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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 3 9 3 9 3 0 5 3 8 4 2 5 8
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