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

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

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

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