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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 5 7 1 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 7 5 7 0 0 0 0 0

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