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

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

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

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