Problem: You are given one polygonal line, which is a collection of line segments. Your task is to calculate the sum of areas enclosed by the polygonal line.

A point is defined to be "enclosed" if and only if the point is unreachable without crossing at least one line segment from the point at infinity.



Input

The first line contains one integers N (2 ≤ N ≤ 100). N is the number of segments.

Each of the following N lines consists of two integers Xi and Yi (-105 ≤ Xi, Yi ≤ 105, 1 ≤ i ≤ N) which represents a vertex. A polygonal line is the segments which connect (Xj, Yj) and (Xj+1, Yj+1) ((Xj, Yj) ≠ (Xj+1, Yj+1), 1 ≤ j ≤ N-1). The distance between a segment Sj and all vertices except the end points on segment Sj is guaranteed to be greater than 0.01.

Output

Output the answer in a line. The answer may be printed with an arbitrary number of decimal digits, but may not contain an absolute or relative error greater than or equal to 10-6.

Examples

Input

5
0 0
1 1
1 0
0 1
0 0


Output

0.5


Input

5
0 0
1 1
1 0
0 1
1 0


Output

0.25


Input

21
1 1
-1 1
-1 2
-2 2
-2 1
-1 1
-1 -1
-2 -1
-2 -2
-1 -2
-1 -1
1 -1
1 -2
2 -2
2 -1
1 -1
1 1
2 1
2 2
1 2
1 1


Output

8


Input

16
0 0
1 0
1 1
0 1
0 2
0 3
1 3
1 2
2 2
2 3
3 3
3 2
3 1
2 1
2 0
3 0


Output

0


Input

7
26 52
33 12
-51 68
16 61
43 -26
87 24
12 10


Output

2714.840579710

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define f first
#define s second
#define mp make_pair
#define pi M_PI
#define inf 1e14
#define eps (1e-5)
#define MAX 200000
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

class Point{
public:
  double x,y;
  Point(double x=0,double y=0):x(x),y(y){}

  Point operator+(Point p){ return Point(x+p.x,y+p.y);}
  Point operator-(Point p){ return Point(x-p.x,y-p.y);}
  Point operator*(double k){ return Point(x*k,y*k);}
  Point operator/(double k){ return Point(x/k,y/k);}
  bool operator<(Point p)const{ return (x!=p.x ? x<p.x : y<p.y);}
  bool operator==(Point p)const{ return fabs(x-p.x)<eps && fabs(y-p.y)<eps;}

  double abs(){ return sqrt(norm());}
  double norm(){ return (x*x+y*y);}
};
typedef Point Vector;
typedef vector<Point> Polygon;

class Segment{
public:
  Point p1,p2;
  Segment(Point p1=Point(),Point p2=Point()):p1(p1),p2(p2){}
};
typedef Segment Line;

double norm(Vector a){ return (a.x*a.x+a.y*a.y);}
double abs(Vector a){ return sqrt(norm(a));}
double dot(Vector a,Vector b){ return (a.x*b.x+a.y*b.y);}
double cross(Vector a,Vector b){ return (a.x*b.y-a.y*b.x);}

bool isParallel(Segment s,Segment t){
  return equals(cross(s.p1-s.p2,t.p1-t.p2),0.0);
}

int ccw(Point p0,Point p1,Point p2){
  Vector a=p1-p0;
  Vector b=p2-p0;
  if(cross(a,b)>eps)return 1;
  if(cross(a,b)<-eps)return -1;
  if(dot(a,b)<-eps)return 2;
  if(a.norm()<b.norm())return -2;
  return 0;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
  return (ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0 &&
          ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);
}

bool intersect(Segment s1,Segment s2){
  return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

Point getCrossPointLL(Line a,Line b){
  double A=cross(a.p2-a.p1,b.p2-b.p1);
  double B=cross(a.p2-a.p1,a.p2-b.p1);
  if(abs(A)<eps || abs(B)<eps)return b.p1;
  return b.p1+(b.p2-b.p1)*(B/A);
}

double getPolygonArea(Polygon p){
  double area=0.0;
  int n=p.size();
  for(int i=0;i<n;i++)area+=cross(p[i%n],p[(i+1)%n]);
  return area/2;
}

typedef vector<vector<int> > Graph;

