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

Example 2:
Input:  6 0 0 0 0 0 5 0 7 1 6 8 8 4 0 0 1 6 0 0 0 1 4 4 5 0 7 8
Output: 0 0 0 0 0 0 0 0 0 0 0 0 6 5 7 1 6 8 8 4 1 6 1 4 4 5 7 8

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

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