<|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 4 7 1 6 9 5 7 7 2 4 3 1 5 0 2 9 3 5 4 5
Output: 1 6 9 5 7 7 2 4 3 1 5 0 2 9 3 5 4 5 1 4 7

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

Example 3:
Input:  9 9 1 5 9 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Output: 5 9 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 2 9 9 1

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 7 8 2 9 6 4 7 3 9 5 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