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 1 2 4 8 7 3 9 0 0 0 0 0 0 0 0 9 3 2 8 8 1 8
Output: 1 8 2 1 2 4 8 7 3 9 0 0 0 0 0 0 0 0 9 3 2 8 8

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

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

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