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:  7 2 9 3 9 1 1 9 8 0 6 3 9 2 2 4 6 6 9
Output: 6 9 7 2 9 3 9 1 1 9 8 0 6 3 9 2 2 4 6

Example 2:
Input:  9 3 8 1 7 9 6 9 6 1 7 3 3 9 6 1 2 1 8
Output: 1 8 9 3 8 1 7 9 6 9 6 1 7 3 3 9 6 1 2

Example 3:
Input:  5 4 7 7 9 7 0 6 2 9 2 3 7 9 5 6 2 9 7
Output: 9 7 5 4 7 7 9 7 0 6 2 9 2 3 7 9 5 6 2

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