Optimal Reclamation Dam

An island's coastline is a simple polygon made only of horizontal and vertical line segments. You may build one straight dam that is horizontal or vertical, connects two points on the coastline, and does not pass through the island interior. The dam and one part of the coastline enclose a sea area that can be reclaimed.

The efficiency of a dam is (reclaimed area) / (dam length). Find the maximum possible efficiency.

The first line contains the number of vertices.

Starting on the second line, the vertex coordinates are given in counterclockwise order. Line breaks between coordinates are not significant. Each coordinate is a positive integer at most 250, and the number of vertices is at most 100.

Print the maximum efficiency rounded to two digits after the decimal point.