1]] -> \\\", \\\"answer\\\": \\\"[[0, 3, 3, 3, 3], [0, 0, 0, 3, 3], [3, 3, 0, 3, 3], [3, 3, 3, 0, 3]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "270c1880-59ac-425a-8c6a-be0746201c7f"}
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[[0, 3, 3, 3, 3], [0, 0, 0, 3, 3], [3, 3, 0, 3, 3], [3, 3, 3, 0, 3]]
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{"id": "270c1880-59ac-425a-8c6a-be0746201c7f", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 2, 2, 0, 0], [2, 2, 2, 2, 0], [0, 0, 2, 2, 0], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 0, 1, 0], [1, 1, 1, 0, 1], [0, 0, 1, 1, 1], [1, 1, 1, 0, 0]] -> [[3, 3, 3, 3, 0], [3, 3, 3, 3, 3], [0, 0, 3, 3, 3], [3, 3, 3, 3, 0]]\n\nExample 2:\n[[2, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 2, 2], [2, 2, 2, 2, 2], [4, 4, 4, 4, 4], [0, 1, 1, 0, 0], [1, 1, 0, 1, 0], [1, 1, 0, 0, 0], [0, 0, 1, 1, 1]] -> [[3, 3, 3, 3, 3], [3, 3, 0, 3, 0], [3, 3, 0, 3, 3], [3, 3, 3, 3, 3]]\n\nExample 3:\n[[0, 0, 0, 0, 0], [0, 2, 2, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [1, 1, 0, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [0, 1, 0, 1, 1]] -> [[3, 3, 0, 0, 3], [3, 3, 3, 3, 3], [3, 3, 3, 0, 3], [3, 3, 3, 3, 3]]\n\nExample 4:\n[[0, 2, 0, 0, 2], [0, 2, 2, 0, 2], [0, 0, 0, 2, 2], [0, 0, 2, 2, 0], [4, 4, 4, 4, 4], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 1, 1, 1, 0]] -> [[3, 3, 3, 0, 3], [3, 3, 3, 3, 3], [0, 0, 0, 3, 3], [0, 3, 3, 3, 0]]\n\n# Test Problem:\n[[0, 2, 2, 2, 2], [0, 0, 0, 2, 0], [0, 2, 0, 0, 0], [2, 2, 2, 0, 2], [4, 4, 4, 4, 4], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 1]] -> ", "answer": "[[0, 3, 3, 3, 3], [0, 0, 0, 3, 3], [3, 3, 0, 3, 3], [3, 3, 3, 0, 3]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[2, 1, 1, 1, 2], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0]] -> [[2, 1, 1, 1, 2], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 4, 4, 4, 4]]
Example 2:
[[0, 0, 0, 1, 2], [0, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 0], [2, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 2], [4, 4, 4, 1, 4], [4, 1, 4, 1, 4], [4, 1, 4, 4, 4], [2, 1, 0, 0, 0]]
Example 3:
[[2, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0]] -> [[2, 4, 4, 4, 4, 0], [1, 1, 1, 1, 4, 0], [0, 0, 4, 4, 4, 0], [0, 0, 4, 1, 1, 1], [0, 0, 4, 4, 4, 2], [0, 0, 0, 0, 0, 0]]
Example 4:
[[0, 0, 0, 0, 0, 2], [0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] -> [[4, 4, 4, 4, 4, 2], [4, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 4], [2, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0]]
Example 5:
[[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [4, 4, 4, 1, 1, 4, 4, 4, 1, 4], [4, 1, 4, 1, 1, 4, 1, 4, 1, 4], [4, 1, 4, 4, 4, 4, 1, 4, 4, 4], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]]
# Test Problem:
[[2, 1, 0, 0, 0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[2, 1, 1, 1, 2], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0]] -> [[2, 1, 1, 1, 2], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 4, 4, 4, 4]]\\n\\nExample 2:\\n[[0, 0, 0, 1, 2], [0, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 0], [2, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 2], [4, 4, 4, 1, 4], [4, 1, 4, 1, 4], [4, 1, 4, 4, 4], [2, 1, 0, 0, 0]]\\n\\nExample 3:\\n[[2, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0]] -> [[2, 4, 4, 4, 4, 0], [1, 1, 1, 1, 4, 0], [0, 0, 4, 4, 4, 0], [0, 0, 4, 1, 1, 1], [0, 0, 4, 4, 4, 2], [0, 0, 0, 0, 0, 0]]\\n\\nExample 4:\\n[[0, 0, 0, 0, 0, 2], [0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] -> [[4, 4, 4, 4, 4, 2], [4, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 4], [2, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0]]\\n\\nExample 5:\\n[[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [4, 4, 4, 1, 1, 4, 4, 4, 1, 4], [4, 1, 4, 1, 1, 4, 1, 4, 1, 4], [4, 1, 4, 4, 4, 4, 1, 4, 4, 4], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]]\\n\\n# Test Problem:\\n[[2, 1, 0, 0, 0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]] -> \", \"answer\": \"[[2, 1, 0, 0, 0, 1, 4, 4, 4, 2], [4, 1, 4, 4, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 4, 4, 1, 4, 4, 4, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ff03fd11-acaa-4115-ba2f-560680d31dff\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[2, 1, 1, 1, 2], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0]] -> [[2, 1, 1, 1, 2], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 4, 4, 4, 4]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 1, 2], [0, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 0], [2, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 2], [4, 4, 4, 1, 4], [4, 1, 4, 1, 4], [4, 1, 4, 4, 4], [2, 1, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[2, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0]] -> [[2, 4, 4, 4, 4, 0], [1, 1, 1, 1, 4, 0], [0, 0, 4, 4, 4, 0], [0, 0, 4, 1, 1, 1], [0, 0, 4, 4, 4, 2], [0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 0, 0, 0, 2], [0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] -> [[4, 4, 4, 4, 4, 2], [4, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 4], [2, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 5:\\\\n[[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [4, 4, 4, 1, 1, 4, 4, 4, 1, 4], [4, 1, 4, 1, 1, 4, 1, 4, 1, 4], [4, 1, 4, 4, 4, 4, 1, 4, 4, 4], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[2, 1, 0, 0, 0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[2, 1, 0, 0, 0, 1, 4, 4, 4, 2], [4, 1, 4, 4, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 4, 4, 1, 4, 4, 4, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "ff03fd11-acaa-4115-ba2f-560680d31dff"}
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[[2, 1, 0, 0, 0, 1, 4, 4, 4, 2], [4, 1, 4, 4, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 4, 4, 1, 4, 4, 4, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]]
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{"id": "ff03fd11-acaa-4115-ba2f-560680d31dff", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[2, 1, 1, 1, 2], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0]] -> [[2, 1, 1, 1, 2], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 1, 0, 1, 4], [4, 4, 4, 4, 4]]\n\nExample 2:\n[[0, 0, 0, 1, 2], [0, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 0], [2, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 2], [4, 4, 4, 1, 4], [4, 1, 4, 1, 4], [4, 1, 4, 4, 4], [2, 1, 0, 0, 0]]\n\nExample 3:\n[[2, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0]] -> [[2, 4, 4, 4, 4, 0], [1, 1, 1, 1, 4, 0], [0, 0, 4, 4, 4, 0], [0, 0, 4, 1, 1, 1], [0, 0, 4, 4, 4, 2], [0, 0, 0, 0, 0, 0]]\n\nExample 4:\n[[0, 0, 0, 0, 0, 2], [0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] -> [[4, 4, 4, 4, 4, 2], [4, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 4], [2, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0]]\n\nExample 5:\n[[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]] -> [[0, 0, 0, 1, 1, 0, 0, 0, 1, 2], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [0, 0, 0, 1, 1, 0, 0, 0, 1, 4], [4, 4, 4, 1, 1, 4, 4, 4, 1, 4], [4, 1, 4, 1, 1, 4, 1, 4, 1, 4], [4, 1, 4, 4, 4, 4, 1, 4, 4, 4], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 1, 0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, 0, 0, 1, 0, 0, 0]]\n\n# Test Problem:\n[[2, 1, 0, 0, 0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]] -> ", "answer": "[[2, 1, 0, 0, 0, 1, 4, 4, 4, 2], [4, 1, 4, 4, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 1, 4, 1, 4, 1, 4, 1, 0, 0], [4, 4, 4, 1, 4, 4, 4, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]] -> [[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 8, 8, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 8, 8, 8, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]]
Example 2:
[[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]] -> [[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 8, 8, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 8, 8, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]]
Example 3:
[[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]] -> [[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 8, 8, 8, 8, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]]
# Test Problem:
[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]] -> [[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 8, 8, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 8, 8, 8, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]]\\n\\nExample 2:\\n[[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]] -> [[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 8, 8, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 8, 8, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]]\\n\\nExample 3:\\n[[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]] -> [[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 8, 8, 8, 8, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]]\\n\\n# Test Problem:\\n[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]] -> \", \"answer\": \"[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 8, 8, 8, 8, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 8, 8, 8, 8, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 8, 8, 8, 8, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"9273a933-d366-4038-9e2b-9c7d294a2b01\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]] -> [[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 8, 8, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 8, 8, 8, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]] -> [[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 8, 8, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 8, 8, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]] -> [[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 8, 8, 8, 8, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]]\\\\n\\\\n# Test Problem:\\\\n[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]] -> \\\", \\\"answer\\\": \\\"[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 8, 8, 8, 8, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 8, 8, 8, 8, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 8, 8, 8, 8, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "9273a933-d366-4038-9e2b-9c7d294a2b01"}
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[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 8, 8, 8, 8, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 8, 8, 8, 8, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 8, 8, 8, 8, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]]
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{"id": "9273a933-d366-4038-9e2b-9c7d294a2b01", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]] -> [[4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 5, 0, 0, 0, 0, 4, 4, 4, 4], [0, 4, 4, 4, 4, 5, 4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 0, 4, 0], [0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 0, 4], [0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 0, 5, 4, 4], [4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 8, 8, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 8, 8, 8, 0, 4, 4, 4, 4, 5, 4, 4, 0, 5, 4], [4, 4, 4, 0, 0, 8, 8, 8, 0, 4, 5, 4, 4, 4, 0, 4, 0, 0, 5], [0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 5, 4, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 5, 5, 4, 0, 4, 0, 4, 4, 5], [4, 4, 4, 4, 4, 5, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 5, 4, 4], [5, 4, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 4, 5, 4, 5, 4, 5, 4, 0, 4, 4, 0, 4, 4, 5, 0], [4, 0, 0, 4, 4, 0, 0, 0, 5, 4, 4, 0, 0, 4, 4, 5, 4, 4, 0]]\n\nExample 2:\n[[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]] -> [[0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2], [2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0], [2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2], [2, 0, 2, 2, 0, 0, 8, 8, 0, 2, 0, 0, 0, 2, 2], [0, 2, 0, 2, 2, 0, 8, 8, 0, 0, 2, 2, 0, 2, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2], [0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2], [0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2], [2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0], [2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0]]\n\nExample 3:\n[[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]] -> [[0, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 3, 3, 0, 3, 3], [0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 0], [3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0, 3, 3, 3], [3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 3, 3], [0, 0, 3, 3, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 0], [3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 0], [3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 3, 3], [0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 8, 8, 8, 8, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 0, 8, 8, 8, 8, 0, 3, 3, 3], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0], [0, 0, 0, 3, 3, 0, 0, 3, 3, 0, 3, 3, 0, 0, 3, 3]]\n\n# Test Problem:\n[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]] -> ", "answer": "[[7, 7, 0, 0, 0, 7, 7, 7, 0, 0, 0, 7, 0, 0, 7, 7, 0, 7, 0, 7, 7], [7, 0, 7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0], [7, 7, 7, 7, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0], [7, 0, 0, 7, 0, 7, 7, 7, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0], [7, 7, 7, 7, 0, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 0, 0, 7, 7, 7, 7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 7, 7], [7, 0, 0, 7, 0, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7], [7, 7, 7, 0, 7, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 7], [7, 7, 7, 0, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7], [0, 7, 7, 0, 7, 0, 7, 0, 0, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0], [7, 7, 0, 0, 0, 7, 7, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 7], [0, 7, 7, 0, 0, 7, 0, 0, 7, 7, 0, 8, 8, 8, 8, 0, 7, 7, 0, 0, 7], [7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 8, 8, 8, 8, 0, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 7, 0, 7, 0, 7, 0, 8, 8, 8, 8, 0, 7, 7, 7, 0, 0], [7, 7, 7, 7, 7, 7, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7, 0, 0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 7, 0, 0, 7], [7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 0, 7, 0, 0, 0, 0, 0, 0], [0, 7, 7, 0, 0, 7, 7, 0, 7, 0, 0, 0, 0, 7, 0, 7, 7, 7, 7, 7, 7], [0, 7, 7, 0, 7, 7, 7, 0, 0, 7, 7, 0, 0, 7, 7, 0, 7, 7, 0, 7, 7]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[8, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 0, 0, 5, 5], [0, 0, 0, 0, 4, 0, 0, 5, 0], [8, 8, 0, 0, 4, 0, 5, 5, 5], [8, 0, 0, 8, 4, 0, 0, 0, 5]] -> [[2, 0, 2, 0], [2, 2, 2, 0], [0, 0, 2, 0], [2, 0, 2, 2], [2, 0, 0, 0]]
Example 2:
[[0, 8, 0, 0, 4, 5, 0, 5, 0], [0, 8, 0, 8, 4, 5, 0, 5, 5], [0, 8, 0, 8, 4, 0, 0, 0, 5], [0, 8, 0, 8, 4, 0, 5, 0, 5], [0, 0, 0, 8, 4, 0, 0, 5, 0]] -> [[2, 2, 2, 0], [2, 2, 2, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 2, 2]]
Example 3:
[[0, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 5, 0, 0, 5], [8, 8, 0, 0, 4, 5, 0, 0, 5], [0, 8, 0, 8, 4, 0, 0, 5, 0], [0, 0, 8, 0, 4, 0, 5, 0, 5]] -> [[0, 0, 2, 0], [0, 2, 0, 0], [0, 2, 0, 2], [0, 2, 2, 2], [0, 2, 2, 2]]
Example 4:
[[0, 0, 0, 8, 4, 0, 5, 5, 5], [0, 8, 8, 8, 4, 0, 5, 0, 0], [8, 0, 0, 0, 4, 0, 5, 0, 5], [8, 0, 8, 8, 4, 5, 5, 5, 0], [0, 8, 8, 0, 4, 5, 0, 0, 5]] -> [[0, 2, 2, 0], [0, 0, 2, 2], [2, 2, 0, 2], [0, 2, 0, 2], [2, 2, 2, 2]]
# Test Problem:
[[0, 8, 0, 0, 4, 5, 0, 0, 0], [0, 8, 0, 8, 4, 5, 5, 0, 5], [8, 8, 0, 8, 4, 0, 0, 5, 5], [8, 8, 8, 8, 4, 5, 0, 5, 5], [0, 0, 8, 8, 4, 5, 0, 5, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[8, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 0, 0, 5, 5], [0, 0, 0, 0, 4, 0, 0, 5, 0], [8, 8, 0, 0, 4, 0, 5, 5, 5], [8, 0, 0, 8, 4, 0, 0, 0, 5]] -> [[2, 0, 2, 0], [2, 2, 2, 0], [0, 0, 2, 0], [2, 0, 2, 2], [2, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 8, 0, 0, 4, 5, 0, 5, 0], [0, 8, 0, 8, 4, 5, 0, 5, 5], [0, 8, 0, 8, 4, 0, 0, 0, 5], [0, 8, 0, 8, 4, 0, 5, 0, 5], [0, 0, 0, 8, 4, 0, 0, 5, 0]] -> [[2, 2, 2, 0], [2, 2, 2, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 2, 2]]\\n\\nExample 3:\\n[[0, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 5, 0, 0, 5], [8, 8, 0, 0, 4, 5, 0, 0, 5], [0, 8, 0, 8, 4, 0, 0, 5, 0], [0, 0, 8, 0, 4, 0, 5, 0, 5]] -> [[0, 0, 2, 0], [0, 2, 0, 0], [0, 2, 0, 2], [0, 2, 2, 2], [0, 2, 2, 2]]\\n\\nExample 4:\\n[[0, 0, 0, 8, 4, 0, 5, 5, 5], [0, 8, 8, 8, 4, 0, 5, 0, 0], [8, 0, 0, 0, 4, 0, 5, 0, 5], [8, 0, 8, 8, 4, 5, 5, 5, 0], [0, 8, 8, 0, 4, 5, 0, 0, 5]] -> [[0, 2, 2, 0], [0, 0, 2, 2], [2, 2, 0, 2], [0, 2, 0, 2], [2, 2, 2, 2]]\\n\\n# Test Problem:\\n[[0, 8, 0, 0, 4, 5, 0, 0, 0], [0, 8, 0, 8, 4, 5, 5, 0, 5], [8, 8, 0, 8, 4, 0, 0, 5, 5], [8, 8, 8, 8, 4, 5, 0, 5, 5], [0, 0, 8, 8, 4, 5, 0, 5, 0]] -> \", \"answer\": \"[[2, 2, 0, 0], [2, 0, 0, 0], [2, 2, 2, 0], [0, 2, 0, 0], [2, 0, 0, 2]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"66305edd-be95-45bc-aef5-df1983895153\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[8, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 0, 0, 5, 5], [0, 0, 0, 0, 4, 0, 0, 5, 0], [8, 8, 0, 0, 4, 0, 5, 5, 5], [8, 0, 0, 8, 4, 0, 0, 0, 5]] -> [[2, 0, 2, 0], [2, 2, 2, 0], [0, 0, 2, 0], [2, 0, 2, 2], [2, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 8, 0, 0, 4, 5, 0, 5, 0], [0, 8, 0, 8, 4, 5, 0, 5, 5], [0, 8, 0, 8, 4, 0, 0, 0, 5], [0, 8, 0, 8, 4, 0, 5, 0, 5], [0, 0, 0, 8, 4, 0, 0, 5, 0]] -> [[2, 2, 2, 0], [2, 2, 2, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 2, 2]]\\\\n\\\\nExample 3:\\\\n[[0, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 5, 0, 0, 5], [8, 8, 0, 0, 4, 5, 0, 0, 5], [0, 8, 0, 8, 4, 0, 0, 5, 0], [0, 0, 8, 0, 4, 0, 5, 0, 5]] -> [[0, 0, 2, 0], [0, 2, 0, 0], [0, 2, 0, 2], [0, 2, 2, 2], [0, 2, 2, 2]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 0, 8, 4, 0, 5, 5, 5], [0, 8, 8, 8, 4, 0, 5, 0, 0], [8, 0, 0, 0, 4, 0, 5, 0, 5], [8, 0, 8, 8, 4, 5, 5, 5, 0], [0, 8, 8, 0, 4, 5, 0, 0, 5]] -> [[0, 2, 2, 0], [0, 0, 2, 2], [2, 2, 0, 2], [0, 2, 0, 2], [2, 2, 2, 2]]\\\\n\\\\n# Test Problem:\\\\n[[0, 8, 0, 0, 4, 5, 0, 0, 0], [0, 8, 0, 8, 4, 5, 5, 0, 5], [8, 8, 0, 8, 4, 0, 0, 5, 5], [8, 8, 8, 8, 4, 5, 0, 5, 5], [0, 0, 8, 8, 4, 5, 0, 5, 0]] -> \\\", \\\"answer\\\": \\\"[[2, 2, 0, 0], [2, 0, 0, 0], [2, 2, 2, 0], [0, 2, 0, 0], [2, 0, 0, 2]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "66305edd-be95-45bc-aef5-df1983895153"}
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[[2, 2, 0, 0], [2, 0, 0, 0], [2, 2, 2, 0], [0, 2, 0, 0], [2, 0, 0, 2]]
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{"id": "66305edd-be95-45bc-aef5-df1983895153", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[8, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 0, 0, 5, 5], [0, 0, 0, 0, 4, 0, 0, 5, 0], [8, 8, 0, 0, 4, 0, 5, 5, 5], [8, 0, 0, 8, 4, 0, 0, 0, 5]] -> [[2, 0, 2, 0], [2, 2, 2, 0], [0, 0, 2, 0], [2, 0, 2, 2], [2, 0, 0, 0]]\n\nExample 2:\n[[0, 8, 0, 0, 4, 5, 0, 5, 0], [0, 8, 0, 8, 4, 5, 0, 5, 5], [0, 8, 0, 8, 4, 0, 0, 0, 5], [0, 8, 0, 8, 4, 0, 5, 0, 5], [0, 0, 0, 8, 4, 0, 0, 5, 0]] -> [[2, 2, 2, 0], [2, 2, 2, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 2, 2]]\n\nExample 3:\n[[0, 8, 0, 0, 4, 0, 5, 5, 0], [8, 8, 0, 8, 4, 5, 0, 0, 5], [8, 8, 0, 0, 4, 5, 0, 0, 5], [0, 8, 0, 8, 4, 0, 0, 5, 0], [0, 0, 8, 0, 4, 0, 5, 0, 5]] -> [[0, 0, 2, 0], [0, 2, 0, 0], [0, 2, 0, 2], [0, 2, 2, 2], [0, 2, 2, 2]]\n\nExample 4:\n[[0, 0, 0, 8, 4, 0, 5, 5, 5], [0, 8, 8, 8, 4, 0, 5, 0, 0], [8, 0, 0, 0, 4, 0, 5, 0, 5], [8, 0, 8, 8, 4, 5, 5, 5, 0], [0, 8, 8, 0, 4, 5, 0, 0, 5]] -> [[0, 2, 2, 0], [0, 0, 2, 2], [2, 2, 0, 2], [0, 2, 0, 2], [2, 2, 2, 2]]\n\n# Test Problem:\n[[0, 8, 0, 0, 4, 5, 0, 0, 0], [0, 8, 0, 8, 4, 5, 5, 0, 5], [8, 8, 0, 8, 4, 0, 0, 5, 5], [8, 8, 8, 8, 4, 5, 0, 5, 5], [0, 0, 8, 8, 4, 5, 0, 5, 0]] -> ", "answer": "[[2, 2, 0, 0], [2, 0, 0, 0], [2, 2, 2, 0], [0, 2, 0, 0], [2, 0, 0, 2]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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]]
# Test Problem:
[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 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, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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\\n# Test Problem:\\n[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 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, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 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, 2, 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, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"02c14a10-b34c-404b-9ab5-282788cf2f78\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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\\\\n# Test Problem:\\\\n[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 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, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 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, 2, 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, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "02c14a10-b34c-404b-9ab5-282788cf2f78"}
