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:  3 3 6 6 8 6 6 3 9 2 2 4 0 0 0 0 0 0 0 0 0 4 1 4 4
Output: 1 4 4 3 3 6 6 8 6 6 3 9 2 2 4 0 0 0 0 0 0 0 0 0 4

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

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

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