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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 2 7 9 8 5 1 1 4 4 9 7 6 3 2 2 0 0 0 9 1 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