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

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

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

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