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 3 4 8 7 8 8 1 1 7 7 6 3 6 4 4
Output: 3 4 8 7 8 8 1 1 7 7 6 3 6 4 4 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 3 0 0 5 7 5 1 8 7 3 3 7 3 1 3
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