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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 9 0 4 8 8 7 4 9 0 1 2 0 3 8 0 0 4 1 3 0 0 0 0 0 6 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