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

Example 2:
Input:  9 3 8 7 3 8 1 9 6 0 0 0 0 0 0 0 0 0 1 5 6 7 6 9
Output: 3 8 1 9 6 0 0 0 0 0 0 0 0 0 1 5 6 7 6 9 9 3 8 7

Example 3:
Input:  1 1 0 0 0 2 2 9 2 4 1 3 6 5 3 6 9 7 6 3 1 5 2 8
Output: 0 2 2 9 2 4 1 3 6 5 3 6 9 7 6 3 1 5 2 8 1 1 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 8 2 1 5 6 7 4 9 6 9 7 8 7 2 0 0 0 0 0 6 6 5 2
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