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:  8 5 2 5 5 0 0 0 0 0 0 0 0 0 0 9 9 8 2 6 8 7 1
Output: 6 8 7 1 8 5 2 5 5 0 0 0 0 0 0 0 0 0 0 9 9 8 2

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 6 4 2 2 6 3 0
Output: 2 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 6 4 2

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 2 7 3 9 9 9 4 9 0 0 0 0 0 0 0 0 0 0 0 0 2 8
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