#!/usr/bin/python3

from math import hypot

n = int(input())
points = [[float(x) for x in input().split()] for _ in range(n)]
xs = [x for x, _ in points]
ys = [y for _, y in points]

one_area = -(sum(xs[i % n]*ys[(i + 1)%n] for i in range(n)) - sum(xs[(i+1) % n]*ys[i%n] for i in range(n))) / 2

main_triangle_area = 1/2 * (3/4)**0.5
lengths = [hypot(x2 - x1, y2 - y1) for ((x1, y1), (x2, y2)) in zip(points, points[1:])]
sum_lengths_squared = sum(length**2 for length in lengths)
if sum_lengths_squared > 0.999999999:
    print(main_triangle_area)
else:
    print(main_triangle_area + 3*one_area / (1 - sum_lengths_squared))