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 2 5 8 7 9 5 5 8 8 8
Output: 8 7 9 5 5 8 8 8 1 0 2 5

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 0 2 7 9 2 6 2 1 7 4
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