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[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 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, 2, 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, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "02c14a10-b34c-404b-9ab5-282788cf2f78", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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\n# Test Problem:\n[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 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, 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, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 2, 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, 2, 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, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[7, 8, 4, 8, 8, 3, 5, 6, 2, 3, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 7, 9, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 4, 5, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 5, 4, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 6, 5, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 1, 8, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [3, 3, 6, 5, 2, 7, 4, 8, 0, 0, 2, 6, 5, 4, 5, 1, 8, 7, 9, 8], [2, 6, 3, 3, 5, 5, 7, 8, 0, 0, 5, 9, 9, 5, 4, 9, 9, 4, 6, 1], [2, 3, 4, 5, 9, 1, 1, 7, 3, 8, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 8, 8, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 3, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 9, 9, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 7, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 9, 9, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 4, 3, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 4, 5, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 1, 9, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 7, 5, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 8, 4, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]] -> [[7, 8, 4, 8, 8, 3, 5, 6, 2, 0, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 0, 0, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 0, 0, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 0, 0, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 0, 0, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 0, 0, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0], [2, 3, 4, 5, 9, 1, 1, 7, 0, 0, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 0, 0, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 0, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 0, 0, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 0, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 0, 0, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 0, 0, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 0, 0, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 0, 0, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 0, 0, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 0, 0, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]]
Example 2:
[[5, 2, 5, 2, 5, 4, 3, 8, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 5, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 8, 7, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 4, 4, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 7, 5, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 9, 1, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 4, 8, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 4, 7, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 8, 3, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 8, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 7, 5, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 4, 3, 1, 4, 8, 0, 0, 9, 6, 3, 2, 4, 4, 8, 7, 2, 9, 4, 2], [3, 5, 7, 8, 2, 4, 0, 0, 1, 6, 4, 7, 4, 7, 2, 3, 9, 4, 5, 2], [8, 1, 4, 3, 9, 6, 9, 9, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 1, 4, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 6, 1, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 6, 3, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 5, 5, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 6, 5, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 7, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]] -> [[5, 2, 5, 2, 5, 4, 0, 0, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 0, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 0, 0, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 0, 0, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 0, 0, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 0, 0, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 0, 0, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 0, 0, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 0, 0, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 0, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 0, 0, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [8, 1, 4, 3, 9, 6, 0, 0, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 0, 0, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 0, 0, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 0, 0, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 0, 0, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 0, 0, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 0, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]]
Example 3:
[[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 3, 1, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 7, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 4, 5, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 6, 4, 8, 7, 6], [3, 1, 3, 1, 7, 6, 4, 7, 5, 1, 8, 2, 6, 2, 0, 0, 5, 2, 5, 5], [7, 8, 7, 3, 4, 2, 5, 6, 2, 2, 3, 1, 5, 6, 0, 0, 5, 3, 8, 6], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 5, 7, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 4, 3, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 1, 3, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 9, 1, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 6, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 4, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 1, 3, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 6, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 5, 8, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 7, 8, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 1, 6, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 1, 7, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 7, 3, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 1, 8, 4, 6, 7, 3]] -> [[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 0, 0, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 0, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 0, 0, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 0, 4, 8, 7, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 0, 0, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 0, 0, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 0, 0, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 0, 0, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 0, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 0, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 0, 0, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 0, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 0, 0, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 0, 0, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 0, 0, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 0, 0, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 0, 0, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 0, 0, 4, 6, 7, 3]]
# Test Problem:
[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 4, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 4, 8, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 8, 1, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 1, 4, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 3, 5, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 9, 5, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 5, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 5, 7, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 8, 3, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 1, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 7, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 6, 7, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 4, 9, 7, 7, 1, 5, 9, 3], [3, 7, 7, 5, 9, 8, 7, 4, 2, 2, 9, 5, 0, 0, 8, 6, 7, 6, 6, 7], [6, 9, 5, 6, 3, 7, 5, 7, 9, 8, 9, 5, 0, 0, 4, 2, 3, 3, 2, 6], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 9, 5, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 5, 3, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 8, 6, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 8, 6, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 7, 5, 4, 3, 6, 3, 9, 5]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[7, 8, 4, 8, 8, 3, 5, 6, 2, 3, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 7, 9, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 4, 5, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 5, 4, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 6, 5, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 1, 8, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [3, 3, 6, 5, 2, 7, 4, 8, 0, 0, 2, 6, 5, 4, 5, 1, 8, 7, 9, 8], [2, 6, 3, 3, 5, 5, 7, 8, 0, 0, 5, 9, 9, 5, 4, 9, 9, 4, 6, 1], [2, 3, 4, 5, 9, 1, 1, 7, 3, 8, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 8, 8, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 3, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 9, 9, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 7, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 9, 9, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 4, 3, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 4, 5, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 1, 9, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 7, 5, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 8, 4, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]] -> [[7, 8, 4, 8, 8, 3, 5, 6, 2, 0, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 0, 0, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 0, 0, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 0, 0, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 0, 0, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 0, 0, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0], [2, 3, 4, 5, 9, 1, 1, 7, 0, 0, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 0, 0, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 0, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 0, 0, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 0, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 0, 0, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 0, 0, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 0, 0, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 0, 0, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 0, 0, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 0, 0, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]]\\n\\nExample 2:\\n[[5, 2, 5, 2, 5, 4, 3, 8, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 5, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 8, 7, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 4, 4, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 7, 5, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 9, 1, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 4, 8, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 4, 7, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 8, 3, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 8, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 7, 5, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 4, 3, 1, 4, 8, 0, 0, 9, 6, 3, 2, 4, 4, 8, 7, 2, 9, 4, 2], [3, 5, 7, 8, 2, 4, 0, 0, 1, 6, 4, 7, 4, 7, 2, 3, 9, 4, 5, 2], [8, 1, 4, 3, 9, 6, 9, 9, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 1, 4, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 6, 1, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 6, 3, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 5, 5, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 6, 5, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 7, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]] -> [[5, 2, 5, 2, 5, 4, 0, 0, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 0, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 0, 0, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 0, 0, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 0, 0, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 0, 0, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 0, 0, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 0, 0, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 0, 0, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 0, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 0, 0, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [8, 1, 4, 3, 9, 6, 0, 0, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 0, 0, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 0, 0, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 0, 0, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 0, 0, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 0, 0, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 0, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]]\\n\\nExample 3:\\n[[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 3, 1, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 7, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 4, 5, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 6, 4, 8, 7, 6], [3, 1, 3, 1, 7, 6, 4, 7, 5, 1, 8, 2, 6, 2, 0, 0, 5, 2, 5, 5], [7, 8, 7, 3, 4, 2, 5, 6, 2, 2, 3, 1, 5, 6, 0, 0, 5, 3, 8, 6], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 5, 7, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 4, 3, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 1, 3, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 9, 1, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 6, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 4, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 1, 3, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 6, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 5, 8, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 7, 8, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 1, 6, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 1, 7, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 7, 3, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 1, 8, 4, 6, 7, 3]] -> [[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 0, 0, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 0, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 0, 0, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 0, 4, 8, 7, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 0, 0, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 0, 0, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 0, 0, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 0, 0, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 0, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 0, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 0, 0, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 0, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 0, 0, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 0, 0, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 0, 0, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 0, 0, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 0, 0, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 0, 0, 4, 6, 7, 3]]\\n\\n# Test Problem:\\n[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 4, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 4, 8, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 8, 1, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 1, 4, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 3, 5, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 9, 5, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 5, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 5, 7, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 8, 3, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 1, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 7, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 6, 7, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 4, 9, 7, 7, 1, 5, 9, 3], [3, 7, 7, 5, 9, 8, 7, 4, 2, 2, 9, 5, 0, 0, 8, 6, 7, 6, 6, 7], [6, 9, 5, 6, 3, 7, 5, 7, 9, 8, 9, 5, 0, 0, 4, 2, 3, 3, 2, 6], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 9, 5, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 5, 3, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 8, 6, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 8, 6, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 7, 5, 4, 3, 6, 3, 9, 5]] -> \", \"answer\": \"[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 0, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 0, 0, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 0, 0, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 0, 0, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 0, 0, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 0, 0, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 0, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 0, 0, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 0, 0, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 0, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 0, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 0, 0, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 0, 0, 7, 7, 1, 5, 9, 3], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 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, 2, 0, 0, 2, 0], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 0, 0, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 0, 0, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 0, 0, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 0, 0, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 0, 0, 4, 3, 6, 3, 9, 5]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"71508105-2f67-4651-acf6-9333bf2da7ab\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[7, 8, 4, 8, 8, 3, 5, 6, 2, 3, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 7, 9, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 4, 5, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 5, 4, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 6, 5, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 1, 8, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [3, 3, 6, 5, 2, 7, 4, 8, 0, 0, 2, 6, 5, 4, 5, 1, 8, 7, 9, 8], [2, 6, 3, 3, 5, 5, 7, 8, 0, 0, 5, 9, 9, 5, 4, 9, 9, 4, 6, 1], [2, 3, 4, 5, 9, 1, 1, 7, 3, 8, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 8, 8, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 3, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 9, 9, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 7, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 9, 9, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 4, 3, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 4, 5, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 1, 9, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 7, 5, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 8, 4, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]] -> [[7, 8, 4, 8, 8, 3, 5, 6, 2, 0, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 0, 0, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 0, 0, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 0, 0, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 0, 0, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 0, 0, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0], [2, 3, 4, 5, 9, 1, 1, 7, 0, 0, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 0, 0, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 0, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 0, 0, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 0, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 0, 0, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 0, 0, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 0, 0, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 0, 0, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 0, 0, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 0, 0, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]]\\\\n\\\\nExample 2:\\\\n[[5, 2, 5, 2, 5, 4, 3, 8, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 5, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 8, 7, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 4, 4, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 7, 5, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 9, 1, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 4, 8, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 4, 7, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 8, 3, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 8, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 7, 5, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 4, 3, 1, 4, 8, 0, 0, 9, 6, 3, 2, 4, 4, 8, 7, 2, 9, 4, 2], [3, 5, 7, 8, 2, 4, 0, 0, 1, 6, 4, 7, 4, 7, 2, 3, 9, 4, 5, 2], [8, 1, 4, 3, 9, 6, 9, 9, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 1, 4, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 6, 1, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 6, 3, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 5, 5, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 6, 5, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 7, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]] -> [[5, 2, 5, 2, 5, 4, 0, 0, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 0, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 0, 0, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 0, 0, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 0, 0, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 0, 0, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 0, 0, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 0, 0, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 0, 0, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 0, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 0, 0, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [8, 1, 4, 3, 9, 6, 0, 0, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 0, 0, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 0, 0, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 0, 0, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 0, 0, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 0, 0, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 0, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]]\\\\n\\\\nExample 3:\\\\n[[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 3, 1, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 7, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 4, 5, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 6, 4, 8, 7, 6], [3, 1, 3, 1, 7, 6, 4, 7, 5, 1, 8, 2, 6, 2, 0, 0, 5, 2, 5, 5], [7, 8, 7, 3, 4, 2, 5, 6, 2, 2, 3, 1, 5, 6, 0, 0, 5, 3, 8, 6], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 5, 7, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 4, 3, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 1, 3, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 9, 1, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 6, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 4, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 1, 3, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 6, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 5, 8, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 7, 8, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 1, 6, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 