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:  8 8 4 8 3 8 6 1 1 8 4 1 3 5 3 3 1 3 7 6
Output: 8 3 8 6 1 1 8 4 1 3 5 3 3 1 3 7 6 8 8 4

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

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

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