Graph SegmentArrangement(vector<Segment> v,vector<Point> &ps){
  for(int i=0;i<v.size();i++){
    ps.push_back(v[i].p1);
    ps.push_back(v[i].p2);
    for(int j=i+1;j<v.size();j++){
      if(intersect(v[i],v[j]))
        ps.push_back(getCrossPointLL(v[i],v[j]));
    }
  }
  sort(ps.begin(),ps.end());
  ps.erase(unique(ps.begin(),ps.end()),ps.end());
  Graph g(ps.size());
  for(int i=0;i<v.size();i++){
    vector<pair<double,int> > list;
    for(int j=0;j<ps.size();j++)
      if(ccw(v[i].p1,v[i].p2,ps[j])==0)
        list.push_back(mp(norm(v[i].p1-ps[j]),j));
    sort(list.begin(),list.end());
    for(int j=0;j+1<list.size();j++){
      int a=list[j].s,b=list[j+1].s;
      g[a].push_back(b);
      g[b].push_back(a);
    }
  }
  return g;
}

bool merge_if_able(Segment &s,Segment t) {
  if(!isParallel(s,t))return false;
  if(abs(ccw(s.p1,s.p2,t.p1))==1 || 
     abs(ccw(s.p1,s.p2,t.p2))==1)return false;
  if(ccw(s.p1,s.p2,t.p1)==-2 || 
     ccw(t.p1,t.p2,s.p1)==-2)return false;
  s=Segment(min(s.p1,t.p1),max(s.p2,t.p2));
  return true;
}

void merge(vector<Segment>& v) {
  for(int i=0;i<v.size();i++){
    if(v[i].p2<v[i].p1)swap(v[i].p2,v[i].p1);
  }
  for(int i=0;i<v.size();i++){
    for(int j=i+1;j<v.size();j++){
      if(merge_if_able(v[i],v[j])){
        v[j--]=v.back();
        v.pop_back();
      }
    }
  }
}

Graph e;
vector<Segment> vs;
vector<Point> vp;
Polygon p;
int start=-1;
double ans=0.0;

double getAngle(Vector a,Vector b){
  double tmp=dot(a,b)/(abs(a)*abs(b));
  if(tmp<-1.0)tmp=-1.0;
  if(1.0<tmp)tmp=1.0;
  double r=acos(tmp)*180.0/pi;
  if(cross(a,b)<-eps)r=360.0-r;
  return r;
}

void dfs(int now,int before){
  if(now==start)return;
  vector<pair<double,int> > vd;
  for(int i=0;i<e[now].size();i++){
    int next=e[now][i];
    double ang=getAngle(vp[before]-vp[now],vp[next]-vp[now]);
    if(next==before)ang=361;
    vd.push_back(mp(ang,next));
  }
  sort(vd.begin(),vd.end());
  p.push_back(vp[now]);
  dfs(vd[0].s,now);
  return;
}

int main()
{
  int n,a,b,c,d;

  cin>>n;
  cin>>a>>b;
  for(int i=1;i<n;i++){
    cin>>c>>d;
    vs.push_back(Segment(Point(a,b),Point(c,d)));
    a=c;b=d;
  }
  merge(vs);
  e=SegmentArrangement(vs,vp);
  Point s(inf,inf);
  for(int i=0;i<vp.size();i++)s=min(s,vp[i]);
  for(int i=0;i<vp.size();i++)if(vp[i]==s)start=i;
  for(int i=0;i<e[start].size();i++){
    p.clear();
    p.push_back(vp[start]);
    dfs(e[start][i],start);
    double res=getPolygonArea(p);
    if(0.0<=res)ans+=res;
  }
  printf("%.10f\n",ans);
  return 0;
}