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

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

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

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