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

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

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

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