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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 8 9 9 6 0 4 6 1 2 2 4 8 5 8 8 1 6 3 5 4 3 2 8 2 1
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