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

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

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

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