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 xA holds yx.

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 ≤ in (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 ```