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

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

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

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