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

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

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

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