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

Example 2:
Input:  3 7 5 6 4 6 3 6 0 0 0 0 0 0 0 0 9 2 4 2 9 9 4 1
Output: 5 6 4 6 3 6 0 0 0 0 0 0 0 0 9 2 4 2 9 9 4 1 3 7

Example 3:
Input:  1 7 3 3 3 9 5 9 0 0 0 0 1 6 4 8 4 4 9 3 4 2 5 6
Output: 3 3 3 9 5 9 0 0 0 0 1 6 4 8 4 4 9 3 4 2 5 6 1 7

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