#include "bits/stdc++.h"
#define rep(i, a, n) for (int i = a; i <= n; ++i)
#define revrep(i, a, n) for (int i = n; i >= a; --i)
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
using namespace std;

string to_string(const string &s) { return '"' + s + '"'; }
template<class A> string to_string(A v) {
	bool first = 1;
	string res = "{";
	for (const auto &x: v) {
		if (!first) res += ", ";
		first = 0;
		res += to_string(x);
	}
	res += "}";
	return res;
}
void debug_out() { cerr << endl; }
template<class H, class... T> void debug_out(H h, T... t) {
	cerr << " " << to_string(h);
	debug_out(t...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

using vi = vector<int>;
using ll = long long;
using pii = pair<int, int>;

template<class T> struct Point {
	using P = Point;
	using type = T;
	static constexpr T eps = 1e-9;

	T x, y; 
	P operator -(P a) const { return P{x - a.x, y - a.y}; }
	
	T dot(P b) { return x * b.x + y * b.y; }
	T cross(P b) { return x * b.y - y * b.x; }
};


int main() {
	ios::sync_with_stdio(0); cin.tie(0);
	
	using T = long double;
	using P = Point<T>;

	int n; cin >> n;
	vector<P> as(n);
	for (auto &[x, y]: as) cin >> x >> y;
	T sum2 = 0;
	T sum_x = 0, sum_y = 0;
	for (auto [x, y]: as) {
		sum2 += x * x + y * y;
		sum_x += x;
		sum_y += y;
	}

	T ans = 0;
	rep(i, 0, n - 1) {
		auto a = as[i];
		auto b = as[(i - 1 + n) % n];
		auto c = as[(i + 1) % n];
		auto th = atan2((a - b).cross(c - a), (a - b).dot(c - a));
		auto [x, y] = as[i];
		T S = sum2 - 2 * sum_x * x - 2 * sum_y * y + (x * x + y * y) * n;
		ans += S * th / 2;
	}
	ans /= n;
	rep(i, 0, n - 1) {
		P a = as[i] - as[0];
		P b = as[(i + 1) % n] - as[0];
		ans += a.cross(b) / 2;
	}
	printf("%.10f\n", (double) ans);
	return 0;
}