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

Example 2:
Input:  0 0 6 2 5 0 0 7 2 3 0 6 9 8 1 3 5 0 0 2 1 4 0 0 1 4
Output: 0 0 0 0 0 0 0 0 0 6 2 5 7 2 3 6 9 8 1 3 5 2 1 4 1 4

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

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