<|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 2 6 5 4 7 4 8 9 8 4 9 6 7 5 2 2 7 7 6 8 2 8 3 6
Output: 2 8 3 6 4 2 6 5 4 7 4 8 9 8 4 9 6 7 5 2 2 7 7 6 8

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

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

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