<|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:  5 2 8 9 5 6 8 0 2 3 7 6 4 1 2 9 3 1 8 8 3 3 2 9 4
Output: 3 2 9 4 5 2 8 9 5 6 8 0 2 3 7 6 4 1 2 9 3 1 8 8 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 7 6 5 5 7 0 0 0 0 0 0 0 0 0 9 6 6 4 7 5 1 9 6 9
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