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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 6 3 6 7 4 2 8 2 4 3 2 0 0 0 0 0 0
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