514. Polygon

Time limit per test: 1.25 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard

You are given lengths of sides of some polygon. You must find the infimum of the possible areas of simple polygons with such side lengths. Infimum of a set of real numbers A is the exact upper bound of the set L of all real numbers y such that for any x ∈ A holds y ≤ x.

A simple polygon is a polygon without self-intersections and self-touchings.

Input
The first line contains integer n, 3 ≤ n ≤ 10 — the number of sides of the polygon. The second line contains n integers a1, a2,..., an, such that for any 1 ≤ i ≤ n (this means that there exists a simple polygon with sides a1, a2,..., an. Also, 1 ≤ ai ≤ 100.

Output
Output one real number — the answer to the problem. Your answer will be considered correct if absolute or relative error is less than 10-6.

Example(s)
sample input
 
sample output
 
3
3 4 5

6.0000000000


sample input
 
sample output
 
4
8 4 3 5

4.4721359550


sample input
 
sample output
 
10
5 5 5 5 5 5 5 5 5 5

0.0000000000