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 7 7 3 6 2 8 7 4 4 9 5 0 6 3 4 5 2 5 7 4 6 9 5 4 5 5 9
Output: 7 3 6 2 8 7 4 4 9 5 0 6 3 4 5 2 5 7 4 6 9 5 4 5 5 9 5 7

Example 2:
Input:  8 8 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 6
Output: 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 6 8 8

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 8 4 2 7 1 9 3 2 7 2 6 6 4 1 8 2 3 9 1 0 0 0 0 0 0 2 5
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