<|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 9 1 0 0 1 5 0 9 0 0 0 4 2 0 0 0 4 0 9 1 0 0 9 8 1 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 1 1 5 9 4 2 4 9 1 9 8 1

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

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

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