1, 7, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 7, 3, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 1, 8, 4, 6, 7, 3]] -> [[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 0, 0, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 0, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 0, 0, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 0, 4, 8, 7, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 0, 0, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 0, 0, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 0, 0, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 0, 0, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 0, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 0, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 0, 0, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 0, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 0, 0, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 0, 0, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 0, 0, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 0, 0, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 0, 0, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 0, 0, 4, 6, 7, 3]]\\\\n\\\\n# Test Problem:\\\\n[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 4, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 4, 8, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 8, 1, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 1, 4, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 3, 5, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 9, 5, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 5, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 5, 7, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 8, 3, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 1, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 7, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 6, 7, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 4, 9, 7, 7, 1, 5, 9, 3], [3, 7, 7, 5, 9, 8, 7, 4, 2, 2, 9, 5, 0, 0, 8, 6, 7, 6, 6, 7], [6, 9, 5, 6, 3, 7, 5, 7, 9, 8, 9, 5, 0, 0, 4, 2, 3, 3, 2, 6], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 9, 5, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 5, 3, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 8, 6, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 8, 6, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 7, 5, 4, 3, 6, 3, 9, 5]] -> \\\", \\\"answer\\\": \\\"[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 0, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 0, 0, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 0, 0, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 0, 0, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 0, 0, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 0, 0, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 0, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 0, 0, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 0, 0, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 0, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 0, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 0, 0, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 0, 0, 7, 7, 1, 5, 9, 3], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 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, 2, 0, 0, 2, 0], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 0, 0, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 0, 0, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 0, 0, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 0, 0, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 0, 0, 4, 3, 6, 3, 9, 5]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "71508105-2f67-4651-acf6-9333bf2da7ab"}
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[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 0, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 0, 0, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 0, 0, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 0, 0, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 0, 0, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 0, 0, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 0, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 0, 0, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 0, 0, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 0, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 0, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 0, 0, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 0, 0, 7, 7, 1, 5, 9, 3], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 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, 2, 0, 0, 2, 0], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 0, 0, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 0, 0, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 0, 0, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 0, 0, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 0, 0, 4, 3, 6, 3, 9, 5]]
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{"id": "71508105-2f67-4651-acf6-9333bf2da7ab", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[7, 8, 4, 8, 8, 3, 5, 6, 2, 3, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 7, 9, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 4, 5, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 5, 4, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 6, 5, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 1, 8, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [3, 3, 6, 5, 2, 7, 4, 8, 0, 0, 2, 6, 5, 4, 5, 1, 8, 7, 9, 8], [2, 6, 3, 3, 5, 5, 7, 8, 0, 0, 5, 9, 9, 5, 4, 9, 9, 4, 6, 1], [2, 3, 4, 5, 9, 1, 1, 7, 3, 8, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 8, 8, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 3, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 9, 9, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 7, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 9, 9, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 4, 3, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 4, 5, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 1, 9, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 7, 5, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 8, 4, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]] -> [[7, 8, 4, 8, 8, 3, 5, 6, 2, 0, 7, 5, 6, 9, 7, 7, 9, 6, 3, 1], [5, 5, 8, 4, 5, 8, 3, 1, 0, 0, 2, 2, 9, 5, 9, 3, 9, 6, 4, 9], [1, 6, 6, 6, 5, 7, 2, 4, 0, 0, 1, 1, 5, 3, 5, 5, 9, 7, 6, 6], [6, 3, 8, 6, 5, 8, 4, 4, 0, 0, 3, 5, 8, 2, 1, 5, 6, 2, 1, 7], [3, 5, 4, 1, 5, 9, 3, 4, 0, 0, 5, 2, 4, 8, 2, 3, 9, 7, 1, 3], [2, 8, 9, 4, 7, 9, 8, 8, 0, 0, 1, 3, 7, 4, 7, 1, 2, 6, 5, 6], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0], [2, 3, 4, 5, 9, 1, 1, 7, 0, 0, 7, 3, 3, 9, 6, 8, 7, 4, 3, 3], [9, 4, 2, 7, 2, 9, 5, 7, 0, 0, 3, 1, 2, 4, 8, 6, 8, 3, 9, 6], [1, 1, 9, 7, 3, 6, 4, 3, 0, 2, 5, 3, 9, 5, 1, 1, 9, 7, 5, 3], [7, 8, 8, 3, 6, 9, 7, 6, 0, 0, 3, 4, 1, 7, 6, 3, 6, 2, 1, 4], [3, 5, 7, 4, 3, 3, 4, 5, 0, 2, 9, 2, 5, 3, 4, 5, 6, 9, 9, 6], [4, 2, 5, 5, 7, 1, 4, 7, 0, 0, 9, 5, 2, 3, 2, 8, 5, 9, 7, 7], [8, 5, 7, 5, 8, 1, 2, 4, 0, 0, 1, 9, 9, 9, 9, 8, 1, 5, 1, 7], [5, 4, 5, 1, 8, 2, 6, 4, 0, 0, 2, 5, 8, 8, 8, 2, 4, 6, 5, 7], [4, 5, 7, 7, 9, 5, 5, 7, 2, 2, 2, 4, 3, 4, 7, 3, 8, 2, 8, 1], [9, 5, 9, 6, 8, 1, 6, 2, 0, 0, 4, 8, 8, 7, 5, 1, 3, 1, 6, 4], [7, 7, 1, 6, 6, 7, 3, 4, 0, 0, 8, 4, 8, 4, 4, 3, 5, 6, 4, 2], [4, 3, 7, 8, 3, 4, 5, 5, 0, 0, 7, 9, 4, 9, 4, 9, 3, 9, 8, 7]]\n\nExample 2:\n[[5, 2, 5, 2, 5, 4, 3, 8, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 5, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 8, 7, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 4, 4, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 7, 5, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 9, 1, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 4, 8, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 4, 7, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 8, 3, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 8, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 7, 5, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 4, 3, 1, 4, 8, 0, 0, 9, 6, 3, 2, 4, 4, 8, 7, 2, 9, 4, 2], [3, 5, 7, 8, 2, 4, 0, 0, 1, 6, 4, 7, 4, 7, 2, 3, 9, 4, 5, 2], [8, 1, 4, 3, 9, 6, 9, 9, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 1, 4, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 6, 1, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 6, 3, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 5, 5, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 6, 5, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 7, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]] -> [[5, 2, 5, 2, 5, 4, 0, 0, 2, 7, 3, 7, 5, 6, 2, 1, 9, 3, 2, 1], [1, 2, 3, 6, 5, 2, 2, 0, 8, 9, 8, 5, 8, 7, 9, 2, 6, 5, 5, 5], [3, 1, 9, 7, 9, 8, 0, 0, 1, 9, 7, 3, 9, 7, 5, 9, 8, 4, 9, 8], [5, 7, 7, 8, 3, 4, 0, 0, 4, 6, 2, 9, 4, 3, 6, 8, 4, 6, 7, 1], [6, 3, 8, 3, 5, 9, 0, 0, 4, 6, 1, 9, 3, 9, 7, 7, 6, 7, 8, 1], [6, 2, 4, 9, 8, 3, 0, 0, 4, 8, 9, 9, 6, 5, 9, 1, 9, 7, 5, 7], [6, 2, 8, 3, 4, 6, 0, 0, 9, 3, 9, 3, 6, 9, 2, 2, 9, 1, 9, 3], [2, 4, 7, 7, 8, 1, 0, 0, 6, 2, 8, 9, 8, 8, 7, 4, 8, 4, 9, 1], [2, 1, 5, 9, 2, 6, 0, 0, 6, 4, 5, 8, 6, 3, 1, 4, 5, 1, 5, 1], [9, 4, 9, 5, 1, 2, 0, 2, 1, 4, 2, 9, 9, 6, 1, 9, 9, 7, 2, 1], [6, 6, 2, 3, 7, 3, 0, 0, 4, 3, 2, 4, 4, 7, 7, 7, 6, 7, 6, 7], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [8, 1, 4, 3, 9, 6, 0, 0, 8, 5, 4, 3, 5, 2, 6, 8, 9, 9, 4, 8], [1, 2, 6, 9, 8, 9, 0, 0, 3, 3, 6, 2, 3, 7, 3, 1, 8, 1, 4, 5], [3, 8, 4, 4, 4, 9, 0, 0, 6, 7, 9, 4, 2, 6, 2, 9, 3, 1, 5, 1], [2, 7, 5, 8, 8, 8, 0, 0, 4, 6, 3, 7, 9, 2, 1, 1, 7, 2, 5, 9], [2, 1, 7, 2, 1, 3, 0, 0, 3, 6, 2, 8, 3, 6, 9, 5, 5, 9, 8, 4], [3, 3, 3, 6, 6, 3, 0, 0, 9, 4, 7, 2, 4, 4, 7, 7, 6, 1, 2, 9], [2, 5, 8, 9, 7, 9, 0, 2, 3, 2, 2, 6, 6, 7, 9, 8, 9, 1, 1, 6]]\n\nExample 3:\n[[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 3, 1, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 7, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 4, 5, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 6, 4, 8, 7, 6], [3, 1, 3, 1, 7, 6, 4, 7, 5, 1, 8, 2, 6, 2, 0, 0, 5, 2, 5, 5], [7, 8, 7, 3, 4, 2, 5, 6, 2, 2, 3, 1, 5, 6, 0, 0, 5, 3, 8, 6], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 5, 7, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 4, 3, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 1, 3, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 9, 1, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 6, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 4, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 1, 3, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 6, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 5, 8, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 7, 8, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 1, 6, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 1, 7, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 7, 3, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 1, 8, 4, 6, 7, 3]] -> [[3, 5, 9, 3, 6, 9, 3, 3, 7, 3, 7, 9, 6, 5, 0, 0, 6, 5, 1, 6], [1, 9, 9, 3, 1, 2, 9, 4, 4, 7, 9, 9, 7, 3, 2, 0, 5, 1, 4, 6], [9, 3, 7, 2, 4, 4, 8, 3, 3, 6, 3, 7, 7, 5, 0, 0, 4, 4, 5, 1], [8, 2, 1, 1, 1, 4, 3, 2, 2, 9, 7, 2, 2, 1, 2, 0, 4, 8, 7, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 1, 4, 8, 2, 3, 3, 6, 6, 3, 7, 7, 9, 3, 0, 0, 6, 4, 3, 8], [6, 3, 3, 7, 4, 8, 2, 8, 7, 6, 4, 1, 8, 5, 0, 0, 4, 5, 4, 1], [8, 1, 2, 6, 9, 5, 9, 4, 6, 8, 2, 6, 8, 9, 0, 0, 8, 4, 7, 4], [6, 7, 7, 2, 9, 8, 7, 5, 6, 3, 7, 7, 3, 7, 0, 0, 5, 1, 2, 2], [1, 2, 2, 5, 8, 8, 4, 2, 3, 5, 2, 2, 6, 7, 2, 0, 3, 6, 3, 9], [3, 6, 9, 1, 8, 4, 6, 5, 7, 9, 2, 9, 7, 4, 0, 2, 9, 4, 4, 6], [2, 6, 5, 2, 6, 6, 8, 7, 6, 6, 1, 5, 2, 9, 0, 0, 3, 4, 9, 7], [2, 9, 8, 1, 7, 3, 2, 9, 6, 6, 9, 7, 7, 2, 2, 0, 7, 5, 9, 5], [4, 4, 1, 5, 2, 7, 6, 3, 5, 7, 2, 1, 6, 1, 0, 0, 8, 8, 8, 7], [7, 5, 2, 3, 8, 6, 9, 2, 3, 9, 9, 5, 6, 6, 0, 0, 9, 5, 8, 4], [6, 7, 1, 9, 2, 1, 2, 1, 6, 4, 5, 8, 1, 1, 0, 0, 7, 9, 8, 8], [7, 6, 5, 8, 3, 5, 9, 6, 4, 9, 6, 8, 7, 9, 0, 0, 9, 9, 1, 2], [1, 4, 8, 4, 2, 2, 6, 3, 5, 6, 6, 7, 5, 8, 0, 0, 6, 1, 7, 7], [5, 3, 3, 4, 8, 9, 8, 9, 5, 3, 2, 2, 5, 8, 0, 0, 4, 6, 7, 3]]\n\n# Test Problem:\n[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 4, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 4, 8, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 8, 1, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 1, 4, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 3, 5, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 9, 5, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 5, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 5, 7, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 8, 3, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 1, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 7, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 6, 7, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 4, 9, 7, 7, 1, 5, 9, 3], [3, 7, 7, 5, 9, 8, 7, 4, 2, 2, 9, 5, 0, 0, 8, 6, 7, 6, 6, 7], [6, 9, 5, 6, 3, 7, 5, 7, 9, 8, 9, 5, 0, 0, 4, 2, 3, 3, 2, 6], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 9, 5, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 5, 3, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 8, 6, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 8, 6, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 7, 5, 4, 3, 6, 3, 9, 5]] -> ", "answer": "[[4, 5, 7, 5, 9, 2, 3, 1, 7, 8, 6, 9, 0, 2, 4, 2, 5, 1, 2, 7], [9, 1, 7, 5, 5, 1, 2, 7, 1, 9, 1, 7, 0, 0, 4, 7, 2, 9, 5, 8], [9, 1, 8, 6, 9, 4, 7, 6, 9, 5, 5, 5, 0, 0, 4, 8, 4, 7, 8, 5], [4, 2, 9, 5, 5, 2, 8, 2, 7, 7, 9, 6, 0, 0, 9, 8, 3, 3, 9, 2], [1, 9, 2, 3, 8, 4, 3, 1, 1, 3, 4, 6, 0, 0, 1, 1, 2, 6, 4, 6], [1, 4, 3, 5, 6, 1, 1, 1, 1, 6, 7, 3, 0, 0, 8, 3, 5, 6, 2, 9], [7, 7, 1, 9, 2, 4, 6, 9, 1, 5, 5, 8, 0, 2, 2, 2, 4, 2, 1, 2], [2, 9, 6, 1, 2, 9, 4, 8, 2, 7, 8, 2, 0, 0, 3, 2, 2, 4, 7, 7], [4, 2, 6, 6, 8, 9, 2, 1, 3, 2, 4, 5, 0, 0, 7, 4, 8, 5, 2, 1], [3, 2, 4, 8, 9, 8, 9, 5, 2, 1, 6, 8, 0, 2, 5, 7, 9, 1, 8, 5], [1, 3, 7, 2, 7, 3, 5, 2, 3, 9, 3, 2, 0, 2, 1, 7, 9, 8, 5, 7], [1, 6, 4, 6, 6, 5, 5, 9, 2, 3, 2, 4, 0, 0, 3, 9, 9, 9, 6, 6], [8, 6, 5, 2, 2, 3, 2, 1, 4, 9, 6, 9, 0, 0, 7, 7, 1, 5, 9, 3], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 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, 2, 0, 0, 2, 0], [2, 8, 5, 3, 5, 6, 7, 1, 4, 7, 4, 4, 0, 0, 1, 3, 4, 4, 4, 7], [7, 8, 4, 7, 9, 5, 7, 8, 7, 4, 6, 8, 0, 0, 3, 1, 4, 1, 9, 7], [4, 5, 9, 9, 4, 5, 5, 7, 9, 8, 5, 8, 0, 0, 2, 8, 3, 7, 2, 4], [1, 6, 1, 4, 3, 6, 5, 4, 1, 7, 4, 7, 0, 0, 5, 9, 5, 4, 9, 9], [2, 9, 2, 6, 7, 8, 9, 9, 6, 4, 5, 8, 0, 0, 4, 3, 6, 3, 9, 5]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 0, 0, 0, 0], [8, 8, 0, 0, 0], [8, 8, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0], [0, 0, 8, 8, 0], [0, 0, 8, 8, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]
Example 3:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 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], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 0, 0, 0], [8, 8, 0, 0, 0], [8, 8, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0], [0, 0, 8, 8, 0], [0, 0, 8, 8, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 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], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 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, 0, 0, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"53357029-21a2-4fa7-9760-50922e226738\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0], [8, 8, 0, 0, 0], [8, 8, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0], [0, 0, 8, 8, 0], [0, 0, 8, 8, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 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], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 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, 0, 0, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "53357029-21a2-4fa7-9760-50922e226738"}
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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 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, 0, 0, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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]]
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{"id": "53357029-21a2-4fa7-9760-50922e226738", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 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, 8, 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, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 0, 0, 0, 0], [8, 8, 0, 0, 0], [8, 8, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] -> [[0, 0, 0, 0, 0], [0, 0, 8, 8, 0], [0, 0, 8, 8, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 8, 8, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 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], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 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]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 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, 0, 0, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 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]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[4, 4], [4, 4]]
Example 2:
[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]
Example 3:
[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]
Example 4:
[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 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], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[2, 2], [2, 2]]
# Test Problem:
[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 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, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[4, 4], [4, 4]]\\n\\nExample 2:\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]\\n\\nExample 3:\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]\\n\\nExample 4:\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 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], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[2, 2], [2, 2]]\\n\\n# Test Problem:\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 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, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[4, 4], [4, 4]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"5f09624a-45ec-4590-a525-ec394481ec47\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[4, 4], [4, 4]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]\\\\n\\\\nExample 4:\\\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 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], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[2, 2], [2, 2]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 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, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[4, 4], [4, 4]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "5f09624a-45ec-4590-a525-ec394481ec47"}
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[[4, 4], [4, 4]]
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{"id": "5f09624a-45ec-4590-a525-ec394481ec47", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[4, 4], [4, 4]]\n\nExample 2:\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]\n\nExample 3:\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]] -> [[2, 2], [2, 2]]\n\nExample 4:\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 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], [5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> [[2, 2], [2, 2]]\n\n# Test Problem:\n[[0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 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, 5, 5, 5, 5, 5], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[4, 4], [4, 4]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0], [3, 0, 0, 0, 0, 0, 3, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 2, 3, 0, 0, 0], [0, 3, 2, 2, 2, 3, 0, 0], [3, 2, 2, 2, 2, 2, 3, 0]]
Example 2:
[[0, 4, 0, 0, 0, 4, 0, 0], [0, 0, 4, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]] -> [[0, 4, 2, 2, 2, 4, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]]
Example 3:
[[0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> [[0, 8, 2, 2, 2, 2, 2, 2, 2, 8, 0, 0], [8, 2, 8, 2, 2, 2, 2, 2, 8, 2, 8, 0], [0, 0, 0, 8, 2, 2, 2, 8, 2, 2, 2, 8], [0, 0, 0, 0, 8, 2, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]
Example 4:
[[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]] -> [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 2, 2, 2, 2, 1], [0, 0, 1, 2, 2, 2, 1, 0], [0, 0, 0, 1, 2, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]]
# Test Problem:
[[0, 0, 6, 0, 0, 0, 0, 0, 6], [0, 6, 0, 6, 0, 0, 0, 6, 0], [6, 0, 0, 0, 6, 0, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0], [3, 0, 0, 0, 0, 0, 3, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 2, 3, 0, 0, 0], [0, 3, 2, 2, 2, 3, 0, 0], [3, 2, 2, 2, 2, 2, 3, 0]]\\n\\nExample 2:\\n[[0, 4, 0, 0, 0, 4, 0, 0], [0, 0, 4, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]] -> [[0, 4, 2, 2, 2, 4, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> [[0, 8, 2, 2, 2, 2, 2, 2, 2, 8, 0, 0], [8, 2, 8, 2, 2, 2, 2, 2, 8, 2, 8, 0], [0, 0, 0, 8, 2, 2, 2, 8, 2, 2, 2, 8], [0, 0, 0, 0, 8, 2, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]\\n\\nExample 4:\\n[[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]] -> [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 2, 2, 2, 2, 1], [0, 0, 1, 2, 2, 2, 1, 0], [0, 0, 0, 1, 2, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 0, 6, 0, 0, 0, 0, 0, 6], [0, 6, 0, 6, 0, 0, 0, 6, 0], [6, 0, 0, 0, 6, 0, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 6, 2, 2, 2, 2, 2, 6], [0, 6, 2, 6, 2, 2, 2, 6, 0], [6, 2, 2, 2, 6, 2, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"199795c9-fc46-40d1-aa84-57c28157fde8\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0], [3, 0, 0, 0, 0, 0, 3, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 2, 3, 0, 0, 0], [0, 3, 2, 2, 2, 3, 0, 0], [3, 2, 2, 2, 2, 2, 3, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 4, 0, 0, 0, 4, 0, 0], [0, 0, 4, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]] -> [[0, 4, 2, 2, 2, 4, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> [[0, 8, 2, 2, 2, 2, 2, 2, 2, 8, 0, 0], [8, 2, 8, 2, 2, 2, 2, 2, 8, 2, 8, 0], [0, 0, 0, 8, 2, 2, 2, 8, 2, 2, 2, 8], [0, 0, 0, 0, 8, 2, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]] -> [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 2, 2, 2, 2, 1], [0, 0, 1, 2, 2, 2, 1, 0], [0, 0, 0, 1, 2, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 6, 0, 0, 0, 0, 0, 6], [0, 6, 0, 6, 0, 0, 0, 6, 0], [6, 0, 0, 0, 6, 0, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 6, 2, 2, 2, 2, 2, 6], [0, 6, 2, 6, 2, 2, 2, 6, 0], [6, 2, 2, 2, 6, 2, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "199795c9-fc46-40d1-aa84-57c28157fde8"}
