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 1 8 5 5 1 0 0 0 6 1 7 8 4 3 1 9
Output: 5 1 0 0 0 6 1 7 8 4 3 1 9 4 1 8 5

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

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

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