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

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

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

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