A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  5 9 4 2 6 3 5 5 5 9 5 9 5 2 6 2 2 4 3 0 0 0 0 0 8
Output: 0 0 8 5 9 4 2 6 3 5 5 5 9 5 9 5 2 6 2 2 4 3 0 0 0

Example 2:
Input:  1 1 6 8 2 1 4 4 7 1 6 9 6 8 7 0 0 0 0 5 4 7 5 7 8
Output: 5 7 8 1 1 6 8 2 1 4 4 7 1 6 9 6 8 7 0 0 0 0 5 4 7

Example 3:
Input:  4 4 8 2 5 0 0 0 0 0 0 4 9 4 1 1 9 1 4 6 1 7 2 5 6
Output: 2 5 6 4 4 8 2 5 0 0 0 0 0 0 4 9 4 1 1 9 1 4 6 1 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 7 4 5 3 4 1 4 7 4 8 2 0 0 0 0 0 0 3 7 6 6 4 8 2
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.
Assistant: Let me solve this step by step.
<think>
user