#include <bits/stdc++.h>
using namespace std;

using llf = long double;

constexpr llf PI = acos(-1);

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> x(n), y(n);
    for (int i = 0; i < n; i++) {
        cin >> x[i] >> y[i];
    }

    vector<llf> sqsum(n);

    const auto gao = [&sqsum, n](vector<int> &v) {
        llf a = 0, b = 0, c = 0;
        for (int i = 0; i < n; i++) {
            a += 1;
            b -= 2 * v[i];
            c += 1LL * v[i] * v[i];
        }

        for (int i = 0; i < n; i++) {
            llf X = v[i];
            sqsum[i] += a * X * X + b * X + c;
        }
    };

    gao(x);
    gao(y);


    llf ans = 0;

    for (int i = 0; i < n; i++) {
        int64_t dx1 = x[i] - x[(i + n - 1) % n];
        int64_t dy1 = y[i] - y[(i + n - 1) % n];

        int64_t dx2 = x[(i + 1) % n] - x[i];
        int64_t dy2 = y[(i + 1) % n] - y[i];

        llf theta = atan2(dx2, dy2) - atan2(dx1, dy1);
        theta = - theta;
        if (theta < 0)
            theta += 2 * PI;

        ans += theta * sqsum[i] / 2;
        // cerr << "theta = deg " << theta/PI*180 << endl;
        // cerr << "sqsum[i] = " << sqsum[i] << endl;
    }

    // cerr << "ans = " << ans << endl;

    ans /= n;
    // cerr << "ans = " << ans << endl;

    llf polygon_area = 0;
    for (int i = 1; i + 1 < n; i++) {
        int64_t dx1 = x[i] - x[0];
        int64_t dy1 = y[i] - y[0];

        int64_t dx2 = x[i + 1] - x[0];
        int64_t dy2 = y[i + 1] - y[0];

        polygon_area += dx1 * dy2 - dx2 * dy1;
    }
    polygon_area /= 2.0;

    ans += polygon_area;

    cout << fixed << setprecision(20);
    cout << ans << '\n';

    return 0;
}