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

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

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

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