#include <bits/stdc++.h>

using namespace std;

typedef long double ld;
typedef long long ll;

const int N = 1e5 + 3;
const ld PI = acos((ld)-1.0);

int n;
pair<ll, ll> v[N];

ld get_angle(ll x1, ll y1, ll x2, ll y2){
    ld val = x1 * x2 + y1 * y2;
    val /= sqrt((ld)x1 * x1 + y1 * y1) * sqrt((ld)x2 * x2 + y2 * y2);
    return acos(val);
}

ld area(ll x1, ll y1, ll x2, ll y2, ll x3, ll y3){
    ll a = x1 * y2 + x2 * y3 + x3 * y1
          -(x1 * y3 + x2 * y1 + x3 * y2);
    return ((ld)a) / 2.0;
}

ld cross(pair<ll, ll> p1, pair<ll, ll> p2){
    return p1.first * p2.second - p2.first * p1.second;
}

ld polygonArea(){
    ld a = cross(v[n], v[1]);
    for(int i = 1; i <= n - 1; ++i){
        a += cross(v[i], v[i + 1]);
    }
    return a / 2;
}

ll sq(ll x){
    return x * x;
}

ll d2(pair<ll, ll> p1, pair<ll, ll> p2){
    return sq(p1.first - p2.first) + sq(p1.second - p2.second);
}

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

    cin >> n;
    for(int i = 1; i <= n; ++i){
        cin >> v[i].first >> v[i].second;
    }
    v[n + 1] = v[1];
    v[0] = v[n];

    ld ans = 0;
    for(int i = 1; i <= n; ++i){
        ld angle = get_angle(v[i].first - v[i - 1].first, v[i].second - v[i - 1].second, v[i].first - v[i + 1].first, v[i].second - v[i + 1].second);
        for(int j = 1; j <= n; ++j)
            ans += (PI - angle) * d2(v[i], v[j]) / 2;
    }
    ans /= n;
    cout << fixed << setprecision(12) <<  ans + polygonArea() << "\n";
}