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:  3 5 0 7 0 6 0 6 0 9 0 7 6 0 3 1 0 6 0 0 0 3 0 0 0 8 0 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 5 7 6 6 9 7 6 3 1 6 3 8 2

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

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

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