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:  0 0 9 9 2 3 3 8 2 8 7 2 5 1 1 8 2 2 2 5 0
Output: 2 5 0 0 0 9 9 2 3 3 8 2 8 7 2 5 1 1 8 2 2

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

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

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