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:  3 3 3 5 8 3 9 4 3 5 9 8 4 1
Output: 3 3 5 8 3 9 4 3 5 9 8 4 1 3

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

Example 3:
Input:  9 8 4 4 3 2 9 0 0 0 0 8 5 2
Output: 8 4 4 3 2 9 0 0 0 0 8 5 2 9

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 7 2 4 5 0 0 0 0 0 0 0 5 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