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

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

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

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