#include <iostream>#include <stdio.h>#include <math.h>#include <string.h>using namespace std;const double esp = 1e-10;struct Point{    double x,y;    Point(double x = 0,double y = 0):x(x),y(y){}};typedef Point Vector;Vector operator + (Vector A ,Vector B) {return Vector(A.x+B.x,A.y+B.y);}Vector operator - (Vector A ,Vector B) {return Vector(A.x-B.x,A.y-B.y);}Vector operator * (Vector A ,double p) {return Vector(A.x*p,A.y*p);}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);}int dcmp(double x){    if(fabs(x)<esp) return 0;    else return x<0?-1:1;}bool operator == (const Point&a,const Point &b){    return dcmp(a.x-b.x) ==0 && dcmp(a.y-b.y) ==0 ;}double Dot(Vector A ,Vector B) {return A.x*B.x+A.y*B.y;}double Length(Vector A) {return sqrt(Dot(A,A));}double Angle(Vector A,Vector B) {return acos(Dot(A,B)/(Length(A)*(Length(B))));}double Cross(Vector A,Vector B) {return A.x*B.y-A.y*B.x;}double Area2(Point A,Point B, Point C) {return Cross(B-A,C-A);}Vector Rotate(Vector A,double rad){//向量旋转    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}//单位方向向量Vector Normal(Vector A){    double L = Length(A);    return Vector(-A.y/L,A.x/L);}//直线相交Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){    Vector u = P-Q;    double t = Cross(w,u)/Cross(v,w);    return P+v*t;}/*点到直线距离*/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);}/*点在线段上投影*/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*/bool SegmentProperIntersection(Point a1,Point a2,Point b1, Point b2){    double c1 = Cross(a2-a1,b1-a1), c2 = Cross(a2-a1,b2-a1),           c3 = Cross(b2-b1,a1-b1), c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;}/*端点相交*/bool OnSegment(Point p,Point a1, Point a2){    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}