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

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

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

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