A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 0 1 0 2 4 4 9 0 0 0 0 7 0 6 7 0 3 0 5 8 0 0 0 0 4 1 2 5
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>.
Assistant: Let me solve this step by step.
<think>
user