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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 2 5 2 2 4 6 1 7 5 0 0 0 2 4 1 5
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