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 4 5 3 7 9 1 7 7 9 7 0 0 0 0 7 2 3 6 2 9 2
Output: 4 5 3 7 9 1 7 7 9 7 0 0 0 0 7 2 3 6 2 9 2 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 6 6 1 4 4 4 0 0 0 0 0 0 0 0 4 4 9 2 9 6 3
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