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:  2 8 0 0 0 0 0 0 0 0 0 0 0 5 3 4 3 1 5 6 2 2 8 2 8 3 7 4 7
Output: 3 7 4 7 2 8 0 0 0 0 0 0 0 0 0 0 0 5 3 4 3 1 5 6 2 2 8 2 8

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 6 8 1 8 5 6 9 6 8 0 0 0 0 0 0 0 0 0 0 0 0 9 4 5 9 1 7 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