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 REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-7)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
#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 a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}
  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }
  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }
};

struct Segment{
  Point p1,p2;
  Segment(Point p1 = Point(),Point p2 = Point()):p1(p1),p2(p2){}
 bool operator == (const Segment& p)const { return ( p.p1 == p1 && p.p2 == p2 ) || ( p.p1 == p2 && p.p2 == p1 ); }
};

typedef Point Vector;
typedef Segment Line;

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

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}

Point crosspoint(Line l,Line m){
  double A = cross(l.p2-l.p1,m.p2-m.p1);
  double B = cross(l.p2-l.p1,l.p2-m.p1);
  if(abs(A) < EPS && abs(B) < EPS){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]);
    return vec[1];
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}

double cross3p(Point p,Point q,Point r){ return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
bool collinear(Point p,Point q,Point r){ return fabs(cross3p(p,q,r)) < EPS; }
bool ccwtest(Point p,Point q,Point r){ return cross3p(p,q,r) > 0; }
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}

double getArea(vector<Point>& vec){
  double sum = 0;
  for(int i=0;i<(int)vec.size();i++) sum += cross(vec[i],vec[(i+1)%vec.size()]);
  return fabs(sum)/2.0;
}

int N;
vector<Point> ps;

bool comp_dist(const Point& a,const Point& b) { return abs(a) < abs(b); }

void makeSegments(vector<Segment> &segs){
  vector<Point> vp;
  rep(i,N-1) {
    vp.clear();
    vp.push_back(ps[i]);
    vp.push_back(ps[i+1]);
    Segment cur_seg = Segment(ps[i],ps[i+1]);
    rep(j,N-1) if( i != j ) {
      Segment seg = Segment(ps[j],ps[j+1]);
      if( equals(cross(cur_seg.p1-cur_seg.p2,seg.p1-seg.p2),0.0) ) {
        if( onSegment(cur_seg.p1,cur_seg.p2,seg.p1) ) {
          vp.push_back(seg.p1);
        }
        if( onSegment(cur_seg.p1,cur_seg.p2,seg.p2) ) {
          vp.push_back(seg.p2);
        }
      } else if( intersectSS(seg,cur_seg) ) {
        vp.push_back(crosspoint(cur_seg,seg));
      }

      rep(k,vp.size()) vp[k] = vp[k] - ps[i];
      sort(vp.begin(),vp.end(),comp_dist);
      vp.erase(unique(vp.begin(),vp.end()),vp.end());
      rep(k,vp.size()) vp[k] = vp[k] + ps[i];

    }
    rep(k,vp.size()) vp[k] = vp[k] - ps[i];
    sort(vp.begin(),vp.end(),comp_dist);
    vp.erase(unique(vp.begin(),vp.end()),vp.end());
    rep(k,vp.size()) vp[k] = vp[k] + ps[i];
    rep(j,(int)vp.size()-1) segs.push_back(Segment(vp[j],vp[j+1]));
  }
}



vector<Point> angle_ps;

struct Data{ 
  int from,to,rev; 
  bool operator < (const Data & a)const{
    Vector vec_a = angle_ps[a.to] - angle_ps[a.from];
    Vector vec_b = angle_ps[to] - angle_ps[from];
    double arg_a = atan2(vec_b.y,vec_b.x);
    double arg_b = atan2(vec_a.y,vec_a.x);
    return !equals(arg_a,arg_b) && arg_a < arg_b;
  }
};

vector<vector<Data> > G;
vector<Point> vp;

void makeGraph(const vector<Segment> &segs){
  map<Point,int> mp;
  int V = 0;
  rep(i,segs.size()) if( !mp.count(segs[i].p1) ) mp[segs[i].p1] = V++;
  if( !mp.count(segs.back().p2) ) mp[segs.back().p2] = V++;
  vp.resize(V);
  for(map<Point,int>::iterator it = mp.begin(); it != mp.end(); it++){
    vp[it->second] = it->first;
  }
  angle_ps = vp;
  G.resize(V,vector<Data>());
  rep(i,segs.size()) {
    int s = mp[segs[i].p1], t = mp[segs[i].p2];
    G[s].push_back((Data){s,t,-1});
    G[t].push_back((Data){t,s,-1});
  }

  rep(i,V) {
    sort(G[i].begin(),G[i].end());
  }
  rep(i,V) rep(j,(int)G[i].size()) if( G[i][j].rev == -1 ) {
    int to = G[i][j].to;
    rep(k,(int)G[to].size())if( G[to][k].to == i ){
      G[i][j].rev = k;
      G[to][k].rev = j;
      break;
    }
  }
}

const int MAX_V = 5000;
bool visited[MAX_V][MAX_V];


bool getPath(int start_node,int node,int edge,vector<Point> &buf){
  if( visited[node][edge] ){
    if( !buf.empty() && node == start_node ) return true;
    return false;
  }
  visited[node][edge] = true;
 
  int next_node = G[node][edge].to;
  int next_edge = (G[node][edge].rev+1)%((int)G[next_node].size());
  buf.push_back(vp[G[node][edge].from]);
  if(getPath(start_node,next_node,next_edge,buf)) return true;
  else return visited[node][edge] = false;
}

void compute(){
  vector<Segment> segs;
  segs.clear();
  makeSegments(segs);
  makeGraph(segs);
  segs.clear();
  ps.clear();
  angle_ps.clear();
  int V = vp.size();
  rep(i,V) rep(j,V) visited[i][j] = false;
  double area = 0;
  rep(i,V) rep(j,(int)G[i].size()) if( !visited[i][j] ){
    vector<Point> buf;
    if( getPath(i,i,j,buf) && !buf.empty() ) area += getArea(buf);
  }
  printf("%.10lf\n",area/2.0);  
}

int main(){
  scanf("%d",&N);
  ps.resize(N);
  rep(i,N) scanf("%lf %lf",&ps[i].x,&ps[i].y);
  compute();
  return 0;
}