<|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:  1 3 9 7 8 1 2 2 1 6 7 7 1 9 7 5 6 3 5 4 3
Output: 7 8 1 2 2 1 6 7 7 1 9 7 5 6 3 5 4 3 1 3 9

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

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

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