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

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

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

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