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:  3 1 7 5 1 6 8 1 9 7 5 4 5
Output: 1 6 8 1 9 7 5 4 5 3 1 7 5

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

Example 3:
Input:  4 6 2 2 6 9 2 4 1 9 6 2 8
Output: 6 9 2 4 1 9 6 2 8 4 6 2 2

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 9 0 0 0 0 4 9 8 5 6 2 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>.
Assistant: Let me solve this step by step.
<think>
user