<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  1 6 9 9 2 4 7 1 4 5 6 6 8 0 0 0 0 0 0 1 2
Output: 2 1 6 9 9 2 4 7 1 4 5 6 6 8 0 0 0 0 0 0 1

Example 2:
Input:  1 2 7 0 0 0 0 9 5 5 1 6 9 9 8 9 3 3 6 2 9
Output: 9 1 2 7 0 0 0 0 9 5 5 1 6 9 9 8 9 3 3 6 2

Example 3:
Input:  3 8 6 4 8 7 7 5 2 1 3 3 6 8 9 6 5 1 4 0 0
Output: 0 3 8 6 4 8 7 7 5 2 1 3 3 6 8 9 6 5 1 4 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 6 9 7 3 3 8 6 7 5 0 0 0 0 4 3 3 5 6 2 1
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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user