|
[[0, 0, 6, 2, 2, 2, 2, 2, 6], [0, 6, 2, 6, 2, 2, 2, 6, 0], [6, 2, 2, 2, 6, 2, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]]
|
{"id": "199795c9-fc46-40d1-aa84-57c28157fde8", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 0, 0], [0, 3, 0, 0, 0, 3, 0, 0], [3, 0, 0, 0, 0, 0, 3, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 2, 3, 0, 0, 0], [0, 3, 2, 2, 2, 3, 0, 0], [3, 2, 2, 2, 2, 2, 3, 0]]\n\nExample 2:\n[[0, 4, 0, 0, 0, 4, 0, 0], [0, 0, 4, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]] -> [[0, 4, 2, 2, 2, 4, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0]]\n\nExample 3:\n[[0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0], [0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> [[0, 8, 2, 2, 2, 2, 2, 2, 2, 8, 0, 0], [8, 2, 8, 2, 2, 2, 2, 2, 8, 2, 8, 0], [0, 0, 0, 8, 2, 2, 2, 8, 2, 2, 2, 8], [0, 0, 0, 0, 8, 2, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]\n\nExample 4:\n[[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]] -> [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 2, 2, 2, 2, 1], [0, 0, 1, 2, 2, 2, 1, 0], [0, 0, 0, 1, 2, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0]]\n\n# Test Problem:\n[[0, 0, 6, 0, 0, 0, 0, 0, 6], [0, 6, 0, 6, 0, 0, 0, 6, 0], [6, 0, 0, 0, 6, 0, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]] -> ", "answer": "[[0, 0, 6, 2, 2, 2, 2, 2, 6], [0, 6, 2, 6, 2, 2, 2, 6, 0], [6, 2, 2, 2, 6, 2, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 3, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 3, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[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, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 3, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 2, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 4, 4, 0], [0, 4, 4, 2, 4], [0, 0, 4, 4, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]
Example 3:
[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 1, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 1, 4, 4], [0, 0, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 0, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 4, 2, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 3, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 3, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[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, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 3, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 2, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 4, 4, 0], [0, 4, 4, 2, 4], [0, 0, 4, 4, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 1, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 1, 4, 4], [0, 0, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 0, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 4, 2, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> \", \"answer\": \"[[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, 0, 0, 0, 0, 0, 0], [0, 4, 4, 0, 4, 4, 0, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"678e7a35-797e-4d2c-967c-2b504d7abe5f\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 3, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 3, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[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, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 3, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 2, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 4, 4, 0], [0, 4, 4, 2, 4], [0, 0, 4, 4, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 1, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 1, 4, 4], [0, 0, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 0, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 4, 2, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> \\\", \\\"answer\\\": \\\"[[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, 0, 0, 0, 0, 0, 0], [0, 4, 4, 0, 4, 4, 0, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "678e7a35-797e-4d2c-967c-2b504d7abe5f"}
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[[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, 0, 0, 0, 0, 0, 0], [0, 4, 4, 0, 4, 4, 0, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 0, 0]]
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{"id": "678e7a35-797e-4d2c-967c-2b504d7abe5f", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 3, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 3, 4, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[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, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 3, 4, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 2, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 4, 4, 0], [0, 4, 4, 2, 4], [0, 0, 4, 4, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\n\nExample 3:\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 4, 4, 1, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 4, 4, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 1, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 4, 4, 4, 0], [0, 0, 4, 4, 1, 4, 4], [0, 0, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 0, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 4, 2, 4, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 4, 4, 4, 4, 4, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]] -> ", "answer": "[[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, 0, 0, 0, 0, 0, 0], [0, 4, 4, 0, 4, 4, 0, 0, 0], [0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 4, 4, 4, 4, 4, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[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], [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], [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], [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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]]
Example 2:
[[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 4, 4, 4, 7, 7, 0, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]]
Example 3:
[[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], [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7], [8, 0, 8, 8, 8, 8, 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, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [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], [3, 0, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 9, 9, 9, 9, 5, 5, 5, 0, 5, 5, 5, 5, 5], [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], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]] -> [[0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 8, 8, 8, 8, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]]
# Test Problem:
[[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], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 5, 5, 5, 5, 5], [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], [3, 3, 3, 0, 3, 3, 3, 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, 9, 9, 0, 9, 9, 9, 9, 9, 9], [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], [4, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\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], [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], [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], [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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 4, 4, 4, 7, 7, 0, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\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], [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7], [8, 0, 8, 8, 8, 8, 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, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [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], [3, 0, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 9, 9, 9, 9, 5, 5, 5, 0, 5, 5, 5, 5, 5], [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], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]] -> [[0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 8, 8, 8, 8, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\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], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 5, 5, 5, 5, 5], [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], [3, 3, 3, 0, 3, 3, 3, 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, 9, 9, 0, 9, 9, 9, 9, 9, 9], [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], [4, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"4ec25878-b671-43e2-8dc4-f9ce07f9ff00\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\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], [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], [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], [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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 4, 4, 4, 7, 7, 0, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\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], [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7], [8, 0, 8, 8, 8, 8, 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, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [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], [3, 0, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 9, 9, 9, 9, 5, 5, 5, 0, 5, 5, 5, 5, 5], [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], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]] -> [[0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 8, 8, 8, 8, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\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], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 5, 5, 5, 5, 5], [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], [3, 3, 3, 0, 3, 3, 3, 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, 9, 9, 0, 9, 9, 9, 9, 9, 9], [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], [4, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "4ec25878-b671-43e2-8dc4-f9ce07f9ff00"}
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[[0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]
|
{"id": "4ec25878-b671-43e2-8dc4-f9ce07f9ff00", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\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], [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], [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], [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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 3, 0, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0]]\n\nExample 2:\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 4, 4, 4, 7, 7, 0, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]] -> [[0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0]]\n\nExample 3:\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], [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 7, 7, 7, 7, 7], [8, 0, 8, 8, 8, 8, 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, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [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], [3, 0, 3, 3, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 9, 9, 9, 9, 5, 5, 5, 0, 5, 5, 5, 5, 5], [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], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]] -> [[0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 8, 8, 8, 8, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]]\n\n# Test Problem:\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], [2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 5, 5, 5, 5, 5], [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], [3, 3, 3, 0, 3, 3, 3, 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, 9, 9, 0, 9, 9, 9, 9, 9, 9], [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], [4, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
|
grid
|
symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 8, 8, 0, 0, 0], [8, 8, 8, 8, 8, 0, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 8, 8, 0, 0], [0, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 1, 1, 0, 0, 0], [3, 3, 1, 1, 4, 0, 0], [0, 3, 2, 0, 4, 4, 0], [0, 2, 2, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
Example 2:
[[0, 8, 0, 0, 8, 0, 0], [8, 8, 0, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 2, 0, 0, 4, 0, 0], [2, 2, 0, 0, 4, 4, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 0, 3, 3, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[8, 8, 8, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0], [8, 8, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 4, 0, 0, 0, 0], [1, 1, 4, 4, 0, 0, 0], [3, 3, 0, 2, 0, 0, 0], [0, 3, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[0, 8, 8, 0, 8, 8, 0], [8, 8, 8, 8, 8, 8, 0], [0, 8, 8, 0, 8, 0, 0], [0, 0, 8, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 8, 8, 0, 0, 0], [8, 8, 8, 8, 8, 0, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 8, 8, 0, 0], [0, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 1, 1, 0, 0, 0], [3, 3, 1, 1, 4, 0, 0], [0, 3, 2, 0, 4, 4, 0], [0, 2, 2, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\n[[0, 8, 0, 0, 8, 0, 0], [8, 8, 0, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 2, 0, 0, 4, 0, 0], [2, 2, 0, 0, 4, 4, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 0, 3, 3, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[8, 8, 8, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0], [8, 8, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 4, 0, 0, 0, 0], [1, 1, 4, 4, 0, 0, 0], [3, 3, 0, 2, 0, 0, 0], [0, 3, 2, 2, 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\\n# Test Problem:\\n[[0, 8, 8, 0, 8, 8, 0], [8, 8, 8, 8, 8, 8, 0], [0, 8, 8, 0, 8, 0, 0], [0, 0, 8, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 2, 4, 0, 1, 1, 0], [2, 2, 4, 4, 1, 1, 0], [0, 3, 3, 0, 2, 0, 0], [0, 0, 3, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"d5b66ceb-9d46-43d2-bafc-60590a075f55\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 8, 8, 0, 0, 0], [8, 8, 8, 8, 8, 0, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 8, 8, 0, 0], [0, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 1, 1, 0, 0, 0], [3, 3, 1, 1, 4, 0, 0], [0, 3, 2, 0, 4, 4, 0], [0, 2, 2, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 8, 0, 0, 8, 0, 0], [8, 8, 0, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 2, 0, 0, 4, 0, 0], [2, 2, 0, 0, 4, 4, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 0, 3, 3, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[8, 8, 8, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0], [8, 8, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 4, 0, 0, 0, 0], [1, 1, 4, 4, 0, 0, 0], [3, 3, 0, 2, 0, 0, 0], [0, 3, 2, 2, 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\\\\n# Test Problem:\\\\n[[0, 8, 8, 0, 8, 8, 0], [8, 8, 8, 8, 8, 8, 0], [0, 8, 8, 0, 8, 0, 0], [0, 0, 8, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 2, 4, 0, 1, 1, 0], [2, 2, 4, 4, 1, 1, 0], [0, 3, 3, 0, 2, 0, 0], [0, 0, 3, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "d5b66ceb-9d46-43d2-bafc-60590a075f55"}
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[[0, 2, 4, 0, 1, 1, 0], [2, 2, 4, 4, 1, 1, 0], [0, 3, 3, 0, 2, 0, 0], [0, 0, 3, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
|
{"id": "d5b66ceb-9d46-43d2-bafc-60590a075f55", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 8, 8, 0, 0, 0], [8, 8, 8, 8, 8, 0, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 8, 8, 0, 0], [0, 0, 0, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 0, 1, 1, 0, 0, 0], [3, 3, 1, 1, 4, 0, 0], [0, 3, 2, 0, 4, 4, 0], [0, 2, 2, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\n\nExample 2:\n[[0, 8, 0, 0, 8, 0, 0], [8, 8, 0, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 8, 8, 0, 8, 8, 0], [0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[0, 2, 0, 0, 4, 0, 0], [2, 2, 0, 0, 4, 4, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 0, 3, 3, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[8, 8, 8, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0], [8, 8, 0, 8, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> [[1, 1, 4, 0, 0, 0, 0], [1, 1, 4, 4, 0, 0, 0], [3, 3, 0, 2, 0, 0, 0], [0, 3, 2, 2, 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\n# Test Problem:\n[[0, 8, 8, 0, 8, 8, 0], [8, 8, 8, 8, 8, 8, 0], [0, 8, 8, 0, 8, 0, 0], [0, 0, 8, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 2, 4, 0, 1, 1, 0], [2, 2, 4, 4, 1, 1, 0], [0, 3, 3, 0, 2, 0, 0], [0, 0, 3, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
|
Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 3, 4, 4, 0, 0], [0, 0, 0, 0, 0, 3, 2, 4, 0, 0], [0, 0, 0, 7, 7, 3, 2, 4, 0, 0], [0, 0, 0, 7, 3, 3, 2, 0, 0, 0], [0, 0, 0, 7, 0, 0, 2, 2, 0, 0], [0, 0, 0, 7, 7, 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]] -> [[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 7, 2, 2, 0, 0], [0, 0, 0, 0, 0, 7, 4, 2, 0, 0], [0, 0, 0, 3, 3, 7, 4, 2, 0, 0], [0, 0, 0, 3, 7, 7, 4, 0, 0, 0], [0, 0, 0, 3, 0, 0, 4, 4, 0, 0], [0, 0, 0, 3, 3, 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]]
Example 2:
[[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 3, 3, 3, 3, 1, 8, 0, 0], [0, 0, 3, 3, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 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]] -> [[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 1, 1, 1, 1, 3, 2, 0, 0], [0, 0, 1, 1, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
Example 3:
[[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 7, 9, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 7, 4, 0, 0, 0, 0], [0, 0, 0, 6, 6, 7, 0, 0, 0, 0], [0, 0, 0, 7, 6, 6, 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, 0, 0, 0, 0]] -> [[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 6, 4, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 6, 9, 0, 0, 0, 0], [0, 0, 0, 7, 7, 6, 0, 0, 0, 0], [0, 0, 0, 6, 7, 7, 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, 0, 0, 0, 0]]
# Test Problem:
[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 8, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 4, 2, 0, 0, 0, 0], [0, 0, 0, 2, 2, 4, 0, 0, 0, 0], [0, 0, 0, 2, 4, 4, 0, 0, 0, 0], [0, 0, 0, 9, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 3, 4, 4, 0, 0], [0, 0, 0, 0, 0, 3, 2, 4, 0, 0], [0, 0, 0, 7, 7, 3, 2, 4, 0, 0], [0, 0, 0, 7, 3, 3, 2, 0, 0, 0], [0, 0, 0, 7, 0, 0, 2, 2, 0, 0], [0, 0, 0, 7, 7, 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]] -> [[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 7, 2, 2, 0, 0], [0, 0, 0, 0, 0, 7, 4, 2, 0, 0], [0, 0, 0, 3, 3, 7, 4, 2, 0, 0], [0, 0, 0, 3, 7, 7, 4, 0, 0, 0], [0, 0, 0, 3, 0, 0, 4, 4, 0, 0], [0, 0, 0, 3, 3, 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\\nExample 2:\\n[[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 3, 3, 3, 3, 1, 8, 0, 0], [0, 0, 3, 3, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 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]] -> [[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 1, 1, 1, 1, 3, 2, 0, 0], [0, 0, 1, 1, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\nExample 3:\\n[[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 7, 9, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 7, 4, 0, 0, 0, 0], [0, 0, 0, 6, 6, 7, 0, 0, 0, 0], [0, 0, 0, 7, 6, 6, 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, 0, 0, 0, 0]] -> [[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 6, 4, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 6, 9, 0, 0, 0, 0], [0, 0, 0, 7, 7, 6, 0, 0, 0, 0], [0, 0, 0, 6, 7, 7, 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, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 8, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 4, 2, 0, 0, 0, 0], [0, 0, 0, 2, 2, 4, 0, 0, 0, 0], [0, 0, 0, 2, 4, 4, 0, 0, 0, 0], [0, 0, 0, 9, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 9, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 2, 0, 0, 0, 0], [0, 0, 0, 4, 2, 2, 0, 0, 0, 0], [0, 0, 0, 8, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"7abffe4a-7b26-40fc-a3ef-20cf1046a951\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 3, 4, 4, 0, 0], [0, 0, 0, 0, 0, 3, 2, 4, 0, 0], [0, 0, 0, 7, 7, 3, 2, 4, 0, 0], [0, 0, 0, 7, 3, 3, 2, 0, 0, 0], [0, 0, 0, 7, 0, 0, 2, 2, 0, 0], [0, 0, 0, 7, 7, 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]] -> [[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 7, 2, 2, 0, 0], [0, 0, 0, 0, 0, 7, 4, 2, 0, 0], [0, 0, 0, 3, 3, 7, 4, 2, 0, 0], [0, 0, 0, 3, 7, 7, 4, 0, 0, 0], [0, 0, 0, 3, 0, 0, 4, 4, 0, 0], [0, 0, 0, 3, 3, 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\\\\nExample 2:\\\\n[[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 3, 3, 3, 3, 1, 8, 0, 0], [0, 0, 3, 3, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 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]] -> [[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 1, 1, 1, 1, 3, 2, 0, 0], [0, 0, 1, 1, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 7, 9, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 7, 4, 0, 0, 0, 0], [0, 0, 0, 6, 6, 7, 0, 0, 0, 0], [0, 0, 0, 7, 6, 6, 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, 0, 0, 0, 0]] -> [[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 6, 4, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 6, 9, 0, 0, 0, 0], [0, 0, 0, 7, 7, 6, 0, 0, 0, 0], [0, 0, 0, 6, 7, 7, 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, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 8, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 4, 2, 0, 0, 0, 0], [0, 0, 0, 2, 2, 4, 0, 0, 0, 0], [0, 0, 0, 2, 4, 4, 0, 0, 0, 0], [0, 0, 0, 9, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 9, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 2, 0, 0, 0, 0], [0, 0, 0, 4, 2, 2, 0, 0, 0, 0], [0, 0, 0, 8, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "7abffe4a-7b26-40fc-a3ef-20cf1046a951"}
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[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 9, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 2, 0, 0, 0, 0], [0, 0, 0, 4, 2, 2, 0, 0, 0, 0], [0, 0, 0, 8, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
