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

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

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

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 0 0 0 4 2 6 3 8 1 9 8 7 7 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