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

Example 2:
Input:  0 0 0 0 0 0 4 6 5 5 3 3 5 3 2 0 0 0 0 0 0
Output: 0 0 0 0 0 0 2 3 5 3 3 5 5 6 4 0 0 0 0 0 0

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

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