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{"id": "7abffe4a-7b26-40fc-a3ef-20cf1046a951", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 3, 4, 4, 0, 0], [0, 0, 0, 0, 0, 3, 2, 4, 0, 0], [0, 0, 0, 7, 7, 3, 2, 4, 0, 0], [0, 0, 0, 7, 3, 3, 2, 0, 0, 0], [0, 0, 0, 7, 0, 0, 2, 2, 0, 0], [0, 0, 0, 7, 7, 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]] -> [[4, 2, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 7, 2, 2, 0, 0], [0, 0, 0, 0, 0, 7, 4, 2, 0, 0], [0, 0, 0, 3, 3, 7, 4, 2, 0, 0], [0, 0, 0, 3, 7, 7, 4, 0, 0, 0], [0, 0, 0, 3, 0, 0, 4, 4, 0, 0], [0, 0, 0, 3, 3, 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\nExample 2:\n[[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 3, 3, 3, 3, 1, 8, 0, 0], [0, 0, 3, 3, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 0, 8, 8, 0, 0], [0, 0, 0, 0, 2, 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]] -> [[1, 3, 0, 0, 0, 0, 0, 0, 0, 0], [2, 8, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 1, 1, 1, 1, 3, 2, 0, 0], [0, 0, 1, 1, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 2, 2, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nExample 3:\n[[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 7, 9, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 7, 4, 0, 0, 0, 0], [0, 0, 0, 6, 6, 7, 0, 0, 0, 0], [0, 0, 0, 7, 6, 6, 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, 0, 0, 0, 0]] -> [[9, 4, 0, 0, 0, 0, 0, 0, 0, 0], [7, 6, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 6, 4, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 6, 9, 0, 0, 0, 0], [0, 0, 0, 7, 7, 6, 0, 0, 0, 0], [0, 0, 0, 6, 7, 7, 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, 0, 0, 0, 0]]\n\n# Test Problem:\n[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 8, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 8, 8, 9, 0, 0, 0], [0, 0, 0, 2, 4, 2, 0, 0, 0, 0], [0, 0, 0, 2, 2, 4, 0, 0, 0, 0], [0, 0, 0, 2, 4, 4, 0, 0, 0, 0], [0, 0, 0, 9, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 9, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 9, 9, 8, 0, 0, 0], [0, 0, 0, 4, 2, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 2, 0, 0, 0, 0], [0, 0, 0, 4, 2, 2, 0, 0, 0, 0], [0, 0, 0, 8, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[6, 6, 6, 6, 5, 0, 5, 0], [6, 0, 0, 0, 5, 5, 0, 0], [6, 0, 6, 6, 0, 0, 5, 5], [0, 0, 6, 0, 0, 5, 5, 0]] -> [[0, 0, 0, 0], [0, 0, 4, 4], [0, 4, 0, 0], [4, 0, 0, 4]]
Example 2:
[[0, 6, 6, 0, 5, 5, 5, 0], [0, 6, 0, 6, 5, 0, 0, 5], [0, 6, 6, 6, 5, 5, 5, 5], [6, 0, 0, 0, 0, 5, 0, 5]] -> [[0, 0, 0, 4], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 4, 0]]
Example 3:
[[6, 6, 6, 0, 5, 0, 5, 5], [6, 0, 0, 0, 0, 5, 5, 5], [6, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 5, 5, 0, 0]] -> [[0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 4, 4], [0, 0, 0, 0]]
Example 4:
[[6, 0, 6, 0, 0, 0, 5, 5], [0, 6, 6, 6, 5, 0, 5, 5], [6, 6, 0, 6, 5, 0, 5, 5], [6, 6, 0, 0, 5, 0, 0, 0]] -> [[0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 4]]
# Test Problem:
[[0, 6, 0, 0, 0, 5, 0, 5], [0, 6, 0, 0, 0, 0, 0, 5], [6, 0, 0, 0, 5, 5, 0, 0], [6, 6, 0, 6, 0, 0, 0, 5]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[6, 6, 6, 6, 5, 0, 5, 0], [6, 0, 0, 0, 5, 5, 0, 0], [6, 0, 6, 6, 0, 0, 5, 5], [0, 0, 6, 0, 0, 5, 5, 0]] -> [[0, 0, 0, 0], [0, 0, 4, 4], [0, 4, 0, 0], [4, 0, 0, 4]]\\n\\nExample 2:\\n[[0, 6, 6, 0, 5, 5, 5, 0], [0, 6, 0, 6, 5, 0, 0, 5], [0, 6, 6, 6, 5, 5, 5, 5], [6, 0, 0, 0, 0, 5, 0, 5]] -> [[0, 0, 0, 4], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 4, 0]]\\n\\nExample 3:\\n[[6, 6, 6, 0, 5, 0, 5, 5], [6, 0, 0, 0, 0, 5, 5, 5], [6, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 5, 5, 0, 0]] -> [[0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 4, 4], [0, 0, 0, 0]]\\n\\nExample 4:\\n[[6, 0, 6, 0, 0, 0, 5, 5], [0, 6, 6, 6, 5, 0, 5, 5], [6, 6, 0, 6, 5, 0, 5, 5], [6, 6, 0, 0, 5, 0, 0, 0]] -> [[0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 4]]\\n\\n# Test Problem:\\n[[0, 6, 0, 0, 0, 5, 0, 5], [0, 6, 0, 0, 0, 0, 0, 5], [6, 0, 0, 0, 5, 5, 0, 0], [6, 6, 0, 6, 0, 0, 0, 5]] -> \", \"answer\": \"[[4, 0, 4, 0], [4, 0, 4, 0], [0, 0, 4, 4], [0, 0, 4, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"a06d5a65-29ff-4a8e-ba11-a08c20e6bf91\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[6, 6, 6, 6, 5, 0, 5, 0], [6, 0, 0, 0, 5, 5, 0, 0], [6, 0, 6, 6, 0, 0, 5, 5], [0, 0, 6, 0, 0, 5, 5, 0]] -> [[0, 0, 0, 0], [0, 0, 4, 4], [0, 4, 0, 0], [4, 0, 0, 4]]\\\\n\\\\nExample 2:\\\\n[[0, 6, 6, 0, 5, 5, 5, 0], [0, 6, 0, 6, 5, 0, 0, 5], [0, 6, 6, 6, 5, 5, 5, 5], [6, 0, 0, 0, 0, 5, 0, 5]] -> [[0, 0, 0, 4], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 4, 0]]\\\\n\\\\nExample 3:\\\\n[[6, 6, 6, 0, 5, 0, 5, 5], [6, 0, 0, 0, 0, 5, 5, 5], [6, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 5, 5, 0, 0]] -> [[0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 4, 4], [0, 0, 0, 0]]\\\\n\\\\nExample 4:\\\\n[[6, 0, 6, 0, 0, 0, 5, 5], [0, 6, 6, 6, 5, 0, 5, 5], [6, 6, 0, 6, 5, 0, 5, 5], [6, 6, 0, 0, 5, 0, 0, 0]] -> [[0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 4]]\\\\n\\\\n# Test Problem:\\\\n[[0, 6, 0, 0, 0, 5, 0, 5], [0, 6, 0, 0, 0, 0, 0, 5], [6, 0, 0, 0, 5, 5, 0, 0], [6, 6, 0, 6, 0, 0, 0, 5]] -> \\\", \\\"answer\\\": \\\"[[4, 0, 4, 0], [4, 0, 4, 0], [0, 0, 4, 4], [0, 0, 4, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "a06d5a65-29ff-4a8e-ba11-a08c20e6bf91"}
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[[4, 0, 4, 0], [4, 0, 4, 0], [0, 0, 4, 4], [0, 0, 4, 0]]
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{"id": "a06d5a65-29ff-4a8e-ba11-a08c20e6bf91", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[6, 6, 6, 6, 5, 0, 5, 0], [6, 0, 0, 0, 5, 5, 0, 0], [6, 0, 6, 6, 0, 0, 5, 5], [0, 0, 6, 0, 0, 5, 5, 0]] -> [[0, 0, 0, 0], [0, 0, 4, 4], [0, 4, 0, 0], [4, 0, 0, 4]]\n\nExample 2:\n[[0, 6, 6, 0, 5, 5, 5, 0], [0, 6, 0, 6, 5, 0, 0, 5], [0, 6, 6, 6, 5, 5, 5, 5], [6, 0, 0, 0, 0, 5, 0, 5]] -> [[0, 0, 0, 4], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 4, 0]]\n\nExample 3:\n[[6, 6, 6, 0, 5, 0, 5, 5], [6, 0, 0, 0, 0, 5, 5, 5], [6, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 5, 5, 0, 0]] -> [[0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 4, 4], [0, 0, 0, 0]]\n\nExample 4:\n[[6, 0, 6, 0, 0, 0, 5, 5], [0, 6, 6, 6, 5, 0, 5, 5], [6, 6, 0, 6, 5, 0, 5, 5], [6, 6, 0, 0, 5, 0, 0, 0]] -> [[0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 4]]\n\n# Test Problem:\n[[0, 6, 0, 0, 0, 5, 0, 5], [0, 6, 0, 0, 0, 0, 0, 5], [6, 0, 0, 0, 5, 5, 0, 0], [6, 6, 0, 6, 0, 0, 0, 5]] -> ", "answer": "[[4, 0, 4, 0], [4, 0, 4, 0], [0, 0, 4, 4], [0, 0, 4, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 2, 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, 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, 6, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 5, 5, 2, 5, 5, 5, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0, 0, 0, 0, 0]]
Example 2:
[[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, 0, 0, 0, 0, 4, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 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, 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, 0, 0, 0], [0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 5, 5, 5, 2, 5, 5, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0]]
Example 3:
[[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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 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, 0, 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, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 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, 0, 0, 0, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 5, 5, 5, 2, 5, 5, 5, 5, 5, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# Test Problem:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 2, 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, 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, 6, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 5, 5, 2, 5, 5, 5, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0, 0, 0, 0, 0]]\\n\\nExample 2:\\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, 0, 0, 0, 0, 4, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 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, 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, 0, 0, 0], [0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 5, 5, 5, 2, 5, 5, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0]]\\n\\nExample 3:\\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 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, 0, 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, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 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, 0, 0, 0, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 5, 5, 5, 2, 5, 5, 5, 5, 5, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\n\\n# Test Problem:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 5, 2, 5, 5, 5, 5, 5, 5, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"1d4be83a-60f6-46e3-b6e4-1ec408e79393\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 2, 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, 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, 6, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 5, 5, 2, 5, 5, 5, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0, 0, 0, 0, 0]]\\\\n\\\\nExample 2:\\\\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, 0, 0, 0, 0, 4, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 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, 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, 0, 0, 0], [0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 5, 5, 5, 2, 5, 5, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0]]\\\\n\\\\nExample 3:\\\\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 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, 0, 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, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 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, 0, 0, 0, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 5, 5, 5, 2, 5, 5, 5, 5, 5, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 5, 2, 5, 5, 5, 5, 5, 5, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
|
PUZZLE##symbolic_hard
|
PUZZLE
|
{"index": "1d4be83a-60f6-46e3-b6e4-1ec408e79393"}
|
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 5, 2, 5, 5, 5, 5, 5, 5, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 0, 0, 0]]
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{"id": "1d4be83a-60f6-46e3-b6e4-1ec408e79393", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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, 2, 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, 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, 6, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 5, 5, 2, 5, 5, 5, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0, 0, 0, 0, 0]]\n\nExample 2:\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, 0, 0, 0, 0, 4, 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, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 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, 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, 0, 0, 0], [0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 5, 5, 5, 2, 5, 5, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 7, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 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, 0]]\n\nExample 3:\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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 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, 0, 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, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 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, 0, 0, 0, 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, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 5, 5, 5, 2, 5, 5, 5, 5, 5, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\n# Test Problem:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 5, 2, 5, 5, 5, 5, 5, 5, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 9, 0, 9, 9, 5, 0, 4], [4, 4, 5, 0, 0, 4, 0, 5, 4, 4], [9, 4, 5, 4, 9, 0, 9, 5, 0, 0], [0, 9, 5, 0, 4, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]] -> [[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 4, 0, 4, 4, 5, 0, 4], [4, 4, 5, 0, 0, 9, 0, 5, 4, 4], [9, 4, 5, 9, 4, 0, 4, 5, 0, 0], [0, 9, 5, 0, 9, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]]
Example 2:
[[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 8, 8, 6, 6, 0, 5, 8], [6, 5, 6, 6, 6, 8, 0, 6, 5, 8], [0, 5, 6, 6, 8, 6, 0, 6, 5, 8], [6, 5, 8, 8, 8, 6, 8, 0, 5, 8], [6, 5, 6, 8, 6, 8, 6, 8, 5, 8], [0, 5, 6, 0, 6, 8, 8, 8, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]] -> [[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 6, 6, 8, 8, 0, 5, 8], [6, 5, 8, 8, 8, 6, 0, 8, 5, 8], [0, 5, 8, 8, 6, 8, 0, 8, 5, 8], [6, 5, 6, 6, 6, 8, 6, 0, 5, 8], [6, 5, 8, 6, 8, 6, 8, 6, 5, 8], [0, 5, 8, 0, 8, 6, 6, 6, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]]
Example 3:
[[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 3, 2, 2, 2, 2, 0, 5, 2], [0, 5, 0, 3, 0, 3, 2, 2, 5, 2], [3, 5, 2, 0, 2, 3, 2, 2, 5, 3], [3, 5, 3, 3, 0, 2, 3, 3, 5, 3], [3, 5, 3, 3, 3, 0, 3, 2, 5, 2], [0, 5, 3, 0, 3, 3, 3, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]] -> [[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 2, 3, 3, 3, 3, 0, 5, 2], [0, 5, 0, 2, 0, 2, 3, 3, 5, 2], [3, 5, 3, 0, 3, 2, 3, 3, 5, 3], [3, 5, 2, 2, 0, 3, 2, 2, 5, 3], [3, 5, 2, 2, 2, 0, 2, 3, 5, 2], [0, 5, 2, 0, 2, 2, 2, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]]
# Test Problem:
[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 1, 0, 1, 7, 5, 7], [0, 5, 7, 1, 7, 0, 1, 7, 5, 1], [7, 5, 7, 7, 0, 1, 7, 1, 5, 1], [7, 5, 0, 1, 7, 0, 7, 7, 5, 1], [1, 5, 7, 7, 1, 1, 1, 1, 5, 0], [0, 5, 1, 7, 7, 7, 7, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 9, 0, 9, 9, 5, 0, 4], [4, 4, 5, 0, 0, 4, 0, 5, 4, 4], [9, 4, 5, 4, 9, 0, 9, 5, 0, 0], [0, 9, 5, 0, 4, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]] -> [[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 4, 0, 4, 4, 5, 0, 4], [4, 4, 5, 0, 0, 9, 0, 5, 4, 4], [9, 4, 5, 9, 4, 0, 4, 5, 0, 0], [0, 9, 5, 0, 9, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]]\\n\\nExample 2:\\n[[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 8, 8, 6, 6, 0, 5, 8], [6, 5, 6, 6, 6, 8, 0, 6, 5, 8], [0, 5, 6, 6, 8, 6, 0, 6, 5, 8], [6, 5, 8, 8, 8, 6, 8, 0, 5, 8], [6, 5, 6, 8, 6, 8, 6, 8, 5, 8], [0, 5, 6, 0, 6, 8, 8, 8, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]] -> [[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 6, 6, 8, 8, 0, 5, 8], [6, 5, 8, 8, 8, 6, 0, 8, 5, 8], [0, 5, 8, 8, 6, 8, 0, 8, 5, 8], [6, 5, 6, 6, 6, 8, 6, 0, 5, 8], [6, 5, 8, 6, 8, 6, 8, 6, 5, 8], [0, 5, 8, 0, 8, 6, 6, 6, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]]\\n\\nExample 3:\\n[[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 3, 2, 2, 2, 2, 0, 5, 2], [0, 5, 0, 3, 0, 3, 2, 2, 5, 2], [3, 5, 2, 0, 2, 3, 2, 2, 5, 3], [3, 5, 3, 3, 0, 2, 3, 3, 5, 3], [3, 5, 3, 3, 3, 0, 3, 2, 5, 2], [0, 5, 3, 0, 3, 3, 3, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]] -> [[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 2, 3, 3, 3, 3, 0, 5, 2], [0, 5, 0, 2, 0, 2, 3, 3, 5, 2], [3, 5, 3, 0, 3, 2, 3, 3, 5, 3], [3, 5, 2, 2, 0, 3, 2, 2, 5, 3], [3, 5, 2, 2, 2, 0, 2, 3, 5, 2], [0, 5, 2, 0, 2, 2, 2, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]]\\n\\n# Test Problem:\\n[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 1, 0, 1, 7, 5, 7], [0, 5, 7, 1, 7, 0, 1, 7, 5, 1], [7, 5, 7, 7, 0, 1, 7, 1, 5, 1], [7, 5, 0, 1, 7, 0, 7, 7, 5, 1], [1, 5, 7, 7, 1, 1, 1, 1, 5, 0], [0, 5, 1, 7, 7, 7, 7, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]] -> \", \"answer\": \"[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 7, 0, 7, 1, 5, 7], [0, 5, 1, 7, 1, 0, 7, 1, 5, 1], [7, 5, 1, 1, 0, 7, 1, 7, 5, 1], [7, 5, 0, 7, 1, 0, 1, 1, 5, 1], [1, 5, 1, 1, 7, 7, 7, 7, 5, 0], [0, 5, 7, 1, 1, 1, 1, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"85ef5e3f-3e82-4a8b-825d-e5113134e38f\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 9, 0, 9, 9, 5, 0, 4], [4, 4, 5, 0, 0, 4, 0, 5, 4, 4], [9, 4, 5, 4, 9, 0, 9, 5, 0, 0], [0, 9, 5, 0, 4, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]] -> [[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 4, 0, 4, 4, 5, 0, 4], [4, 4, 5, 0, 0, 9, 0, 5, 4, 4], [9, 4, 5, 9, 4, 0, 4, 5, 0, 0], [0, 9, 5, 0, 9, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]]\\\\n\\\\nExample 2:\\\\n[[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 8, 8, 6, 6, 0, 5, 8], [6, 5, 6, 6, 6, 8, 0, 6, 5, 8], [0, 5, 6, 6, 8, 6, 0, 6, 5, 8], [6, 5, 8, 8, 8, 6, 8, 0, 5, 8], [6, 5, 6, 8, 6, 8, 6, 8, 5, 8], [0, 5, 6, 0, 6, 8, 8, 8, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]] -> [[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 6, 6, 8, 8, 0, 5, 8], [6, 5, 8, 8, 8, 6, 0, 8, 5, 8], [0, 5, 8, 8, 6, 8, 0, 8, 5, 8], [6, 5, 6, 6, 6, 8, 6, 0, 5, 8], [6, 5, 8, 6, 8, 6, 8, 6, 5, 8], [0, 5, 8, 0, 8, 6, 6, 6, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]]\\\\n\\\\nExample 3:\\\\n[[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 3, 2, 2, 2, 2, 0, 5, 2], [0, 5, 0, 3, 0, 3, 2, 2, 5, 2], [3, 5, 2, 0, 2, 3, 2, 2, 5, 3], [3, 5, 3, 3, 0, 2, 3, 3, 5, 3], [3, 5, 3, 3, 3, 0, 3, 2, 5, 2], [0, 5, 3, 0, 3, 3, 3, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]] -> [[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 2, 3, 3, 3, 3, 0, 5, 2], [0, 5, 0, 2, 0, 2, 3, 3, 5, 2], [3, 5, 3, 0, 3, 2, 3, 3, 5, 3], [3, 5, 2, 2, 0, 3, 2, 2, 5, 3], [3, 5, 2, 2, 2, 0, 2, 3, 5, 2], [0, 5, 2, 0, 2, 2, 2, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]]\\\\n\\\\n# Test Problem:\\\\n[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 1, 0, 1, 7, 5, 7], [0, 5, 7, 1, 7, 0, 1, 7, 5, 1], [7, 5, 7, 7, 0, 1, 7, 1, 5, 1], [7, 5, 0, 1, 7, 0, 7, 7, 5, 1], [1, 5, 7, 7, 1, 1, 1, 1, 5, 0], [0, 5, 1, 7, 7, 7, 7, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]] -> \\\", \\\"answer\\\": \\\"[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 7, 0, 7, 1, 5, 7], [0, 5, 1, 7, 1, 0, 7, 1, 5, 1], [7, 5, 1, 1, 0, 7, 1, 7, 5, 1], [7, 5, 0, 7, 1, 0, 1, 1, 5, 1], [1, 5, 1, 1, 7, 7, 7, 7, 5, 0], [0, 5, 7, 1, 1, 1, 1, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "85ef5e3f-3e82-4a8b-825d-e5113134e38f"}
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[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 7, 0, 7, 1, 5, 7], [0, 5, 1, 7, 1, 0, 7, 1, 5, 1], [7, 5, 1, 1, 0, 7, 1, 7, 5, 1], [7, 5, 0, 7, 1, 0, 1, 1, 5, 1], [1, 5, 1, 1, 7, 7, 7, 7, 5, 0], [0, 5, 7, 1, 1, 1, 1, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]]
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{"id": "85ef5e3f-3e82-4a8b-825d-e5113134e38f", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 9, 0, 9, 9, 5, 0, 4], [4, 4, 5, 0, 0, 4, 0, 5, 4, 4], [9, 4, 5, 4, 9, 0, 9, 5, 0, 0], [0, 9, 5, 0, 4, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]] -> [[9, 4, 0, 0, 4, 9, 0, 0, 9, 9], [4, 9, 9, 4, 9, 9, 0, 0, 9, 0], [0, 0, 5, 5, 5, 5, 5, 5, 0, 9], [9, 4, 5, 4, 0, 4, 4, 5, 0, 4], [4, 4, 5, 0, 0, 9, 0, 5, 4, 4], [9, 4, 5, 9, 4, 0, 4, 5, 0, 0], [0, 9, 5, 0, 9, 0, 0, 5, 0, 4], [0, 4, 5, 5, 5, 5, 5, 5, 4, 4], [9, 0, 9, 9, 4, 0, 9, 0, 0, 0], [9, 9, 9, 0, 9, 4, 9, 9, 0, 0]]\n\nExample 2:\n[[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 8, 8, 6, 6, 0, 5, 8], [6, 5, 6, 6, 6, 8, 0, 6, 5, 8], [0, 5, 6, 6, 8, 6, 0, 6, 5, 8], [6, 5, 8, 8, 8, 6, 8, 0, 5, 8], [6, 5, 6, 8, 6, 8, 6, 8, 5, 8], [0, 5, 6, 0, 6, 8, 8, 8, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]] -> [[0, 0, 8, 6, 0, 6, 0, 8, 0, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 5, 0, 6, 6, 8, 8, 0, 5, 8], [6, 5, 8, 8, 8, 6, 0, 8, 5, 8], [0, 5, 8, 8, 6, 8, 0, 8, 5, 8], [6, 5, 6, 6, 6, 8, 6, 0, 5, 8], [6, 5, 8, 6, 8, 6, 8, 6, 5, 8], [0, 5, 8, 0, 8, 6, 6, 6, 5, 8], [8, 5, 5, 5, 5, 5, 5, 5, 5, 6], [8, 8, 8, 0, 8, 8, 6, 0, 6, 6]]\n\nExample 3:\n[[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 3, 2, 2, 2, 2, 0, 5, 2], [0, 5, 0, 3, 0, 3, 2, 2, 5, 2], [3, 5, 2, 0, 2, 3, 2, 2, 5, 3], [3, 5, 3, 3, 0, 2, 3, 3, 5, 3], [3, 5, 3, 3, 3, 0, 3, 2, 5, 2], [0, 5, 3, 0, 3, 3, 3, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]] -> [[0, 0, 3, 3, 3, 3, 2, 0, 2, 0], [3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 2, 3, 3, 3, 3, 0, 5, 2], [0, 5, 0, 2, 0, 2, 3, 3, 5, 2], [3, 5, 3, 0, 3, 2, 3, 3, 5, 3], [3, 5, 2, 2, 0, 3, 2, 2, 5, 3], [3, 5, 2, 2, 2, 0, 2, 3, 5, 2], [0, 5, 2, 0, 2, 2, 2, 0, 5, 3], [0, 5, 5, 5, 5, 5, 5, 5, 5, 3], [2, 0, 3, 3, 3, 2, 3, 2, 3, 0]]\n\n# Test Problem:\n[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 1, 0, 1, 7, 5, 7], [0, 5, 7, 1, 7, 0, 1, 7, 5, 1], [7, 5, 7, 7, 0, 1, 7, 1, 5, 1], [7, 5, 0, 1, 7, 0, 7, 7, 5, 1], [1, 5, 7, 7, 1, 1, 1, 1, 5, 0], [0, 5, 1, 7, 7, 7, 7, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]] -> ", "answer": "[[7, 0, 1, 1, 7, 0, 0, 7, 7, 7], [1, 5, 5, 5, 5, 5, 5, 5, 5, 7], [1, 5, 0, 0, 7, 0, 7, 1, 5, 7], [0, 5, 1, 7, 1, 0, 7, 1, 5, 1], [7, 5, 1, 1, 0, 7, 1, 7, 5, 1], [7, 5, 0, 7, 1, 0, 1, 1, 5, 1], [1, 5, 1, 1, 7, 7, 7, 7, 5, 0], [0, 5, 7, 1, 1, 1, 1, 0, 5, 7], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0], [0, 1, 7, 1, 0, 7, 0, 0, 7, 7]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[2, 4, 0, 5, 8, 0, 0, 2, 4], [4, 4, 0, 8, 8, 0, 0, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 0, 9, 5, 0, 0, 3, 3], [9, 9, 0, 9, 5, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 4, 4, 0, 0, 8, 3], [2, 4, 0, 2, 2, 0, 0, 8, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 0, 9, 9], [1, 2, 0, 2, 1, 0, 0, 7, 9]] -> [[5, 8], [5, 8], [0, 0], [2, 3], [2, 3], [0, 0], [3, 3], [8, 8], [0, 0], [9, 9], [9, 7]]
Example 2:
[[2, 4, 0, 4, 2, 0, 0, 8, 6], [4, 4, 0, 4, 4, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 2, 1, 0, 0, 5, 5], [2, 2, 0, 2, 1, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 8, 3, 0, 0, 3, 3], [3, 3, 0, 8, 8, 0, 0, 3, 7]] -> [[6, 8], [8, 8], [0, 0], [4, 5], [4, 5], [0, 0], [8, 8], [8, 3]]
