#include<bits/stdc++.h>

#define EQ(a,b) (abs((a)-(b)) < EPS)
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define fs first
#define sc second
#define pb push_back
#define sz size()
#define all(a) (a).begin(),(a).end()

using namespace std;
typedef long double D;
typedef complex<D> P;
typedef pair<P,P> L;
typedef vector<P> Poly;
typedef pair<P,D> C;

typedef vector<int> vi;
typedef pair<int,int> pii;
typedef pair<D,int> pdi;

const D EPS = 1e-11;
const D PI = acos(-1);

bool lessP(const P &a,const P &b){
  return EQ(real(a),real(b))?imag(a)<imag(b):real(a)<real(b);
}
bool eqP(const P &a, const P &b){return EQ(a,b);}

bool lessL(const L &a,const L &b){
  return eqP(a.fs,b.fs)?lessP(a.sc,b.sc):lessP(a.fs,b.fs);
}
bool eqL(const L &a, const L &b){return eqP(a.fs,b.fs)&&eqP(a.sc,b.sc);}


//for vector
inline D dot(P x, P y){return real(conj(x)*y);}
inline D cross(P x, P y){return imag(conj(x)*y);}

//for line(segment)
int ccw(P a,P b,P c){
  b -= a;c -= a;
  if (cross(b,c)>EPS) return 1;   //counter clockwise
  if (cross(b,c)<-EPS) return -1; //clockwise
  if (dot(b, c)<-EPS) return 2;   //c--a--b on line
  if (abs(b)<abs(c)) return -2;   //a--b--c on line
  return 0;                       //on segment
}

inline bool para(L a,L b){return abs(cross(a.fs-a.sc,b.fs-b.sc))<EPS;}

inline P line_cp(L a,L b){
  return a.fs+(a.sc-a.fs)*cross(b.sc-b.fs,b.fs-a.fs)/cross(b.sc-b.fs,a.sc-a.fs);
}

inline bool is_cp(L a,L b){
  if(ccw(a.fs,a.sc,b.fs)*ccw(a.fs,a.sc,b.sc)<=0)
    if(ccw(b.fs,b.sc,a.fs)*ccw(b.fs,b.sc,a.sc)<=0)return true;
  return false;
}

//for polygon
inline D area(Poly p){
  if(p.sz<3)return 0;
  D res = cross(p[p.sz-1],p[0]);
  rep(i,p.sz-1)res += cross(p[i],p[i+1]);
  return res/2;
}

//b divides a into segments
inline vector<L> seg_cut(L a, L b){
  vector<L> res;
  
  if(!is_cp(a,b))res.pb(a);
  else{
    if(para(a,b)){
      int cpf = ccw(a.fs,a.sc,b.fs), cps = ccw(a.fs,a.sc,b.sc);
      if(!cpf && !cps){
	if(ccw(a.fs,b.fs,b.sc)==0){
	  res.pb(L(a.fs,b.sc)); res.pb(L(b.sc,b.fs)); res.pb(L(b.fs,a.sc));
	}else{
	  res.pb(L(a.fs,b.fs)); res.pb(L(b.fs,b.sc)); res.pb(L(b.sc,a.sc));
	}
      }else if(!cpf){
	res.pb(L(a.fs,b.fs)); res.pb(L(a.sc,b.fs));
      }else if(!cps){
	res.pb(L(a.fs,b.sc)); res.pb(L(a.sc,b.sc));
      }else res.pb(a);
    }else{
      P cp = line_cp(a,b);
      if(!EQ(a.fs,cp) && !EQ(a.sc,cp)){
	res.pb(L(a.fs,cp)); res.pb(L(a.sc,cp));
      }else{
	res.pb(a);
      }
    }
  }
  return res;
}

inline vector<L> seg_set_cut(vector<L> l){
  vector< vector<L> > vl(l.sz);
  rep(i,l.sz)vl[i].pb(l[i]);
  
  rep(i,l.sz)for(int j=i+1;j<(int)l.sz;j++){
    rep(ii,vl[i].sz)rep(jj,vl[j].sz){
      if(is_cp(vl[i][ii],vl[j][jj])){
	vector<L> a = seg_cut(vl[i][ii],vl[j][jj]);
	vector<L> b = seg_cut(vl[j][jj],vl[i][ii]);

	while(a.sz>1){vl[i].pb(a.back()); a.pop_back();}
	vl[i][ii] = a[0];
	while(b.sz>1){vl[j].pb(b.back()); b.pop_back();}
	vl[j][jj] = b[0];
	goto END;
      }
    }
    END:;
  }

  vector<L> res;
  rep(i,l.sz)rep(j,vl[i].size()){
    if(lessP(vl[i][j].sc,vl[i][j].fs))swap(vl[i][j].fs,vl[i][j].sc);
    res.pb(vl[i][j]);
  }
  sort(all(res),lessL);
  res.erase(unique(all(res),eqL),res.end());
  return res;
}

inline void seg_arrange(vector<L> input_segs, vector<P> &vp,
			vector<pii> &ve, vector< vector<pii> > &graph){
  vector<L> vl = seg_set_cut(input_segs);

