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 7 8 8 2 1 8 1 2 5 5 1 0 0 0 0 0 0 0 0 3 2 1
Output: 7 8 8 2 1 8 1 2 5 5 1 0 0 0 0 0 0 0 0 3 2 1 7

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 3 3 8 8 8 7 9 9 3 6 3 1 6 2 3 5 9 3 4 0 2 3
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