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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 8 7 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 8 5

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

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