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:  2 2 1 6 1 6 3 3 9 0 3 6 9 4 1 8 3 4 2 2 7
Output: 2 7 2 2 1 6 1 6 3 3 9 0 3 6 9 4 1 8 3 4 2

Example 2:
Input:  3 9 9 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
Output: 1 1 3 9 9 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 4 3 9 8 3 2 6 6 6 3 9 5 9 5 3 0 0 1 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