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

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

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

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