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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 4 4 9 3 8 3 9 6 7 7 1 9 1 2 2 0 0 0 0 5 4 7 2 3 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