<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 5 8 3 7 2 4 4 2 6 7 2 5 0 0 0 0 6 2 4 7 3 2 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user