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:  4 3 7 4 4 1 0 0 0 0 0 8 1 2
Output: 1 2 4 3 7 4 4 1 0 0 0 0 0 8

Example 2:
Input:  3 6 3 8 5 6 6 3 2 7 5 6 3 3
Output: 3 3 3 6 3 8 5 6 6 3 2 7 5 6

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

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