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 3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 6 7 8
Output: 6 7 8 8 3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3

Example 2:
Input:  7 6 5 0 0 0 0 0 8 6 7 2 3 7 7 4 1 5 1 9 1
Output: 1 9 1 7 6 5 0 0 0 0 0 8 6 7 2 3 7 7 4 1 5

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

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