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 1 7 5 2 0 0 0 0 0 0 0 0 8 6 9 2
Output: 7 5 2 0 0 0 0 0 0 0 0 8 6 9 2 4 1

Example 2:
Input:  6 9 9 7 3 8 1 7 5 8 2 0 0 0 0 2 5
Output: 9 7 3 8 1 7 5 8 2 0 0 0 0 2 5 6 9

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 9 7 0 1 5 8 8 7 4 5 3 6 8 9 4 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