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

Example 2:
Input:  0 9 8 7 9 2 6 7 2 8 4 7 2 8 9 5 2 8 5 0
Output: 9 2 6 7 2 8 4 7 2 8 9 5 2 8 5 0 0 9 8 7

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 8 1 0 0 0 0 0 0 0 0 0 0 5 9 4 2 2 6 6
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