<|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:  7 2 5 7 0 0 2 5 2 9 1 3 2 7 7 4 7 8 9 2 5 5 3 1 4 7 8 5 7 4
Output: 4 7 2 5 7 0 0 2 5 2 9 1 3 2 7 7 4 7 8 9 2 5 5 3 1 4 7 8 5 7

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 6 8 2 7 9 6 3 6 6 2 4 7 1 6 1 6 1 9 4 8 2 0 0 1 4 8 3 4 5
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