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:  4 8 6 5 1 4 2 2 8 4 3 1 3 7 1 3 4 6 5
Output: 5 4 8 6 5 1 4 2 2 8 4 3 1 3 7 1 3 4 6

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

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

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 0 4 3 2 4 4 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