  /*  
  cout << vl.sz << endl;
  rep(i,vl.sz)cout << vl[i].fs.real() << " " << vl[i].fs.imag() << " "
  		   << vl[i].sc.real() << " " << vl[i].sc.imag() << endl;
  */
  vp.clear();
  rep(i,vl.sz){
    vp.pb(vl[i].fs);
    vp.pb(vl[i].sc);
  }
  sort(all(vp),lessP);
  vp.erase(unique(all(vp),eqP),vp.end());

  ve.resize(vl.sz);
  vector< vector<pdi> > edges(vp.sz);

  rep(i,vl.sz){
    int s,t;
    rep(j,vp.sz){
      if(EQ(vl[i].fs,vp[j]))s = j;
      if(EQ(vl[i].sc,vp[j]))t = j;
    }
      /*
    int s = lower_bound(all(vp),vl[i].fs,lessP)-vp.begin();
    int t = lower_bound(all(vp),vl[i].sc,lessP)-vp.begin();
      */
    ve[i] = pii(s,t);
    edges[s].push_back(pdi(arg(vp[t]-vp[s]),i));
    edges[t].push_back(pdi(arg(vp[s]-vp[t]),i));
  }

  graph.resize(vp.sz);
  rep(i,vp.sz){
    sort(all(edges[i]));
    graph[i].clear();
    rep(j,edges[i].sz){
      int id = edges[i][j].sc;
      int v = (ve[id].fs == i)?ve[id].sc:ve[id].fs;
      graph[i].pb(pii(v,id));
    }
  }
}

inline vector<Poly> extract_poly(vector<L> set_l){
  vector<P> p;
  vector<pii> l;
  vector< vector<pii> > e;
  seg_arrange(set_l,p,l,e);

  /*
  int num = 0;
  rep(i,e.sz)num += e[i].sz;
  cout << num << endl;
  rep(i,e.sz){
    rep(j,e[i].sz){
      int id = e[i][j].sc;
      cout << p[l[id].fs].real() << " " << p[l[id].fs].imag() << " "
	   << p[l[id].sc].real() << " " << p[l[id].sc].imag() << endl;
    }
  }
  */

  vector<vi> g(l.sz,vi(2,-1));
  vector<Poly> PolySet;

  rep(i,l.sz)rep(j,2){
    int cur = i, dir = j;
    if(g[cur][dir]>=0)continue;

    //D area = 0;
    Poly poly;
    while(true){
      g[cur][dir] = 0;
      
      int node = dir?l[cur].fs:l[cur].sc;
      int prv = dir?l[cur].sc:l[cur].fs;
      poly.push_back(p[node]);
      //area += cross(p[prv],p[node]);

      int s = e[node].sz;
      int nxt = find(all(e[node]),pii(prv,cur))-e[node].begin();
      cur = e[node][(nxt+s-1)%s].sc;
      dir = (l[cur].fs==node)?0:1;

      if(g[cur][dir]>=0)break;
    }
    
    //cout << area(poly) << endl;
    //rep(i,poly.sz)cout << poly[i] << " ";cout << endl;
    if(area(poly)>EPS)PolySet.pb(poly);
  }
  return PolySet;
}


int main(){
  int n;
  cin >> n;

  vector<P> p(n);
  rep(i,n){
    int x,y;
    cin >> x >> y;
    p[i] = P(x,y);
  }

  vector<L> l(n-1);
  rep(i,n-1)l[i] = L(p[i],p[i+1]);

  vector<Poly> poly = extract_poly(l);

  /*
  vector<L> vl;
  rep(i,poly.sz){
    rep(j,poly[i].sz)vl.push_back(L(poly[i][j],poly[i][(j+1)%poly[i].sz]));
  }
  cout << vl.sz << endl;
  rep(i,vl.sz)cout << vl[i].fs.real() << " " << vl[i].fs.imag() << " "
		   << vl[i].sc.real() << " " << vl[i].sc.imag() << endl;
  */

  vector<D> a(poly.sz);
  rep(i,poly.sz)a[i] = area(poly[i]);
  sort(all(a));
  D res = 0;
  rep(i,a.sz)res += a[i];
  cout << fixed << setprecision(10) << res << endl;
}

Measured memory_bytes: 2688