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

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

Example 3:
Input:  4 9 1 0 0 0 0 0 0 0 0 4 4 9 1 7 1 9 7
Output: 1 0 0 0 0 0 0 0 0 4 4 9 1 7 1 9 7 4 9

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