Example

Input

4
5
8
58
85


Output

2970.000000000

Source: aizu | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
from itertools import permutations
from math import acos, sin, cos, pi
import sys
readline = sys.stdin.readline
write = sys.stdout.write

def solve():
	N = int(readline())
	R = [int(readline()) for i in range(N)]
	R.sort(reverse=1)
	ans = 0
	for l in range(3, N + 1):
		for rs in permutations(R[:l]):
			C = [rs[i] * rs[i - l + 1] for i in range(l)]
			if C.index(min(C)) != 0:
				continue
			left = 0
			right = pi + 1e-09
			while right - left > 1e-09:
				mid = (left + right) / 2
				s = mid
				cv = cos(mid)
				for i in range(1, l):
					s += acos(C[0] * cv / C[i])
				if s > 2 * pi:
					right = mid
				else:
					left = mid
			if left < 1e-09:
				continue
			res = C[0] * sin(left)
			cv = cos(left)
			v2 = (C[0] * cos(left)) ** 2
			for i in range(1, l):
				res += (C[i] ** 2 - v2) ** 0.5
			ans = max(ans, res)
	ans /= 2
	write('%.16f\n' % ans)
solve()