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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 1 6 7 6 7 7 4 5 7 4 9 8 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