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

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

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

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
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