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 selfintersections and selftouchings.
Input
The first line contains integer
n, 3 ≤
n ≤ 10 — the number of sides of the polygon. The second line contains
n integers
a_{1},
a_{2},...,
a_{n}, such that
for any 1 ≤
i ≤
n (this means that there exists a simple polygon with sides
a_{1},
a_{2},...,
a_{n}. Also, 1 ≤
a_{i} ≤ 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
