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 6 1 2 0 1 0 0 2 1 8 0 0 0 4 0 0 0 0 7 9 5 0 0 0 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 1 2 1 2 1 8 4 7 9 5 2

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

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

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