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

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

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

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