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

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

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

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