<|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:  0 0 0 0 0 0 0 3 2 7 3 6 3 7 1 2 8 4 8 5 0 0 0 0 0
Output: 0 0 0 0 3 2 7 3 6 3 7 1 2 8 4 8 5 0 0 0 0 0 0 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 1 5 4 5 1 8 4 3 6 4 6 0 0 0 0 0 0 0 0 0 3 4 1 5
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