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

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

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

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