#!/usr/bin/env python3
from math import dist


def area_trapezoid(points):
    return sum(
        (bx - ax) * (ay + by) / 2
        for (ax, ay), (bx, by) in zip(points, points[1:])
    )


n = int(input())
points = [tuple(map(float, input().split())) for _ in range(n)]
line_area = area_trapezoid(points)
line_lengths = [dist(a, b) for a, b in zip(points, points[1:])]
#print(line_area, line_lengths, [l ** 2 * line_area for l in line_lengths])
base = 3 ** 0.5 / 4
if n == 2: exit(print(base))
"""
print(base)
print(base + 3 * line_area)
print(base + 3 * line_area + 3 * sum(l ** 2 * line_area for l in line_lengths))
print()
print(line_area)
area = base + 3 * line_area
orig_line_lengths = line_lengths
for i in range(1, 12):
    a = sum(l ** 2 * line_area for l in line_lengths)
    area += 3 * a
    print(a, len(line_lengths), line_lengths[0])
    from itertools import product
    line_lengths = [a * b for a, b in product(line_lengths, orig_line_lengths)]
print(area)
"""
#ratio = sum(l ** 2 * line_area for l in line_lengths) / line_area
ratio = sum(l ** 2 for l in line_lengths)
#print(ratio)
# SUM(a + ar + ar² + ...) = a / (1 - r)
#print(line_area / (1 - ratio))
print(base + line_area / (1 - ratio ** 3))  # WA: I don't know, man