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 9 4 7 4 7 3 7 6 6 6 3
Output: 6 3 3 9 4 7 4 7 3 7 6 6

Example 2:
Input:  5 3 9 2 7 0 0 7 9 4 6 1
Output: 6 1 5 3 9 2 7 0 0 7 9 4

Example 3:
Input:  6 5 9 8 7 6 0 9 8 8 8 6
Output: 8 6 6 5 9 8 7 6 0 9 8 8

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 7 1 4 6 9 7 3 2 5 3 7
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