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

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

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

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