#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
#define rep(i,a,b) for(int i = a; i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define PB push_back
#define FS first
#define SD second
#define ary(k) array<int,k>
template<class A, class B> void cmx(A& x, B y){ x = max<A>(x,y); }
template<class A, class B> void cmn(A& x, B y){ x = min<A>(x,y); }
typedef pair<int,int> pii;
typedef vector<int> vi;

typedef double ld;
const ld EPS = 1e-9;
int sgn(ld x) { return (x > EPS) - (x < -EPS);}
template<class T> struct Point {
    typedef Point P;
    T x,y;
    Point(T _x=0, T _y=0) : x(_x), y(_y) {}

    P operator+(P p) const { return P(x+p.x,y+p.y); }
    P operator-(P p) const { return P(x-p.x,y-p.y); }
    P operator*(T d) const { return P(x*d,y*d); }
    P operator/(T d) const { return P(x/d,y/d); }
    T dist2() const { return x*x + y*y; }
    double dist() const { return sqrt((double)dist2()); }
    T dot(P p) const { return x*p.x + y*p.y; }
    T cross(P p) const { return x*p.y-y*p.x;}
    T cross(P a, P b) const { return (a-*this).cross(b-*this); }
    friend ostream& operator<<(ostream& os, P p) {
        return os << "(" << p.x << "," << p.y << ")";
    }
};
typedef Point<ld> P;

template<class P>
P lineInter(P s1, P e1, P s2, P e2) {
    auto d = (e1-s1).cross(e2-s2);
    auto p = s2.cross(e1, e2), q = s2.cross(e2, s1);
    return (s1*p+e1*q) / d;
}
vector<P> segInter(P a, P b, P c, P d) {
    auto oa = c.cross(d, a), ob = c.cross(d, b),
        oc = a.cross(b, c), od = a.cross(b, d);
    if (sgn(oa)*sgn(ob) < EPS && sgn(oc)*sgn(od) < EPS)
        return {(a*ob-b*oa) / (ob-oa)};
//    set<P> s;
//    if (onSegment(c, d, a)) s.insert(a);
//    if (onSegment(c, d, b)) s.insert(a);
//    if (onSegment(a, b, c)) s.insert(c);
//    if (onSegment(a, b, d)) s.insert(d);
//    return {all(s)};
    return {};
}

bool onRight(P s, P e, P p) {
    return s.cross(e, p) < -EPS;
}
bool onLeft(P s, P e, P p) {
    return s.cross(e, p) > EPS;
}

bool onSegment(P s, P e, P p) {
    return abs(p.cross(s, e)) < EPS && (s-p).dot(e-p) < EPS;
}

bool inPolygon(vector<P> p, P a, bool strict) {
    int cnt = 0, n = sz(p);
    rep(i,0,n) {
        P q = p[(i+1)%n];
        if (onSegment(p[i], q, a)) return !strict;
        cnt ^= ((a.y<p[i].y) - (a.y<q.y)) * a.cross(p[i], q) > 0;
    }
    return cnt;
}

bool cmp(P p1, P p2) {
    P p = p1-p2;
    ld a = max(abs(p.x), abs(p.y));
    return a < 1e-6;
}