# Test Problem:
[[1, 1, 0, 1, 1, 0, 0, 4, 4], [2, 1, 0, 1, 2, 0, 0, 3, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 5, 2, 0, 0, 3, 3], [5, 5, 0, 5, 2, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 0, 6, 8, 0, 0, 7, 7], [8, 8, 0, 6, 8, 0, 0, 4, 4]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[2, 4, 0, 5, 8, 0, 0, 2, 4], [4, 4, 0, 8, 8, 0, 0, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 0, 9, 5, 0, 0, 3, 3], [9, 9, 0, 9, 5, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 4, 4, 0, 0, 8, 3], [2, 4, 0, 2, 2, 0, 0, 8, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 0, 9, 9], [1, 2, 0, 2, 1, 0, 0, 7, 9]] -> [[5, 8], [5, 8], [0, 0], [2, 3], [2, 3], [0, 0], [3, 3], [8, 8], [0, 0], [9, 9], [9, 7]]\\n\\nExample 2:\\n[[2, 4, 0, 4, 2, 0, 0, 8, 6], [4, 4, 0, 4, 4, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 2, 1, 0, 0, 5, 5], [2, 2, 0, 2, 1, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 8, 3, 0, 0, 3, 3], [3, 3, 0, 8, 8, 0, 0, 3, 7]] -> [[6, 8], [8, 8], [0, 0], [4, 5], [4, 5], [0, 0], [8, 8], [8, 3]]\\n\\n# Test Problem:\\n[[1, 1, 0, 1, 1, 0, 0, 4, 4], [2, 1, 0, 1, 2, 0, 0, 3, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 5, 2, 0, 0, 3, 3], [5, 5, 0, 5, 2, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 0, 6, 8, 0, 0, 7, 7], [8, 8, 0, 6, 8, 0, 0, 4, 4]] -> \", \"answer\": \"[[4, 4], [4, 3], [0, 0], [1, 3], [1, 3], [0, 0], [7, 4], [7, 4]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"eb4b441a-ef92-4e4f-8112-3b9944c07c34\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[2, 4, 0, 5, 8, 0, 0, 2, 4], [4, 4, 0, 8, 8, 0, 0, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 0, 9, 5, 0, 0, 3, 3], [9, 9, 0, 9, 5, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 4, 4, 0, 0, 8, 3], [2, 4, 0, 2, 2, 0, 0, 8, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 0, 9, 9], [1, 2, 0, 2, 1, 0, 0, 7, 9]] -> [[5, 8], [5, 8], [0, 0], [2, 3], [2, 3], [0, 0], [3, 3], [8, 8], [0, 0], [9, 9], [9, 7]]\\\\n\\\\nExample 2:\\\\n[[2, 4, 0, 4, 2, 0, 0, 8, 6], [4, 4, 0, 4, 4, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 2, 1, 0, 0, 5, 5], [2, 2, 0, 2, 1, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 8, 3, 0, 0, 3, 3], [3, 3, 0, 8, 8, 0, 0, 3, 7]] -> [[6, 8], [8, 8], [0, 0], [4, 5], [4, 5], [0, 0], [8, 8], [8, 3]]\\\\n\\\\n# Test Problem:\\\\n[[1, 1, 0, 1, 1, 0, 0, 4, 4], [2, 1, 0, 1, 2, 0, 0, 3, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 5, 2, 0, 0, 3, 3], [5, 5, 0, 5, 2, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 0, 6, 8, 0, 0, 7, 7], [8, 8, 0, 6, 8, 0, 0, 4, 4]] -> \\\", \\\"answer\\\": \\\"[[4, 4], [4, 3], [0, 0], [1, 3], [1, 3], [0, 0], [7, 4], [7, 4]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "eb4b441a-ef92-4e4f-8112-3b9944c07c34"}
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[[4, 4], [4, 3], [0, 0], [1, 3], [1, 3], [0, 0], [7, 4], [7, 4]]
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{"id": "eb4b441a-ef92-4e4f-8112-3b9944c07c34", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[2, 4, 0, 5, 8, 0, 0, 2, 4], [4, 4, 0, 8, 8, 0, 0, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 0, 9, 5, 0, 0, 3, 3], [9, 9, 0, 9, 5, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 4, 4, 0, 0, 8, 3], [2, 4, 0, 2, 2, 0, 0, 8, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 0, 9, 9], [1, 2, 0, 2, 1, 0, 0, 7, 9]] -> [[5, 8], [5, 8], [0, 0], [2, 3], [2, 3], [0, 0], [3, 3], [8, 8], [0, 0], [9, 9], [9, 7]]\n\nExample 2:\n[[2, 4, 0, 4, 2, 0, 0, 8, 6], [4, 4, 0, 4, 4, 0, 0, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 2, 1, 0, 0, 5, 5], [2, 2, 0, 2, 1, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 7, 0, 8, 3, 0, 0, 3, 3], [3, 3, 0, 8, 8, 0, 0, 3, 7]] -> [[6, 8], [8, 8], [0, 0], [4, 5], [4, 5], [0, 0], [8, 8], [8, 3]]\n\n# Test Problem:\n[[1, 1, 0, 1, 1, 0, 0, 4, 4], [2, 1, 0, 1, 2, 0, 0, 3, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 5, 2, 0, 0, 3, 3], [5, 5, 0, 5, 2, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 0, 6, 8, 0, 0, 7, 7], [8, 8, 0, 6, 8, 0, 0, 4, 4]] -> ", "answer": "[[4, 4], [4, 3], [0, 0], [1, 3], [1, 3], [0, 0], [7, 4], [7, 4]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 0, 0, 0, 0, 0, 0, 5, 3, 1, 1, 5, 3, 1, 1, 0, 0, 0, 0, 0, 3, 1, 1, 5, 3], [3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 1, 1, 3, 3, 3], [5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 0, 0, 0, 0, 0, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 0, 0, 0, 0, 0, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 0, 0, 0, 0, 0, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [0, 0, 0, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]] -> [[5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]]
Example 2:
[[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 0, 0, 0, 0, 0, 0, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 0, 0, 0, 0, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [3, 7, 0, 0, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 0, 0, 0, 0, 7, 4], [7, 6, 0, 0, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 0, 0, 0, 0, 6, 5], [4, 5, 0, 0, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 0, 0, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 0, 0, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 0, 0, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 0, 0, 0, 0, 0, 0, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]] -> [[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]]
Example 3:
[[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 0, 0, 0, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 0, 0, 0, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 0, 0, 0, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 7, 5, 7, 5, 3, 1, 3, 1, 0, 0, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]] -> [[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]]
# Test Problem:
[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 0, 0, 0, 0, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 0, 0, 0, 0, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 0, 0, 0, 0, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [5, 0, 0, 0, 0, 0, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 0, 0, 3], [4, 0, 0, 0, 0, 0, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 0, 0, 6], [3, 0, 0, 0, 0, 0, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 0, 0, 9], [2, 0, 0, 0, 0, 0, 5, 1, 2, 7, 3, 8, 4, 0, 0, 0, 0, 0, 0, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 0, 0, 0, 0, 0, 0, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 0, 0, 0, 0, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 0, 0, 0, 0, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 0, 0, 0, 0, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 0, 0, 0, 0, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]] ->
|
{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 0, 0, 0, 0, 0, 0, 5, 3, 1, 1, 5, 3, 1, 1, 0, 0, 0, 0, 0, 3, 1, 1, 5, 3], [3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 1, 1, 3, 3, 3], [5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 0, 0, 0, 0, 0, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 0, 0, 0, 0, 0, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 0, 0, 0, 0, 0, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [0, 0, 0, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]] -> [[5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]]\\n\\nExample 2:\\n[[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 0, 0, 0, 0, 0, 0, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 0, 0, 0, 0, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [3, 7, 0, 0, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 0, 0, 0, 0, 7, 4], [7, 6, 0, 0, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 0, 0, 0, 0, 6, 5], [4, 5, 0, 0, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 0, 0, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 0, 0, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 0, 0, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 0, 0, 0, 0, 0, 0, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]] -> [[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]]\\n\\nExample 3:\\n[[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 0, 0, 0, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 0, 0, 0, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 0, 0, 0, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 7, 5, 7, 5, 3, 1, 3, 1, 0, 0, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]] -> [[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]]\\n\\n# Test Problem:\\n[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 0, 0, 0, 0, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 0, 0, 0, 0, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 0, 0, 0, 0, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [5, 0, 0, 0, 0, 0, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 0, 0, 3], [4, 0, 0, 0, 0, 0, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 0, 0, 6], [3, 0, 0, 0, 0, 0, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 0, 0, 9], [2, 0, 0, 0, 0, 0, 5, 1, 2, 7, 3, 8, 4, 0, 0, 0, 0, 0, 0, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 0, 0, 0, 0, 0, 0, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 0, 0, 0, 0, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 0, 0, 0, 0, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 0, 0, 0, 0, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 0, 0, 0, 0, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]] -> \", \"answer\": \"[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"e6b921ed-6fd4-49e2-b63d-272f1d5c43c0\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 0, 0, 0, 0, 0, 0, 5, 3, 1, 1, 5, 3, 1, 1, 0, 0, 0, 0, 0, 3, 1, 1, 5, 3], [3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 1, 1, 3, 3, 3], [5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 0, 0, 0, 0, 0, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 0, 0, 0, 0, 0, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 0, 0, 0, 0, 0, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [0, 0, 0, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]] -> [[5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]]\\\\n\\\\nExample 2:\\\\n[[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 0, 0, 0, 0, 0, 0, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 0, 0, 0, 0, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [3, 7, 0, 0, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 0, 0, 0, 0, 7, 4], [7, 6, 0, 0, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 0, 0, 0, 0, 6, 5], [4, 5, 0, 0, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 0, 0, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 0, 0, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 0, 0, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 0, 0, 0, 0, 0, 0, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]] -> [[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]]\\\\n\\\\nExample 3:\\\\n[[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 0, 0, 0, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 0, 0, 0, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 0, 0, 0, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 7, 5, 7, 5, 3, 1, 3, 1, 0, 0, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]] -> [[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]]\\\\n\\\\n# Test Problem:\\\\n[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 0, 0, 0, 0, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 0, 0, 0, 0, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 0, 0, 0, 0, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [5, 0, 0, 0, 0, 0, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 0, 0, 3], [4, 0, 0, 0, 0, 0, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 0, 0, 6], [3, 0, 0, 0, 0, 0, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 0, 0, 9], [2, 0, 0, 0, 0, 0, 5, 1, 2, 7, 3, 8, 4, 0, 0, 0, 0, 0, 0, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 0, 0, 0, 0, 0, 0, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 0, 0, 0, 0, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 0, 0, 0, 0, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 0, 0, 0, 0, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 0, 0, 0, 0, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]] -> \\\", \\\"answer\\\": \\\"[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "e6b921ed-6fd4-49e2-b63d-272f1d5c43c0"}
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[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]]
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{"id": "e6b921ed-6fd4-49e2-b63d-272f1d5c43c0", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 0, 0, 0, 0, 0, 0, 5, 3, 1, 1, 5, 3, 1, 1, 0, 0, 0, 0, 0, 3, 1, 1, 5, 3], [3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 1, 1, 3, 3, 3], [5, 1, 3, 0, 0, 0, 0, 0, 0, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 0, 0, 0, 0, 0, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 0, 0, 0, 0, 0, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 0, 0, 0, 0, 0, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [0, 0, 0, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]] -> [[5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1], [5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1, 5, 1, 5, 3, 1, 5, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3, 5, 1, 3, 5, 1, 5, 1, 3], [1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 5, 3], [3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3]]\n\nExample 2:\n[[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 0, 0, 0, 0, 0, 0, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 0, 0, 0, 0, 0, 0, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 0, 0, 0, 0, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [3, 7, 0, 0, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 0, 0, 0, 0, 7, 4], [7, 6, 0, 0, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 0, 0, 0, 0, 6, 5], [4, 5, 0, 0, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 0, 0, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 0, 0, 0, 0, 0, 0, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 0, 0, 0, 0, 0, 0, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 0, 0, 0, 0, 0, 0, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]] -> [[3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6], [1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7, 3, 6, 2, 5, 1, 1, 4, 7], [3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5, 6, 5, 6, 7, 1, 3, 4, 5], [7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6, 2, 6, 2, 5, 1, 7, 3, 6], [4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7, 5, 7, 5, 3, 1, 4, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4, 1, 3, 7, 4], [7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5, 4, 4, 3, 2, 1, 7, 6, 5], [4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6, 7, 5, 6, 7, 1, 4, 5, 6]]\n\nExample 3:\n[[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 0, 0, 0, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 0, 0, 0, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 0, 0, 0, 0, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 0, 0, 0, 7, 1, 3], [0, 0, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 0, 0, 0, 5, 1, 5], [0, 0, 7, 5, 7, 5, 3, 1, 3, 1, 0, 0, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 0, 0, 0, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]] -> [[3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3], [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7, 5, 7, 5, 3, 1, 3, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3, 5, 3, 5, 7, 1, 7, 1, 3]]\n\n# Test Problem:\n[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 0, 0, 0, 0, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 0, 0, 0, 0, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 0, 0, 0, 0, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [5, 0, 0, 0, 0, 0, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 0, 0, 3], [4, 0, 0, 0, 0, 0, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 0, 0, 6], [3, 0, 0, 0, 0, 0, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 0, 0, 9], [2, 0, 0, 0, 0, 0, 5, 1, 2, 7, 3, 8, 4, 0, 0, 0, 0, 0, 0, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 0, 0, 0, 0, 0, 0, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 0, 0, 0, 0, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 0, 0, 0, 0, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 0, 0, 0, 0, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 0, 0, 0, 0, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]] -> ", "answer": "[[5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9], [2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3, 8, 4, 9, 5, 1, 2, 7, 3], [4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1, 4, 1, 4, 7, 1, 4, 7, 1], [3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4, 9, 4, 9, 5, 1, 3, 8, 4], [2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7, 5, 7, 5, 3, 1, 2, 9, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3, 2, 4, 3, 2, 1, 5, 4, 3], [4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6, 7, 7, 8, 9, 1, 4, 5, 6], [3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9, 3, 1, 4, 7, 1, 3, 6, 9]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[9, 8, 8, 8, 9], [8, 8, 2, 8, 8], [8, 2, 2, 2, 8], [8, 8, 2, 8, 8], [9, 8, 8, 8, 9]] -> [[9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [8, 2, 2, 2, 8, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [9, 9, 9, 9, 9, 2, 2, 8, 9, 2], [2, 2, 2, 2, 2, 2, 8, 8, 9, 2], [8, 8, 8, 8, 8, 8, 8, 9, 9, 2], [9, 9, 9, 9, 9, 9, 9, 9, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8]]
Example 2:
[[2, 3, 3, 3, 2], [3, 3, 5, 3, 3], [3, 5, 5, 5, 3], [3, 3, 5, 3, 3], [2, 3, 3, 3, 2]] -> [[2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [3, 5, 5, 5, 3, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [2, 2, 2, 2, 2, 5, 5, 3, 2, 5], [5, 5, 5, 5, 5, 5, 3, 3, 2, 5], [3, 3, 3, 3, 3, 3, 3, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 3]]
# Test Problem:
[[5, 1, 1, 1, 5], [1, 1, 9, 1, 1], [1, 9, 9, 9, 1], [1, 1, 9, 1, 1], [5, 1, 1, 1, 5]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[9, 8, 8, 8, 9], [8, 8, 2, 8, 8], [8, 2, 2, 2, 8], [8, 8, 2, 8, 8], [9, 8, 8, 8, 9]] -> [[9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [8, 2, 2, 2, 8, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [9, 9, 9, 9, 9, 2, 2, 8, 9, 2], [2, 2, 2, 2, 2, 2, 8, 8, 9, 2], [8, 8, 8, 8, 8, 8, 8, 9, 9, 2], [9, 9, 9, 9, 9, 9, 9, 9, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8]]\\n\\nExample 2:\\n[[2, 3, 3, 3, 2], [3, 3, 5, 3, 3], [3, 5, 5, 5, 3], [3, 3, 5, 3, 3], [2, 3, 3, 3, 2]] -> [[2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [3, 5, 5, 5, 3, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [2, 2, 2, 2, 2, 5, 5, 3, 2, 5], [5, 5, 5, 5, 5, 5, 3, 3, 2, 5], [3, 3, 3, 3, 3, 3, 3, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 3]]\\n\\n# Test Problem:\\n[[5, 1, 1, 1, 5], [1, 1, 9, 1, 1], [1, 9, 9, 9, 1], [1, 1, 9, 1, 1], [5, 1, 1, 1, 5]] -> \", \"answer\": \"[[5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [1, 9, 9, 9, 1, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [5, 5, 5, 5, 5, 9, 9, 1, 5, 9], [9, 9, 9, 9, 9, 9, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 1, 5, 5, 9], [5, 5, 5, 5, 5, 5, 5, 5, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"0e04a9a2-59ed-4a83-a403-cd0968d63b15\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[9, 8, 8, 8, 9], [8, 8, 2, 8, 8], [8, 2, 2, 2, 8], [8, 8, 2, 8, 8], [9, 8, 8, 8, 9]] -> [[9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [8, 2, 2, 2, 8, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [9, 9, 9, 9, 9, 2, 2, 8, 9, 2], [2, 2, 2, 2, 2, 2, 8, 8, 9, 2], [8, 8, 8, 8, 8, 8, 8, 9, 9, 2], [9, 9, 9, 9, 9, 9, 9, 9, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8]]\\\\n\\\\nExample 2:\\\\n[[2, 3, 3, 3, 2], [3, 3, 5, 3, 3], [3, 5, 5, 5, 3], [3, 3, 5, 3, 3], [2, 3, 3, 3, 2]] -> [[2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [3, 5, 5, 5, 3, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [2, 2, 2, 2, 2, 5, 5, 3, 2, 5], [5, 5, 5, 5, 5, 5, 3, 3, 2, 5], [3, 3, 3, 3, 3, 3, 3, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 3]]\\\\n\\\\n# Test Problem:\\\\n[[5, 1, 1, 1, 5], [1, 1, 9, 1, 1], [1, 9, 9, 9, 1], [1, 1, 9, 1, 1], [5, 1, 1, 1, 5]] -> \\\", \\\"answer\\\": \\\"[[5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [1, 9, 9, 9, 1, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [5, 5, 5, 5, 5, 9, 9, 1, 5, 9], [9, 9, 9, 9, 9, 9, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 1, 5, 5, 9], [5, 5, 5, 5, 5, 5, 5, 5, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "0e04a9a2-59ed-4a83-a403-cd0968d63b15"}
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[[5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [1, 9, 9, 9, 1, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [5, 5, 5, 5, 5, 9, 9, 1, 5, 9], [9, 9, 9, 9, 9, 9, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 1, 5, 5, 9], [5, 5, 5, 5, 5, 5, 5, 5, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]
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{"id": "0e04a9a2-59ed-4a83-a403-cd0968d63b15", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[9, 8, 8, 8, 9], [8, 8, 2, 8, 8], [8, 2, 2, 2, 8], [8, 8, 2, 8, 8], [9, 8, 8, 8, 9]] -> [[9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [8, 2, 2, 2, 8, 9, 2, 8, 9, 2], [8, 8, 2, 8, 8, 9, 2, 8, 9, 2], [9, 8, 8, 8, 9, 9, 2, 8, 9, 2], [9, 9, 9, 9, 9, 2, 2, 8, 9, 2], [2, 2, 2, 2, 2, 2, 8, 8, 9, 2], [8, 8, 8, 8, 8, 8, 8, 9, 9, 2], [9, 9, 9, 9, 9, 9, 9, 9, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8]]\n\nExample 2:\n[[2, 3, 3, 3, 2], [3, 3, 5, 3, 3], [3, 5, 5, 5, 3], [3, 3, 5, 3, 3], [2, 3, 3, 3, 2]] -> [[2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [3, 5, 5, 5, 3, 2, 5, 3, 2, 5], [3, 3, 5, 3, 3, 2, 5, 3, 2, 5], [2, 3, 3, 3, 2, 2, 5, 3, 2, 5], [2, 2, 2, 2, 2, 5, 5, 3, 2, 5], [5, 5, 5, 5, 5, 5, 3, 3, 2, 5], [3, 3, 3, 3, 3, 3, 3, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 3]]\n\n# Test Problem:\n[[5, 1, 1, 1, 5], [1, 1, 9, 1, 1], [1, 9, 9, 9, 1], [1, 1, 9, 1, 1], [5, 1, 1, 1, 5]] -> ", "answer": "[[5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [1, 9, 9, 9, 1, 5, 9, 1, 5, 9], [1, 1, 9, 1, 1, 5, 9, 1, 5, 9], [5, 1, 1, 1, 5, 5, 9, 1, 5, 9], [5, 5, 5, 5, 5, 9, 9, 1, 5, 9], [9, 9, 9, 9, 9, 9, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 1, 5, 5, 9], [5, 5, 5, 5, 5, 5, 5, 5, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
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grid
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symbolic_hard
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Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples.
Please output your answer within a code block (```), formatted as a grid of numbers.
