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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 9 6 4 0 0 0 8 7 1 3 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