<|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 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 4 5 0

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

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

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