<|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:  4 9 2 2 4 5 9 8 9 0 7 1 7 5 4 7 8 2 8 4 8 4
Output: 2 4 5 9 8 9 0 7 1 7 5 4 7 8 2 8 4 8 4 4 9 2

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

Example 3:
Input:  5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 5 3 0

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