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

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

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

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