#include 
     
      #include 
      
       const double eps = 1e-10;struct Point{    double x,y;    Point(double x = 0, double y = 0):x(x),y(y){} //初始化列表构造函数};typedef Point Vector;//向量+向量 = 向量， 点 +　向量 = 向量Vector operator + (Vector A, Vector B){
   return Vector(A.x+B.x, A.y+B.y);}//点-点=向量Vector operator - (Point A,Point B){
   return Vector(A.x-B.x, A.y - B.y);}//向量*数=向量Vector operator * (Vector A, double p){
   return Vector(A.x*p, A.y*p);}//向量/数 = 向量Vector operator /(Vector A, double p){
   return Vector(A.x/p, A.y/p);}bool operator < (const Point& a,const Point& b){
   return a.x < b.x || (a.x == b.x && a.y < b.y);}//三态函数int dcmp(double x){
   if(fabs(x) < eps ) return 0;else return x <  0 ? -1 : 1;}//判断两个点是否相等bool operator == (const Point& a,const Point& b){
   return dcmp(a.x - b.x) == 0 && dcmp(a.y-b.y)  == 0;}//求向量的极角double polar_angle(Vector A){
   return atan2(A.y,A.x);}//点积double Dot(Vector A, Vector B){
   return A.x*B.x + A.y*B.y;}//求向量的长度double Length(Vector A){
   return sqrt(Dot(A,A));}//求向量之间的夹角double Angle(Vector A,Vector B){
   return acos(Dot(A,B)/Length(A)/Length(B));}//两个向量的叉积double Cross(Vector A,Vector B){
   return A.x*B.y - A.y*B.y;}//求有向面积double Area2(Point A, Point B, Point C ){ return Cross(B-A,C-A);}//向量旋转Vector Rotate(Vector A,double rad){    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}//向量的单位法向量Vector Normal(Vector A){    double L = Length(A);    return Vector(-A.y/L,A.x/L);}//求两条直线的交点Point GetLineIntersection(Point P,Vector v, Point Q, Vector w){    Vector u = P-Q;    double t =Cross(w,u)/Cross(v,w);   //注意当Cross(v,w)!=0时才有交点    return P+v*t;}//点到直线的距离double DistanceToLine(Point P,Point A,Point B){    Vector v1 = B-A, v2 = P-A;    return fabs(Cross(v1,v2))/Length(v1);}//点到线段的距离double DistanceToSegment(Point P,Point A,Point B){    if (A==B) return Length(P-A);    Vector v1 = B-A, v2 = P-A, v3 = P-B;    if (dcmp(Dot(v1,v2)) < 0) return Length(v2);    else if (dcmp(Dot(v1,v3)) > 0) return Length(v3);    else return fabs(Cross(v1,v2))/Length(v1);}//点在直线上的投影Point GetLineProjection(Point P, Point A, Point B){    Vector v = B-A;    return A+v*(Dot(v,P-A)/Dot(v,v));}//线段相交判断bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){    double c1 = Cross(a2-a1,b1-a1);    double c2 = Cross(a2-a1,b2-a1);    double c3 = Cross(b2-b1,a1-b1);    double c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(c4) < 0;}//点是否在线段上bool OnSegment(Point p,Point a1, Point a2){    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p)) < 0;}