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

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

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

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