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

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

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

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