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

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

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

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