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

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

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

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