#!/usr/bin/env python3
n = int(input())
pts = []
for i in range(n):
    pts.append([float(i) for i in input().split()])
#Compute netto area of one of the "sides"
#Use recursion A = I + (l1^2)A + (l2^2)A + ... + (l{n-1}^2)A
#Determine area I under polyline, i.e. depth 0
I = 0
for i in range(1,n):
    #compute integral per trapezoid
    I += 0.5 * (pts[i][1] + pts[i-1][1]) * (pts[i][0] - pts[i-1][0])
#Also compute 1 - l1^2 - ... - l{n-1}^2
f = 1
for i in range(1,n):
    li2 = (pts[i][0] - pts[i-1][0]) ** 2 + (pts[i][1] - pts[i-1][1]) ** 2
    f -= li2
#Note that we can do all the above directly when reading the input, split here for clarity
#Add area three times to area initial triangle (i.e. sqrt(3)/4)
print((3 ** 0.5 / 4) + 3 * (I / f))