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

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

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

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