#!/usr/bin/env python3

#WA: iterates up to a fixed depth (2000000 just about solves all small-steps cases)
depth = 2000000

n = int(input())
pts = []
for i in range(n):
    pts.append([float(i) for i in input().split()])
#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])
#Do efficient by keeping a running square length, likely no contestant
#will do this without solving the entire recursion but this should
#exclude even the fasters recursions.
len2 = 0
for i in range(1,n):
    li2 = (pts[i][0] - pts[i-1][0]) ** 2 + (pts[i][1] - pts[i-1][1]) ** 2
    len2 += li2
currlen2 = 1.
area = 0.
for i in range(depth):
    area += currlen2 * I
    currlen2 *= len2

#Add area three times to area initial triangle (i.e. sqrt(3)/4)
print((3 ** 0.5 / 4) + 3 * area)