<|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:  1 1 7 7 3 3 8 6 6 1 3 3 5 1 0 0 0 7 6 5
Output: 6 5 1 1 7 7 3 3 8 6 6 1 3 3 5 1 0 0 0 7

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

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

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