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:  1 0 0 0 0 0 3 8 6 6 1 8 1 8 1 9 7 2 4 4
Output: 0 0 0 0 3 8 6 6 1 8 1 8 1 9 7 2 4 4 1 0

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

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

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