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

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

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

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