# Examples
Example 1:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 1, 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, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 0, 7, 1, 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, 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]]
Example 2:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 6, 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, 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, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 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, 0, 0, 0]]
Example 3:
[[8, 0, 0, 0, 0, 0, 0, 9, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 6, 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, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 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, 0, 0, 0]]
# Test Problem:
[[6, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 9, 0, 0, 7, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 2, 0, 0, 6, 0], [7, 0, 0, 0, 0, 0, 0, 8, 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, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0]] ->
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{"ground_truth": "{\"prompt\": \"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\n\\n# Examples\\n\\nExample 1:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 1, 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, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 0, 7, 1, 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, 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\\nExample 2:\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 6, 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, 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, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 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, 0, 0, 0]]\\n\\nExample 3:\\n[[8, 0, 0, 0, 0, 0, 0, 9, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 6, 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, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 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, 0, 0, 0]]\\n\\n# Test Problem:\\n[[6, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 9, 0, 0, 7, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 2, 0, 0, 6, 0], [7, 0, 0, 0, 0, 0, 0, 8, 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, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0]] -> \", \"answer\": \"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 9, 7, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 2, 6, 0, 0], [0, 7, 7, 7, 8, 8, 8, 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, 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, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\", \"task_name\": \"symbolic_hard\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"3b08abee-4b3d-4395-b49c-b8b5c361ff0c\\\", \\\"question\\\": \\\"Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \\\\nPlease output your answer within a code block (```), formatted as a grid of numbers.\\\\n\\\\n# Examples\\\\n\\\\nExample 1:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 1, 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, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 0, 7, 1, 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, 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\\\\nExample 2:\\\\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 6, 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, 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, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 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, 0, 0, 0]]\\\\n\\\\nExample 3:\\\\n[[8, 0, 0, 0, 0, 0, 0, 9, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 6, 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, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 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, 0, 0, 0]]\\\\n\\\\n# Test Problem:\\\\n[[6, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 9, 0, 0, 7, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 2, 0, 0, 6, 0], [7, 0, 0, 0, 0, 0, 0, 8, 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, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0]] -> \\\", \\\"answer\\\": \\\"[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 9, 7, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 2, 6, 0, 0], [0, 7, 7, 7, 8, 8, 8, 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, 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, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\\\", \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"logic_puzzle\\\", \\\"source_url\\\": \\\"human_collect\\\", \\\"dataset_name\\\": \\\"symbolic_hard\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "grid"}
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PUZZLE##symbolic_hard
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PUZZLE
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{"index": "3b08abee-4b3d-4395-b49c-b8b5c361ff0c"}
|
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 9, 7, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 2, 6, 0, 0], [0, 7, 7, 7, 8, 8, 8, 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, 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, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
|
{"id": "3b08abee-4b3d-4395-b49c-b8b5c361ff0c", "question": "Figure out the pattern in the following examples and apply it to the test case. Your answer must follow the format of the examples. \nPlease output your answer within a code block (```), formatted as a grid of numbers.\n\n# Examples\n\nExample 1:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 1, 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, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 2, 0, 0, 0, 0, 0, 0], [0, 0, 7, 1, 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, 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\nExample 2:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 6, 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, 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, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 3, 3, 4, 4, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 0, 0, 0], [0, 0, 0, 8, 8, 6, 6, 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, 0, 0, 0]]\n\nExample 3:\n[[8, 0, 0, 0, 0, 0, 0, 9, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 6, 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, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 8, 8, 8, 9, 9, 9, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 0, 0, 0], [0, 7, 7, 7, 6, 6, 6, 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, 0, 0, 0]]\n\n# Test Problem:\n[[6, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 9, 0, 0, 7, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 0, 0], [0, 5, 5, 5, 5, 5, 5, 0, 0, 0, 2, 0, 0, 6, 0], [7, 0, 0, 0, 0, 0, 0, 8, 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, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0]] -> ", "answer": "[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 9, 7, 0, 0], [0, 7, 7, 7, 8, 8, 8, 0, 0, 0, 0, 2, 6, 0, 0], [0, 7, 7, 7, 8, 8, 8, 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, 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, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]", "rationale": "", "split": "test", "type": "logic_puzzle", "source_url": "human_collect", "dataset_name": "symbolic_hard", "difficulty_level": "hard", "language": "en"}
|
grid
|
symbolic_hard
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | X |
---------
| | O
---------
X | X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | X | \\n---------\\n | | O\\n---------\\nX | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"\"], [\"\", \"X\", \"O\"], [\"X\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_407\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | X | \\\\n---------\\\\n | | O\\\\n---------\\\\nX | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_407"}
|
[['O', 'X', ''], ['', 'X', 'O'], ['X', 'X', 'O']]
|
{"id": "ttt_hard_407", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | X | \n---------\n | | O\n---------\nX | X | O\n\n\n", "current_board": [["O", "X", ""], ["", "", "O"], ["X", "X", "O"]], "active_player": "X", "answer": [["O", "X", ""], ["", "X", "O"], ["X", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| |
---------
O | | X
---------
O | X | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | | \\n---------\\nO | | X\\n---------\\nO | X | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"\", \"\"], [\"O\", \"\", \"X\"], [\"O\", \"X\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_168\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | | \\\\n---------\\\\nO | | X\\\\n---------\\\\nO | X | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_168"}
|
[['O', '', ''], ['O', '', 'X'], ['O', 'X', 'X']]
|
{"id": "ttt_hard_168", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | | \n---------\nO | | X\n---------\nO | X | X\n\n\n", "current_board": [["", "", ""], ["O", "", "X"], ["O", "X", "X"]], "active_player": "O", "answer": [["O", "", ""], ["O", "", "X"], ["O", "X", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | O | X
---------
X | O |
---------
O | X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | O | X\\n---------\\nX | O | \\n---------\\nO | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"X\"], [\"X\", \"O\", \"X\"], [\"O\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_739\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | O | X\\\\n---------\\\\nX | O | \\\\n---------\\\\nO | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_739"}
|
[['X', 'O', 'X'], ['X', 'O', 'X'], ['O', 'X', 'O']]
|
{"id": "ttt_hard_739", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | O | X\n---------\nX | O | \n---------\nO | X | O\n\n\n", "current_board": [["X", "O", "X"], ["X", "O", ""], ["O", "X", "O"]], "active_player": "X", "answer": [["X", "O", "X"], ["X", "O", "X"], ["O", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | O |
---------
| X |
---------
X | X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | O | \\n---------\\n | X | \\n---------\\nX | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"\", \"X\", \"\"], [\"X\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_492\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | O | \\\\n---------\\\\n | X | \\\\n---------\\\\nX | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_492"}
|
[['O', 'O', 'X'], ['', 'X', ''], ['X', 'X', 'O']]
|
{"id": "ttt_hard_492", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | O | \n---------\n | X | \n---------\nX | X | O\n\n\n", "current_board": [["O", "O", ""], ["", "X", ""], ["X", "X", "O"]], "active_player": "X", "answer": [["O", "O", "X"], ["", "X", ""], ["X", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | |
---------
| O | O
---------
X | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | | \\n---------\\n | O | O\\n---------\\nX | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"\"], [\"O\", \"O\", \"O\"], [\"X\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_542\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | | \\\\n---------\\\\n | O | O\\\\n---------\\\\nX | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_542"}
|
[['X', '', ''], ['O', 'O', 'O'], ['X', '', 'X']]
|
{"id": "ttt_hard_542", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | | \n---------\n | O | O\n---------\nX | | X\n\n\n", "current_board": [["X", "", ""], ["", "O", "O"], ["X", "", "X"]], "active_player": "O", "answer": [["X", "", ""], ["O", "O", "O"], ["X", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | X | O
---------
X | O | X
---------
X | O |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | X | O\\n---------\\nX | O | X\\n---------\\nX | O | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"O\"], [\"X\", \"O\", \"X\"], [\"X\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_974\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | X | O\\\\n---------\\\\nX | O | X\\\\n---------\\\\nX | O | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_974"}
|
[['O', 'X', 'O'], ['X', 'O', 'X'], ['X', 'O', 'X']]
|
{"id": "ttt_hard_974", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | X | O\n---------\nX | O | X\n---------\nX | O | \n\n\n", "current_board": [["O", "X", "O"], ["X", "O", "X"], ["X", "O", ""]], "active_player": "X", "answer": [["O", "X", "O"], ["X", "O", "X"], ["X", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
O | O | X
---------
X | |
---------
| X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nO | O | X\\n---------\\nX | | \\n---------\\n | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"X\", \"O\", \"\"], [\"\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_993\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nO | O | X\\\\n---------\\\\nX | | \\\\n---------\\\\n | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_993"}
|
[['O', 'O', 'X'], ['X', 'O', ''], ['', 'X', '']]
|
{"id": "ttt_hard_993", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nO | O | X\n---------\nX | | \n---------\n | X | \n\n\n", "current_board": [["O", "O", "X"], ["X", "", ""], ["", "X", ""]], "active_player": "O", "answer": [["O", "O", "X"], ["X", "O", ""], ["", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | X | O
---------
X | O | O
---------
X | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | X | O\\n---------\\nX | O | O\\n---------\\nX | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"O\"], [\"X\", \"O\", \"O\"], [\"X\", \"X\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_600\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | X | O\\\\n---------\\\\nX | O | O\\\\n---------\\\\nX | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_600"}
|
[['O', 'X', 'O'], ['X', 'O', 'O'], ['X', 'X', 'X']]
|
{"id": "ttt_hard_600", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | X | O\n---------\nX | O | O\n---------\nX | | X\n\n\n", "current_board": [["O", "X", "O"], ["X", "O", "O"], ["X", "", "X"]], "active_player": "X", "answer": [["O", "X", "O"], ["X", "O", "O"], ["X", "X", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| |
---------
X | | X
---------
O | | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | | \\n---------\\nX | | X\\n---------\\nO | | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"\", \"\"], [\"X\", \"X\", \"X\"], [\"O\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_471\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | | \\\\n---------\\\\nX | | X\\\\n---------\\\\nO | | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_471"}
|
[['', '', ''], ['X', 'X', 'X'], ['O', '', 'O']]
|
{"id": "ttt_hard_471", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | | \n---------\nX | | X\n---------\nO | | O\n\n\n", "current_board": [["", "", ""], ["X", "", "X"], ["O", "", "O"]], "active_player": "X", "answer": [["", "", ""], ["X", "X", "X"], ["O", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | | X
---------
X | | O
---------
O | | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | | X\\n---------\\nX | | O\\n---------\\nO | | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"X\", \"X\"], [\"X\", \"\", \"O\"], [\"O\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_805\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | | X\\\\n---------\\\\nX | | O\\\\n---------\\\\nO | | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_805"}
|
[['X', 'X', 'X'], ['X', '', 'O'], ['O', '', 'O']]
|
{"id": "ttt_hard_805", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | | X\n---------\nX | | O\n---------\nO | | O\n\n\n", "current_board": [["X", "", "X"], ["X", "", "O"], ["O", "", "O"]], "active_player": "X", "answer": [["X", "X", "X"], ["X", "", "O"], ["O", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | O |
---------
| X | O
---------
X | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | O | \\n---------\\n | X | O\\n---------\\nX | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"\", \"X\", \"O\"], [\"X\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_562\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | O | \\\\n---------\\\\n | X | O\\\\n---------\\\\nX | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_562"}
|
[['O', 'O', 'X'], ['', 'X', 'O'], ['X', '', 'X']]
|
{"id": "ttt_hard_562", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | O | \n---------\n | X | O\n---------\nX | | X\n\n\n", "current_board": [["O", "O", ""], ["", "X", "O"], ["X", "", "X"]], "active_player": "X", "answer": [["O", "O", "X"], ["", "X", "O"], ["X", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | | X
---------
X | O | O
---------
O | X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | | X\\n---------\\nX | O | O\\n---------\\nO | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"X\"], [\"X\", \"O\", \"O\"], [\"O\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_183\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | | X\\\\n---------\\\\nX | O | O\\\\n---------\\\\nO | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"O\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"O\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_183"}
|
[['X', 'O', 'X'], ['X', 'O', 'O'], ['O', 'X', '']]
|
{"id": "ttt_hard_183", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | | X\n---------\nX | O | O\n---------\nO | X | \n\n\n", "current_board": [["X", "", "X"], ["X", "O", "O"], ["O", "X", ""]], "active_player": "O", "answer": [["X", "O", "X"], ["X", "O", "O"], ["O", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| X | X
---------
O | O | X
---------
X | | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | X | X\\n---------\\nO | O | X\\n---------\\nX | | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"X\"], [\"O\", \"O\", \"X\"], [\"X\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_53\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | X | X\\\\n---------\\\\nO | O | X\\\\n---------\\\\nX | | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"X\\\", \\\"X\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"X\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_53"}
|
[['O', 'X', 'X'], ['O', 'O', 'X'], ['X', '', 'O']]
|
{"id": "ttt_hard_53", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | X | X\n---------\nO | O | X\n---------\nX | | O\n\n\n", "current_board": [["", "X", "X"], ["O", "O", "X"], ["X", "", "O"]], "active_player": "O", "answer": [["O", "X", "X"], ["O", "O", "X"], ["X", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | X |
---------
O | O |
---------
| |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | X | \\n---------\\nO | O | \\n---------\\n | | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"X\", \"X\"], [\"O\", \"O\", \"\"], [\"\", \"\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_433\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | X | \\\\n---------\\\\nO | O | \\\\n---------\\\\n | | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"O\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_433"}
|
[['X', 'X', 'X'], ['O', 'O', ''], ['', '', '']]
|
{"id": "ttt_hard_433", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | X | \n---------\nO | O | \n---------\n | | \n\n\n", "current_board": [["X", "X", ""], ["O", "O", ""], ["", "", ""]], "active_player": "X", "answer": [["X", "X", "X"], ["O", "O", ""], ["", "", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| |
---------
| X |
---------
X | O | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | | \\n---------\\n | X | \\n---------\\nX | O | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"\"], [\"\", \"X\", \"\"], [\"X\", \"O\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_726\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | | \\\\n---------\\\\n | X | \\\\n---------\\\\nX | O | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_726"}
|
[['X', '', ''], ['', 'X', ''], ['X', 'O', 'O']]
|
{"id": "ttt_hard_726", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | | \n---------\n | X | \n---------\nX | O | O\n\n\n", "current_board": [["", "", ""], ["", "X", ""], ["X", "O", "O"]], "active_player": "X", "answer": [["X", "", ""], ["", "X", ""], ["X", "O", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | | X
---------
X | O | O
---------
O | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | | X\\n---------\\nX | O | O\\n---------\\nO | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"X\"], [\"X\", \"O\", \"O\"], [\"O\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_202\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | | X\\\\n---------\\\\nX | O | O\\\\n---------\\\\nO | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_202"}
|
[['X', 'O', 'X'], ['X', 'O', 'O'], ['O', '', 'X']]
|
{"id": "ttt_hard_202", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | | X\n---------\nX | O | O\n---------\nO | | X\n\n\n", "current_board": [["X", "", "X"], ["X", "O", "O"], ["O", "", "X"]], "active_player": "O", "answer": [["X", "O", "X"], ["X", "O", "O"], ["O", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| O | O
---------
X | | X
---------
| O | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | O | O\\n---------\\nX | | X\\n---------\\n | O | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"O\", \"O\"], [\"X\", \"X\", \"X\"], [\"\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_185\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | O | O\\\\n---------\\\\nX | | X\\\\n---------\\\\n | O | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_185"}
|
[['', 'O', 'O'], ['X', 'X', 'X'], ['', 'O', 'X']]
|
{"id": "ttt_hard_185", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | O | O\n---------\nX | | X\n---------\n | O | X\n\n\n", "current_board": [["", "O", "O"], ["X", "", "X"], ["", "O", "X"]], "active_player": "X", "answer": [["", "O", "O"], ["X", "X", "X"], ["", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | X | O
---------
O | | X
---------
| X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | X | O\\n---------\\nO | | X\\n---------\\n | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"X\", \"O\"], [\"O\", \"O\", \"X\"], [\"\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_744\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | X | O\\\\n---------\\\\nO | | X\\\\n---------\\\\n | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_744"}
|
[['X', 'X', 'O'], ['O', 'O', 'X'], ['', 'X', 'O']]
|
{"id": "ttt_hard_744", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | X | O\n---------\nO | | X\n---------\n | X | O\n\n\n", "current_board": [["X", "X", "O"], ["O", "", "X"], ["", "X", "O"]], "active_player": "O", "answer": [["X", "X", "O"], ["O", "O", "X"], ["", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| X | X
---------
| |
---------
O | O | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | X | X\\n---------\\n | | \\n---------\\nO | O | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"X\"], [\"\", \"\", \"\"], [\"O\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_797\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | X | X\\\\n---------\\\\n | | \\\\n---------\\\\nO | O | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_797"}
|
[['O', 'X', 'X'], ['', '', ''], ['O', 'O', 'X']]
|
{"id": "ttt_hard_797", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | X | X\n---------\n | | \n---------\nO | O | X\n\n\n", "current_board": [["", "X", "X"], ["", "", ""], ["O", "O", "X"]], "active_player": "O", "answer": [["O", "X", "X"], ["", "", ""], ["O", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
O | |
---------
X | X | O
---------
X | |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nO | | \\n---------\\nX | X | O\\n---------\\nX | | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"\", \"O\"], [\"X\", \"X\", \"O\"], [\"X\", \"\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_888\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nO | | \\\\n---------\\\\nX | X | O\\\\n---------\\\\nX | | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_888"}
|
[['O', '', 'O'], ['X', 'X', 'O'], ['X', '', '']]
|
{"id": "ttt_hard_888", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nO | | \n---------\nX | X | O\n---------\nX | | \n\n\n", "current_board": [["O", "", ""], ["X", "X", "O"], ["X", "", ""]], "active_player": "O", "answer": [["O", "", "O"], ["X", "X", "O"], ["X", "", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | |
---------
O | | X
---------
| O | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | | \\n---------\\nO | | X\\n---------\\n | O | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"\"], [\"O\", \"\", \"X\"], [\"\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_128\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | | \\\\n---------\\\\nO | | X\\\\n---------\\\\n | O | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_128"}
|
[['X', 'O', ''], ['O', '', 'X'], ['', 'O', 'X']]
|
{"id": "ttt_hard_128", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | | \n---------\nO | | X\n---------\n | O | X\n\n\n", "current_board": [["X", "", ""], ["O", "", "X"], ["", "O", "X"]], "active_player": "O", "answer": [["X", "O", ""], ["O", "", "X"], ["", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
O | | X
---------
X | X |
---------
| | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nO | | X\\n---------\\nX | X | \\n---------\\n | | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"X\", \"X\", \"\"], [\"\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_712\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nO | | X\\\\n---------\\\\nX | X | \\\\n---------\\\\n | | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_712"}
|
[['O', 'O', 'X'], ['X', 'X', ''], ['', '', 'O']]
|
{"id": "ttt_hard_712", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nO | | X\n---------\nX | X | \n---------\n | | O\n\n\n", "current_board": [["O", "", "X"], ["X", "X", ""], ["", "", "O"]], "active_player": "O", "answer": [["O", "O", "X"], ["X", "X", ""], ["", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| X | O
---------
| |
---------
X | X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | X | O\\n---------\\n | | \\n---------\\nX | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"X\", \"O\"], [\"\", \"O\", \"\"], [\"X\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_804\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | X | O\\\\n---------\\\\n | | \\\\n---------\\\\nX | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_804"}
