Dodecahedron
A dodecahedron is a regular polyhedron with 12 faces, each shaped like a regular pentagon. Two police officers are positioned on some of these faces (possibly the same one) and are pursuing Z. Hussein, the world's most wanted terrorist, who is also on one of the dodecahedron's faces. The chase proceeds in turns: first, one of the police officers (either one) moves, followed by Hussein. Each move consists of moving to an adjacent face, where an adjacent face shares an edge with the current face. Staying on the same face during a move is not allowed. This sequence of moves continues until Hussein is captured. If Hussein moves to a face occupied by a police officer during his turn, he will be caught on the following turn. Conversely, if a police officer moves to the face where Hussein is located during his turn, Hussein is caught immediately.
Input
The distance n between the police officers on the dodecahedron is provided. This distance is defined as the minimum number of moves required for one officer to reach the same face as the other.
Output
Determine the maximum number of moves needed to ensure Z. Hussein is captured, regardless of his starting position on the dodecahedron. The police officers always know Hussein's location, and vice versa. Additionally, the police officers are aware of each other's positions at all times.