#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); ++i)
#define R(i, j, k) for(int i = (j); i >= (k); --i)
#define ll long long
#define sz(a) ((int) (a).size())
#define vi vector < int > 
#define me(a, x) memset(a, x, sizeof(a))
#define ull unsigned long long
#define ld __float128
#define double long double 
using namespace std;
const int N = 1e6 + 7;
double x[N], y[N];
int n;
const double pi = acos(-1);
int main() {
	ios :: sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	cin >> n;
	double s = 0;
	L(i, 1, n) {
		cin >> x[i] >> y[i];
	}
	L(i, 1, n) {
		s += x[i] * y[i % n + 1] - x[i % n + 1] * y[i];
	}
	s /= 2;
	double ns = 0, tmp = 0, all = 0, qx = 0, qy = 0;
	L(i, 1, n) all += x[i] * x[i] + y[i] * y[i], qx += x[i], qy += y[i];
	L(i, 1, n) {
		int lst = (i + n - 2) % n + 1, nxt = i % n + 1;
		double qc = atan2(y[lst] - y[i], x[lst] - x[i]) - atan2(y[nxt] - y[i], x[nxt] - x[i]);
		if(qc < 0) qc += pi * 2;
		double w = pi - qc;
		assert(w >= 1e-8);
		tmp += w;
		
		double qwq = 0;
		qwq -= 2 * qx * x[i];
		qwq -= 2 * qy * y[i];
		qwq += all;
		qwq += (x[i] * x[i] + y[i] * y[i]) * n;
		ns += qwq * w;
	}
	cout.precision(12), cout << fixed;
	cout << ns / n / 2 + s << '\n';
	return 0;
}
/*
3
1 1
1 -1
-1 2
*/