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

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

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

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