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:  0 0 0 0 0 0 0 0 0 0 0 0 6 3 8 1 5 6 8 8 1 1 0
Output: 8 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 6 3 8 1 5 6 8

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

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

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