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:  2 9 9 3 5 2 8 9 2 5 1 0 0 0 0 0 8 8 9
Output: 0 8 8 9 2 9 9 3 5 2 8 9 2 5 1 0 0 0 0

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

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

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