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 1 0 0 0 0 5 4 0 0 0 7 4 0 2 4 0 0 0 0 0 3 3 9 0 0 3
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 4 7 4 2 4 3 3 9 3

Example 2:
Input:  1 0 5 0 2 9 6 6 0 0 0 9 3 9 8 1 0 0 0 0 0 4 8 0 0 0 4
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 2 9 6 6 9 3 9 8 1 4 8 4

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 0 1 9 0 7 0 2 5 6 0 4 8 0 1 0 4 6 3 9 0 0 6 0 0 2 7
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