A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 5 6 2 3 8 4 2 6 8 3 6 6
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>.
Assistant: Let me solve this step by step.
<think>
user