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

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

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