int sgn(double x){return x<-eps?-1:x<eps?0:1;}
struct Point{
    double x,y;
    Point(){}
    Point(double _x,double _y){
        x=_x;y=_y;
    }
};
struct Seg{
    Point s,e;
    Seg(){}
    Seg(Point _s,Point _e){
        s=_s;e=_e;
    }
    Seg(double a,double b,double c,double d){
        s.x=a;s.y=b;
        e.x=c;e.y=d;
    }
};
double cross(Point a,Point b,Point c){
    return (b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x);
}
double dist(Point a,Point b){
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
/*兩線段交點*/
Point inter(Seg a,Seg b){
    Point p1,p2,p3,p4;
    p1=a.s;p2=a.e;p3=b.s;p4=b.e;
    double a1=p1.y-p2.y;
    double b1=p2.x-p1.x;
    double c1=p1.x*p2.y-p2.x*p1.y;

    double a2=p3.y-p4.y;
    double b2=p4.x-p3.x;
    double c2=p3.x*p4.y-p4.x*p3.y;

    double x=(c2*b1-c1*b2)/(a1*b2-a2*b1);
    double y=(c2*a1-c1*a2)/(a2*b1-a1*b2);

    return Point(x,y);
}
/*線段相交*/
bool jiao(Seg a,Seg b){
    Point p1,p2,p3,p4;
    p1=a.s;p2=a.e;
    p3=b.s;p4=b.e;
    if(min(p1.x,p2.x)<=max(p3.x,p4.x) &&
    min(p3.x,p4.x)<=max(p1.x,p2.x) &&
    min(p1.y,p2.y)<=max(p3.y,p4.y) &&
    min(p3.y,p4.y)<=max(p1.y,p2.y) &&
    sgn(cross(p1,p2,p3))*sgn(cross(p1,p2,p4))<=0 &&
    sgn(cross(p3,p4,p1))*sgn(cross(p3,p4,p2))<=0 ) return true;
    return false;
}
/*凸包graham演算法*/
Point tmp;
bool cmp(const Point &a,const Point &b){
    int ret=sgn(cross(tmp,a,b));
    if(ret==0) return dist(tmp,a)<dist(tmp,b);
    return ret>0;
}
int graham(Point p[],int n,Point convex[]){
    int mi=0;
    for(int i=1;i<n;i++)  if(sgn(p[mi].y-p[i].y)>0 || sgn(p[mi].y-p[i].y)==0  && sgn(p[mi].x-p[i].x)>0) mi=i;
    swap(p[0],p[mi]);
    tmp=p[0];
    sort(p+1,p+n,cmp);
    int top=0;
    convex[top++]=p[0];
    convex[top++]=p[1];
    int k=2;
    while(k<=n){
        while(top>=2 && sgn(cross(convex[top-2],p[k%n],convex[top-1]))>=0) top--;
        convex[top++]=p[k%n];
        k++;
    }
    return top;
}
double pi=acos(-1.0);