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

Example 2:
Input:  8 0 0 0 6 9 7 3 2 4 9 9 5 2 8 9 2 1
Output: 9 2 1 8 0 0 0 6 9 7 3 2 4 9 9 5 2 8

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 2 7 9 7 0 0 0 0 0 5 1 6 5 3 2 7 4
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