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 5 6 8 2 3 7 2 4 6 2 2 2 4 0 0 8 7 5 7 5
Output: 5 7 5 4 5 6 8 2 3 7 2 4 6 2 2 2 4 0 0 8 7

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 1 5 1 4 7 1 8 2 1 3 0 0 0 0 0 0 1 4 4 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