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

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

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