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

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

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

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