— Oh, Boss, I can see you!
From the animated film 'Investigation Held by Kolobki'
During their investigation, detectives Boss and Colleague got into an
empty warehouse to look for evidence of crime. The warehouse is
a polygon without self-intersections and self-tangencies,
not necessarily convex. The detectives investigate the territory of
warehouse in such a way that each of them can always see the other one.
Boss and Colleague can see each other if all the points of a segment
connecting them lie either inside the warehouse or on its border.
Find the maximal possible distance between the detectives.
The first line of input contains an integer n: the number of vertices
of the polygon (3 ≤ n ≤ 200).
Next n lines contain two integers xi, yi each: coordinates
of vertices in clockwise or counterclockwise order
(−1000 ≤ xi, yi ≤ 1000).
It is guaranteed that polygon has neither self-intersections
Output the maximal possible distance between Boss and Colleague.
The answer must be given with absolute or relative error
not exceeding 10−6.
Problem Author: Mikhail Rubinchik (prepared by Egor Scshelkonogov)
Problem Source: Ural FU contest. Kontur Cup. Petrozavodsk training camp. Winter 2013