<|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:  6 0 8 3 3 0 0 0 3 4 0 4 8 5 1 9 0 7 0 4 1 1 0 5 0 0 1 2 0
Output: 0 0 0 0 0 0 0 0 0 0 0 6 8 3 3 3 4 4 8 5 1 9 7 4 1 1 5 1 2

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

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

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