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

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

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

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