#include <cmath>
#include <iostream>
#include <iomanip>
#include <vector>

using namespace std;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    long long n;
    cin >> n;
    // Just try the most efficient approach of brute force calculating the geometric series. Likely if contestants do this they can also solve the recursion,
    // but this should provide a good upper bound of the accuracy that can be achieved by any iterating algorithm.
    std::vector<long double> xs(n), ys(n);
    for (int i = 0; i < n; i++)
    {
        cin >> xs[i] >> ys[i];
    }
    long double len2 = 0.0;
    long double ar = 0.0;
    for (int i = 1; i < n; i++)
    {
        len2 += (xs[i] - xs[i-1]) * (xs[i] - xs[i-1]) + (ys[i] - ys[i-1]) * (ys[i] - ys[i-1]);
        ar += 0.5f * (ys[i] + ys[i-1]) * (xs[i] - xs[i-1]);
    }
    long double area = 0.0, prev = -1.0;
    long double currlen2 = 1.0;
    long long i = 0;
    while (prev != area)
    {
        prev = area;
        area += currlen2 * ar;
        currlen2 *= len2;
        i++;
    }

    cerr << "Iterations: " << i << '\n';
    cout << setprecision(19) << sqrt(3) / 4 + 3 * area << '\n';
    return 0;
}