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

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

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

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