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:  2 0 0 0 0 0 4 2 7 9 3 7 1 6 1 3
Output: 1 6 1 3 2 0 0 0 0 0 4 2 7 9 3 7

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

Example 3:
Input:  9 6 8 6 4 0 0 0 0 0 0 9 9 4 7 3
Output: 9 4 7 3 9 6 8 6 4 0 0 0 0 0 0 9

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 6 4 4 8 0 4 2 4 3 6 9 2 4 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