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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 3 6 2 3 7 8 1 7 8 2 0 0 0 0 0 0 1 2
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