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

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

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

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