<|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:  4 0 0 0 4 0 2 6 0 0 0 0 6 1 2 0 2 0 0 0 0 0 0 6 9 0 0 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 2 6 6 1 2 2 6 9 2

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

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

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