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

Example 2:
Input:  1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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