<|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:  3 0 8 7 3 9 1 7 6 7 1 6 7 5
Output: 3 9 1 7 6 7 1 6 7 5 3 0 8 7

Example 2:
Input:  2 8 9 6 2 7 4 6 7 0 0 0 8 2
Output: 2 7 4 6 7 0 0 0 8 2 2 8 9 6

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 2 0 0 8 2 1 9 2 6 7 6 1 2
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