<|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:  6 8 6 0 5 9 7 9 4 7 6 1 6 7 3 1 9 1 2 8 3 5 1 1 7 9 5 2 9
Output: 5 9 7 9 4 7 6 1 6 7 3 1 9 1 2 8 3 5 1 1 7 9 5 2 9 6 8 6 0

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

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

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