|
[['', 'X', 'O'], ['', 'O', ''], ['X', 'X', 'O']]
|
{"id": "ttt_hard_804", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | X | O\n---------\n | | \n---------\nX | X | O\n\n\n", "current_board": [["", "X", "O"], ["", "", ""], ["X", "X", "O"]], "active_player": "O", "answer": [["", "X", "O"], ["", "O", ""], ["X", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | | O
---------
| X |
---------
| X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | | O\\n---------\\n | X | \\n---------\\n | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"O\"], [\"\", \"X\", \"\"], [\"\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_634\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | | O\\\\n---------\\\\n | X | \\\\n---------\\\\n | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_634"}
|
[['O', 'X', 'O'], ['', 'X', ''], ['', 'X', '']]
|
{"id": "ttt_hard_634", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | | O\n---------\n | X | \n---------\n | X | \n\n\n", "current_board": [["O", "", "O"], ["", "X", ""], ["", "X", ""]], "active_player": "X", "answer": [["O", "X", "O"], ["", "X", ""], ["", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | X |
---------
X | |
---------
O | O | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | X | \\n---------\\nX | | \\n---------\\nO | O | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"\"], [\"X\", \"\", \"X\"], [\"O\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_186\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | X | \\\\n---------\\\\nX | | \\\\n---------\\\\nO | O | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"X\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_186"}
|
[['O', 'X', ''], ['X', '', 'X'], ['O', 'O', 'X']]
|
{"id": "ttt_hard_186", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | X | \n---------\nX | | \n---------\nO | O | X\n\n\n", "current_board": [["O", "X", ""], ["X", "", ""], ["O", "O", "X"]], "active_player": "X", "answer": [["O", "X", ""], ["X", "", "X"], ["O", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | O | X
---------
X | X | O
---------
| O |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | O | X\\n---------\\nX | X | O\\n---------\\n | O | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"X\"], [\"X\", \"X\", \"O\"], [\"O\", \"O\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_701\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | O | X\\\\n---------\\\\nX | X | O\\\\n---------\\\\n | O | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"O\\\", \\\"O\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_701"}
|
[['X', 'O', 'X'], ['X', 'X', 'O'], ['O', 'O', '']]
|
{"id": "ttt_hard_701", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | O | X\n---------\nX | X | O\n---------\n | O | \n\n\n", "current_board": [["X", "O", "X"], ["X", "X", "O"], ["", "O", ""]], "active_player": "O", "answer": [["X", "O", "X"], ["X", "X", "O"], ["O", "O", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | O | X
---------
| X |
---------
O | X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | O | X\\n---------\\n | X | \\n---------\\nO | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"X\"], [\"O\", \"X\", \"\"], [\"O\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_606\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | O | X\\\\n---------\\\\n | X | \\\\n---------\\\\nO | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"O\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_606"}
|
[['X', 'O', 'X'], ['O', 'X', ''], ['O', 'X', 'O']]
|
{"id": "ttt_hard_606", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | O | X\n---------\n | X | \n---------\nO | X | O\n\n\n", "current_board": [["X", "O", "X"], ["", "X", ""], ["O", "X", "O"]], "active_player": "O", "answer": [["X", "O", "X"], ["O", "X", ""], ["O", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| O | O
---------
| X | X
---------
| X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | O | O\\n---------\\n | X | X\\n---------\\n | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"O\", \"O\"], [\"X\", \"X\", \"X\"], [\"\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_456\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | O | O\\\\n---------\\\\n | X | X\\\\n---------\\\\n | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"O\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"\\\", \\\"O\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_456"}
|
[['', 'O', 'O'], ['X', 'X', 'X'], ['', 'X', 'O']]
|
{"id": "ttt_hard_456", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | O | O\n---------\n | X | X\n---------\n | X | O\n\n\n", "current_board": [["", "O", "O"], ["", "X", "X"], ["", "X", "O"]], "active_player": "X", "answer": [["", "O", "O"], ["X", "X", "X"], ["", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | | O
---------
X | X |
---------
| O | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | | O\\n---------\\nX | X | \\n---------\\n | O | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"O\"], [\"X\", \"X\", \"X\"], [\"\", \"O\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_528\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | | O\\\\n---------\\\\nX | X | \\\\n---------\\\\n | O | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"], [\\\"\\\", \\\"O\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_528"}
|
[['X', '', 'O'], ['X', 'X', 'X'], ['', 'O', 'O']]
|
{"id": "ttt_hard_528", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | | O\n---------\nX | X | \n---------\n | O | O\n\n\n", "current_board": [["X", "", "O"], ["X", "X", ""], ["", "O", "O"]], "active_player": "X", "answer": [["X", "", "O"], ["X", "X", "X"], ["", "O", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| | X
---------
O | | X
---------
| |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | | X\\n---------\\nO | | X\\n---------\\n | | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"\", \"X\"], [\"O\", \"\", \"X\"], [\"\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_654\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | | X\\\\n---------\\\\nO | | X\\\\n---------\\\\n | | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_654"}
|
[['', '', 'X'], ['O', '', 'X'], ['', '', 'O']]
|
{"id": "ttt_hard_654", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | | X\n---------\nO | | X\n---------\n | | \n\n\n", "current_board": [["", "", "X"], ["O", "", "X"], ["", "", ""]], "active_player": "O", "answer": [["", "", "X"], ["O", "", "X"], ["", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | | X
---------
| O |
---------
| | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | | X\\n---------\\n | O | \\n---------\\n | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"\", \"X\"], [\"\", \"O\", \"X\"], [\"\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_220\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | | X\\\\n---------\\\\n | O | \\\\n---------\\\\n | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_220"}
|
[['O', '', 'X'], ['', 'O', 'X'], ['', '', 'X']]
|
{"id": "ttt_hard_220", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | | X\n---------\n | O | \n---------\n | | X\n\n\n", "current_board": [["O", "", "X"], ["", "O", ""], ["", "", "X"]], "active_player": "X", "answer": [["O", "", "X"], ["", "O", "X"], ["", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| | X
---------
O | |
---------
| O | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | | X\\n---------\\nO | | \\n---------\\n | O | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"X\"], [\"O\", \"\", \"\"], [\"\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_208\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | | X\\\\n---------\\\\nO | | \\\\n---------\\\\n | O | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_208"}
|
[['X', '', 'X'], ['O', '', ''], ['', 'O', 'X']]
|
{"id": "ttt_hard_208", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | | X\n---------\nO | | \n---------\n | O | X\n\n\n", "current_board": [["", "", "X"], ["O", "", ""], ["", "O", "X"]], "active_player": "X", "answer": [["X", "", "X"], ["O", "", ""], ["", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| O | X
---------
| O |
---------
X | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | O | X\\n---------\\n | O | \\n---------\\nX | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"O\", \"X\"], [\"\", \"O\", \"\"], [\"X\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_767\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | O | X\\\\n---------\\\\n | O | \\\\n---------\\\\nX | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"X\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_767"}
|
[['', 'O', 'X'], ['', 'O', ''], ['X', 'O', 'X']]
|
{"id": "ttt_hard_767", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | O | X\n---------\n | O | \n---------\nX | | X\n\n\n", "current_board": [["", "O", "X"], ["", "O", ""], ["X", "", "X"]], "active_player": "O", "answer": [["", "O", "X"], ["", "O", ""], ["X", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
O | | X
---------
X | X |
---------
O | O | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nO | | X\\n---------\\nX | X | \\n---------\\nO | O | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"\", \"X\"], [\"X\", \"X\", \"O\"], [\"O\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_273\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nO | | X\\\\n---------\\\\nX | X | \\\\n---------\\\\nO | O | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_273"}
|
[['O', '', 'X'], ['X', 'X', 'O'], ['O', 'O', 'X']]
|
{"id": "ttt_hard_273", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nO | | X\n---------\nX | X | \n---------\nO | O | X\n\n\n", "current_board": [["O", "", "X"], ["X", "X", ""], ["O", "O", "X"]], "active_player": "O", "answer": [["O", "", "X"], ["X", "X", "O"], ["O", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | |
---------
O | |
---------
X | X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | | \\n---------\\nO | | \\n---------\\nX | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"\"], [\"O\", \"\", \"\"], [\"X\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_139\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | | \\\\n---------\\\\nO | | \\\\n---------\\\\nX | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_139"}
|
[['O', 'X', ''], ['O', '', ''], ['X', 'X', '']]
|
{"id": "ttt_hard_139", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | | \n---------\nO | | \n---------\nX | X | \n\n\n", "current_board": [["O", "", ""], ["O", "", ""], ["X", "X", ""]], "active_player": "X", "answer": [["O", "X", ""], ["O", "", ""], ["X", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| | O
---------
| X | O
---------
| X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | | O\\n---------\\n | X | O\\n---------\\n | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"X\", \"O\"], [\"\", \"X\", \"O\"], [\"\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_463\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | | O\\\\n---------\\\\n | X | O\\\\n---------\\\\n | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_463"}
|
[['', 'X', 'O'], ['', 'X', 'O'], ['', 'X', '']]
|
{"id": "ttt_hard_463", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | | O\n---------\n | X | O\n---------\n | X | \n\n\n", "current_board": [["", "", "O"], ["", "X", "O"], ["", "X", ""]], "active_player": "X", "answer": [["", "X", "O"], ["", "X", "O"], ["", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| X | X
---------
X | O |
---------
| O |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | X | X\\n---------\\nX | O | \\n---------\\n | O | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"X\", \"X\"], [\"X\", \"O\", \"\"], [\"\", \"O\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_886\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | X | X\\\\n---------\\\\nX | O | \\\\n---------\\\\n | O | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"X\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"X\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_886"}
|
[['O', 'X', 'X'], ['X', 'O', ''], ['', 'O', '']]
|
{"id": "ttt_hard_886", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | X | X\n---------\nX | O | \n---------\n | O | \n\n\n", "current_board": [["", "X", "X"], ["X", "O", ""], ["", "O", ""]], "active_player": "O", "answer": [["O", "X", "X"], ["X", "O", ""], ["", "O", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | | O
---------
| O |
---------
| X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | | O\\n---------\\n | O | \\n---------\\n | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"O\"], [\"\", \"O\", \"\"], [\"X\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_815\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | | O\\\\n---------\\\\n | O | \\\\n---------\\\\n | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"X\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_815"}
|
[['X', '', 'O'], ['', 'O', ''], ['X', 'X', '']]
|
{"id": "ttt_hard_815", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | | O\n---------\n | O | \n---------\n | X | \n\n\n", "current_board": [["X", "", "O"], ["", "O", ""], ["", "X", ""]], "active_player": "X", "answer": [["X", "", "O"], ["", "O", ""], ["X", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | O |
---------
| | O
---------
X | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | O | \\n---------\\n | | O\\n---------\\nX | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"O\"], [\"\", \"\", \"O\"], [\"X\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_172\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | O | \\\\n---------\\\\n | | O\\\\n---------\\\\nX | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"O\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_172"}
|
[['X', 'O', 'O'], ['', '', 'O'], ['X', '', 'X']]
|
{"id": "ttt_hard_172", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | O | \n---------\n | | O\n---------\nX | | X\n\n\n", "current_board": [["X", "O", ""], ["", "", "O"], ["X", "", "X"]], "active_player": "O", "answer": [["X", "O", "O"], ["", "", "O"], ["X", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| X | X
---------
| O |
---------
O | X | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | X | X\\n---------\\n | O | \\n---------\\nO | X | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"X\", \"X\"], [\"\", \"O\", \"\"], [\"O\", \"X\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_519\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | X | X\\\\n---------\\\\n | O | \\\\n---------\\\\nO | X | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_519"}
|
[['X', 'X', 'X'], ['', 'O', ''], ['O', 'X', 'O']]
|
{"id": "ttt_hard_519", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | X | X\n---------\n | O | \n---------\nO | X | O\n\n\n", "current_board": [["", "X", "X"], ["", "O", ""], ["O", "X", "O"]], "active_player": "X", "answer": [["X", "X", "X"], ["", "O", ""], ["O", "X", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | | O
---------
O | | X
---------
O | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | | O\\n---------\\nO | | X\\n---------\\nO | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"O\"], [\"O\", \"X\", \"X\"], [\"O\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_288\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | | O\\\\n---------\\\\nO | | X\\\\n---------\\\\nO | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_288"}
|
[['X', '', 'O'], ['O', 'X', 'X'], ['O', '', 'X']]
|
{"id": "ttt_hard_288", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | | O\n---------\nO | | X\n---------\nO | | X\n\n\n", "current_board": [["X", "", "O"], ["O", "", "X"], ["O", "", "X"]], "active_player": "X", "answer": [["X", "", "O"], ["O", "X", "X"], ["O", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
O | O | X
---------
X | X | O
---------
| | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nO | O | X\\n---------\\nX | X | O\\n---------\\n | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"X\", \"X\", \"O\"], [\"O\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_418\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nO | O | X\\\\n---------\\\\nX | X | O\\\\n---------\\\\n | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_418"}
|
[['O', 'O', 'X'], ['X', 'X', 'O'], ['O', '', 'X']]
|
{"id": "ttt_hard_418", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nO | O | X\n---------\nX | X | O\n---------\n | | X\n\n\n", "current_board": [["O", "O", "X"], ["X", "X", "O"], ["", "", "X"]], "active_player": "O", "answer": [["O", "O", "X"], ["X", "X", "O"], ["O", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | | O
---------
O | | X
---------
X | |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | | O\\n---------\\nO | | X\\n---------\\nX | | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"O\"], [\"O\", \"O\", \"X\"], [\"X\", \"\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_262\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | | O\\\\n---------\\\\nO | | X\\\\n---------\\\\nX | | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_262"}
|
[['X', '', 'O'], ['O', 'O', 'X'], ['X', '', '']]
|
{"id": "ttt_hard_262", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | | O\n---------\nO | | X\n---------\nX | | \n\n\n", "current_board": [["X", "", "O"], ["O", "", "X"], ["X", "", ""]], "active_player": "O", "answer": [["X", "", "O"], ["O", "O", "X"], ["X", "", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| X |
---------
O | | O
---------
| | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | X | \\n---------\\nO | | O\\n---------\\n | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"X\", \"\"], [\"O\", \"X\", \"O\"], [\"\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_786\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | X | \\\\n---------\\\\nO | | O\\\\n---------\\\\n | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"\\\", \\\"O\\\"], [\\\"\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"\\\", \\\"X\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"O\\\"], [\\\"\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_786"}
|
[['', 'X', ''], ['O', 'X', 'O'], ['', '', 'X']]
|
{"id": "ttt_hard_786", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | X | \n---------\nO | | O\n---------\n | | X\n\n\n", "current_board": [["", "X", ""], ["O", "", "O"], ["", "", "X"]], "active_player": "X", "answer": [["", "X", ""], ["O", "X", "O"], ["", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
X | | O
---------
O | X | X
---------
| O |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nX | | O\\n---------\\nO | X | X\\n---------\\n | O | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"O\"], [\"O\", \"X\", \"X\"], [\"\", \"O\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_982\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nX | | O\\\\n---------\\\\nO | X | X\\\\n---------\\\\n | O | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"O\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_982"}
|
[['X', '', 'O'], ['O', 'X', 'X'], ['', 'O', 'X']]
|
{"id": "ttt_hard_982", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nX | | O\n---------\nO | X | X\n---------\n | O | \n\n\n", "current_board": [["X", "", "O"], ["O", "X", "X"], ["", "O", ""]], "active_player": "X", "answer": [["X", "", "O"], ["O", "X", "X"], ["", "O", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | O | X
---------
| X | X
---------
| | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | O | X\\n---------\\n | X | X\\n---------\\n | | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"X\", \"X\", \"X\"], [\"\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_910\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | O | X\\\\n---------\\\\n | X | X\\\\n---------\\\\n | | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"X\\\", \\\"X\\\"], [\\\"\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_910"}
|
[['O', 'O', 'X'], ['X', 'X', 'X'], ['', '', 'O']]
|
{"id": "ttt_hard_910", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | O | X\n---------\n | X | X\n---------\n | | O\n\n\n", "current_board": [["O", "O", "X"], ["", "X", "X"], ["", "", "O"]], "active_player": "X", "answer": [["O", "O", "X"], ["X", "X", "X"], ["", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
| | O
---------
O | |
---------
X | | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\n | | O\\n---------\\nO | | \\n---------\\nX | | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"\", \"O\"], [\"O\", \"\", \"\"], [\"X\", \"\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_992\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\n | | O\\\\n---------\\\\nO | | \\\\n---------\\\\nX | | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"X\\\", \\\"\\\", \\\"O\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_992"}
|
[['X', '', 'O'], ['O', '', ''], ['X', '', 'X']]
|
{"id": "ttt_hard_992", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\n | | O\n---------\nO | | \n---------\nX | | X\n\n\n", "current_board": [["", "", "O"], ["O", "", ""], ["X", "", "X"]], "active_player": "X", "answer": [["X", "", "O"], ["O", "", ""], ["X", "", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
X | | X
---------
O | |
---------
X | | O
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\nX | | X\\n---------\\nO | | \\n---------\\nX | | O\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"X\", \"O\", \"X\"], [\"O\", \"\", \"\"], [\"X\", \"\", \"O\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_848\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\nX | | X\\\\n---------\\\\nO | | \\\\n---------\\\\nX | | O\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"X\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"O\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"X\\\", \\\"\\\", \\\"O\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_848"}
|
[['X', 'O', 'X'], ['O', '', ''], ['X', '', 'O']]
|
{"id": "ttt_hard_848", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\nX | | X\n---------\nO | | \n---------\nX | | O\n\n\n", "current_board": [["X", "", "X"], ["O", "", ""], ["X", "", "O"]], "active_player": "O", "answer": [["X", "O", "X"], ["O", "", ""], ["X", "", "O"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as X.
Current board:
O | O | X
---------
X | O |
---------
O | X | X
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as X.\\nCurrent board:\\nO | O | X\\n---------\\nX | O | \\n---------\\nO | X | X\\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"O\", \"O\", \"X\"], [\"X\", \"O\", \"X\"], [\"O\", \"X\", \"X\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_607\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as X.\\\\nCurrent board:\\\\nO | O | X\\\\n---------\\\\nX | O | \\\\n---------\\\\nO | X | X\\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"]], \\\"active_player\\\": \\\"X\\\", \\\"answer\\\": [[\\\"O\\\", \\\"O\\\", \\\"X\\\"], [\\\"X\\\", \\\"O\\\", \\\"X\\\"], [\\\"O\\\", \\\"X\\\", \\\"X\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_607"}
|
[['O', 'O', 'X'], ['X', 'O', 'X'], ['O', 'X', 'X']]
|
{"id": "ttt_hard_607", "question": "\nYou are playing tic-tac-toe as X.\nCurrent board:\nO | O | X\n---------\nX | O | \n---------\nO | X | X\n\n\n", "current_board": [["O", "O", "X"], ["X", "O", ""], ["O", "X", "X"]], "active_player": "X", "answer": [["O", "O", "X"], ["X", "O", "X"], ["O", "X", "X"]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
Tic Tac Toe Game Rules:
1. The board consists of 3x3 cells.
2. Players take turns placing their mark on an empty cell, one move per turn. The two players use "O" or "X".
3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.
4. If the board is completely filled without a winner, the game is a draw.
You are playing tic-tac-toe as O.
Current board:
| | X
---------
O | |
---------
| X |
Question: What is the best next move? Please provide only your move and display the board.
Answer format:
- Please output your answer within a code block (```), for example:
```
"X" "O" ""
"" "X" ""
"O" "" "X"
```
|
{"ground_truth": "{\"prompt\": \"\\nTic Tac Toe Game Rules:\\n1. The board consists of 3x3 cells.\\n2. Players take turns placing their mark on an empty cell, one move per turn. The two players use \\\"O\\\" or \\\"X\\\".\\n3. A player wins by placing three of their marks consecutively in a row, column, or diagonal.\\n4. If the board is completely filled without a winner, the game is a draw.\\n\\n\\nYou are playing tic-tac-toe as O.\\nCurrent board:\\n | | X\\n---------\\nO | | \\n---------\\n | X | \\n\\n\\n\\n\\nQuestion: What is the best next move? Please provide only your move and display the board.\\n\\nAnswer format:\\n- Please output your answer within a code block (```), for example:\\n```\\n\\\"X\\\" \\\"O\\\" \\\"\\\"\\n\\\"\\\" \\\"X\\\" \\\"\\\"\\n\\\"O\\\" \\\"\\\" \\\"X\\\"\\n```\\n\", \"answer\": [[\"\", \"\", \"X\"], [\"O\", \"O\", \"\"], [\"\", \"X\", \"\"]], \"task_name\": \"tic_tac_toe\", \"ability\": \"PUZZLE\", \"language\": \"en\", \"meta\": \"{\\\"id\\\": \\\"ttt_hard_593\\\", \\\"question\\\": \\\"\\\\nYou are playing tic-tac-toe as O.\\\\nCurrent board:\\\\n | | X\\\\n---------\\\\nO | | \\\\n---------\\\\n | X | \\\\n\\\\n\\\\n\\\", \\\"current_board\\\": [[\\\"\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"active_player\\\": \\\"O\\\", \\\"answer\\\": [[\\\"\\\", \\\"\\\", \\\"X\\\"], [\\\"O\\\", \\\"O\\\", \\\"\\\"], [\\\"\\\", \\\"X\\\", \\\"\\\"]], \\\"rationale\\\": \\\"\\\", \\\"split\\\": \\\"test\\\", \\\"type\\\": \\\"partially_observable\\\", \\\"source_url\\\": \\\"auto-generated\\\", \\\"dataset_name\\\": \\\"tic_tac_toe\\\", \\\"difficulty_level\\\": \\\"hard\\\", \\\"language\\\": \\\"en\\\"}\"}", "style": "search"}
|
PUZZLE##tic_tac_toe
|
PUZZLE
|
{"index": "ttt_hard_593"}
|
[['', '', 'X'], ['O', 'O', ''], ['', 'X', '']]
|
{"id": "ttt_hard_593", "question": "\nYou are playing tic-tac-toe as O.\nCurrent board:\n | | X\n---------\nO | | \n---------\n | X | \n\n\n", "current_board": [["", "", "X"], ["O", "", ""], ["", "X", ""]], "active_player": "O", "answer": [["", "", "X"], ["O", "O", ""], ["", "X", ""]], "rationale": "", "split": "test", "type": "partially_observable", "source_url": "auto-generated", "dataset_name": "tic_tac_toe", "difficulty_level": "hard", "language": "en"}
|
search
|
tic_tac_toe
|
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