<|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:  8 3 0 0 0 9 0 1 1 0 8 3 6 3 0 6 8 0 8 0 1 0 9 3 7 0
Output: 0 0 0 0 0 0 0 0 0 0 8 3 9 1 1 8 3 6 3 6 8 8 1 9 3 7

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 0 3 8 0 0 2 1 0 0 0 8 4 5 1 0 3 1 0 0 0 0 4 5 7 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