vector<P> cutPolygon(vector<P> poly, P sa, P sb, P start) {
    int startid = -1;
    for (int i = 0; i < sz(poly); i++) {
        if (segInter(poly[i], poly[(i+1)%sz(poly)], sa, sb).size()) {
            if (onLeft(sa, sb, poly[i])) {
                startid = i;
                break;
            } else if (onLeft(sa, sb, poly[(i+1)%sz(poly)])) {
                startid = i + 1;
                break;
            }
        }
    }
    if (startid == -1)
        return poly;
    vector<P> res;
    bool skip = false;
    for (int i = startid+1; i <= sz(poly) + startid; i++) {
        P p = poly[i%sz(poly)], prevv = poly[(i+sz(poly)-1)%sz(poly)];
        cerr << "cut " << p << " " << prevv << "\n";
        if (!onRight(sa, sb, p) && !onLeft(sa, sb, p)) {
            cerr << "mid\n";
            if (!skip)
                res.PB(p);
            continue;
        } else if (onLeft(sa, sb, p)) {
            cerr << "l\n";
            if (skip) {
                auto si = segInter(sa, sb, p, prevv);
                if (sz(si))
                    res.PB(si[0]);
                cerr << "lineinter " << sz(si) << "\n";
            }
            skip = false;
        } else {
            if (!skip) {
                auto si = segInter(sa, sb, p, prevv);
                cerr << p << " " << prevv << " " << sz(si) << "seginter\n";
                if (!si.empty())
                    res.PB(si[0]), skip = true;
            }
        }
        if (!skip)
            res.PB(p);
    }
    vector<P> rres;
    for (auto p : res) {
        if (rres.empty() || !cmp(rres.back(), p))
            rres.PB(p);
    }
    return rres;
}

ld polygonArea(vector<P> v) {
    ld a = v.back().cross(v[0]);
    rep(i,0,sz(v)-1) a += v[i].cross(v[i+1]);
    return a/2;
}

signed main(){
	cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit);
    int n;
    cin >> n;
    vector<P> poly;
    for (int i = 0; i < n; i++) {
        int x, y;
        cin >> x >> y;
        poly.PB({x, y});
    }
    vector<vector<P>> sidePoly;
    for (int i = 0; i < n; i++) {
        P v1 = poly[i], v2 = poly[(i+1)%n], v3 = poly[(i+2)%n];
        if (onRight(v1, v2, v3)) {
            cerr << v1 << " " << v2 << " " << v3 << "\n";
            vector<P> vp = {v2, v3};
            pair<ld, P> inter = {1000000000000000001ll, P(0, 0)};
            for (int j = i + 3; j < i+n; j++) {
                auto r = segInter(v1, v1 + (v2-v1)*1000000000, poly[j%n], poly[(j-1)%n]);
                if (r.empty())
                    continue;
                if ((v1-r[0]).dist2() < inter.FS)
                    inter = pair<ld, P>{(v1-r[0]).dist2(), r[0]};
            }
            cerr << inter.SD << "\n";
            for (int j = i + 3; j < 3*n; j++) {
                P vprev = poly[(j-1)%n];
                P v4 = poly[j%n];
                if (onSegment(v4, vprev, inter.SD)) {
                    vp.PB(inter.SD);
                    break;
                } else {
                    vp.PB(v4);
                }
            }
            cerr << "\nrem\n";
            for (auto p : vp) {
                cerr << p << "\n";
            }
            sidePoly.PB(vp);
        }
    }
    cerr << "start\n\n";
    vector<P> res = poly;
    for (auto vp : sidePoly) {
        P sa = vp[0], sb = vp.back();
        P vleft, vright; int foundleft = 0;
        for (auto p : res) {
            cerr << p << "\n";
        }
        cerr << "\n";
        cerr << sa << " " << sb << "\n\n";
        for (auto p : res) {
            if (onLeft(sa, sb, p)) {
                foundleft = 1;
                vleft = p;
            }
            if (onRight(sa, sb, p)) {
                vright = p;
            }
        }
        if (foundleft) {
            cerr << "found left\n";
            res = cutPolygon(res, sa, sb, vleft);
        } else {
            cerr << "not left\n";
            cerr << vright << "\n";
            for (auto p : vp) {
                cerr << p << "\n";
            }
            if (inPolygon(vp, vright, false)) {
                cerr << "zero!\n";
                cout << "0\n";
                return 0;
            }
        }
    }
    cerr << "\n\n";
    for (auto p : res) {
        cerr << p << "\n";
    }
    cout << fixed << setprecision(10) << polygonArea(res) << "\n";
}