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

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

Example 3:
Input:  4 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 5 1 3 8 4 5
Output: 8 4 5 4 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 5 1 3

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