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 8 9 4 5 8 0 0 0 0 0 0 3 3 1 3 3 3 2 8
Output: 4 5 8 0 0 0 0 0 0 3 3 1 3 3 3 2 8 8 5 8 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 8 2 2 9 3 1 2 8 8 1 8 9 7 8 9 4 4 3 3 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