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

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

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

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