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

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

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

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