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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 5 0 6 3 8 2 2 6 7 7 8 7 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