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

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

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

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