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:  5 1 8 8 4 6 8 3 1 9 4 1 6 2 6 6 4 1 9 5 5 8 0
Output: 5 8 0 5 1 8 8 4 6 8 3 1 9 4 1 6 2 6 6 4 1 9 5

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

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

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 9 9 5 9 9 1 4 2 4 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