// CONVEX HULL I
// modified by rr 不能去掉點集中重合的點
#include <stdlib.h>
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
struct point{double x,y;};

//計算cross product (P1-P0)x(P2-P0)
double xmult(point p1,point p2,point p0){
	return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
//graham算法順時針構造包含所有共線點的凸包,O(nlogn)
point p1,p2;
int graham_cp(const void* a,const void* b){
	double ret=xmult(*((point*)a),*((point*)b),p1);
	return zero(ret)?(xmult(*((point*)a),*((point*)b),p2)>0?1:-1):(ret>0?1:-1);
}
void _graham(int n,point* p,int& s,point* ch){
	int i,k=0;
	for (p1=p2=p[0],i=1;i<n;p2.x+=p[i].x,p2.y+=p[i].y,i++)
		if (p1.y-p[i].y>eps||(zero(p1.y-p[i].y)&&p1.x>p[i].x))
			p1=p[k=i];
	p2.x/=n,p2.y/=n;
	p[k]=p[0],p[0]=p1;
	qsort(p+1,n-1,sizeof(point),graham_cp);
	for (ch[0]=p[0],ch[1]=p[1],ch[2]=p[2],s=i=3;i<n;ch[s++]=p[i++])
		for (;s>2&&xmult(ch[s-2],p[i],ch[s-1])<-eps;s--);
}

//構造凸包接口函數,傳入原始點集大小n,點集p(p原有順序被打亂!)
//返回凸包大小,凸包的點在convex中
//參數maxsize為1包含共線點,為0不包含共線點,缺省為1
//參數clockwise為1順時針構造,為0逆時針構造,缺省為1
//在輸入僅有若干共線點時算法不穩定,可能有此類情況請另行處理!
//不能去掉點集中重合的點
int graham(int n,point* p,point* convex,int maxsize=1,int dir=1){
	point* temp=new point[n];
	int s,i;
	_graham(n,p,s,temp);
	for (convex[0]=temp[0],n=1,i=(dir?1:(s-1));dir?(i<s):i;i+=(dir?1:-1))
		if (maxsize||!zero(xmult(temp[i-1],temp[i],temp[(i+1)%s])))
			convex[n++]=temp[i];
	delete []temp;
	return n;
}

// CONVEX HULL II
// modified by mgmg 去掉點集中重合的點

#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
struct point{double x,y;};

//計算cross product (P1-P0)x(P2-P0)
double xmult(point p1,point p2,point p0){
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
//graham算法順時針構造包含所有共線點的凸包,O(nlogn)
point p1,p2;
int graham_cp(const void* a,const void* b){
    double ret=xmult(*((point*)a),*((point*)b),p1);
    return zero(ret)?(xmult(*((point*)a),*((point*)b),p2)>0?1:-1):(ret>0?1:-1);
}
void _graham(int n,point* p,int& s,point* ch){
    int i,k=0;
    for (p1=p2=p[0],i=1;i<n;p2.x+=p[i].x,p2.y+=p[i].y,i++)
        if (p1.y-p[i].y>eps||(zero(p1.y-p[i].y)&&p1.x>p[i].x))
            p1=p[k=i];
    p2.x/=n,p2.y/=n;
    p[k]=p[0],p[0]=p1;
    qsort(p+1,n-1,sizeof(point),graham_cp);
    for (ch[0]=p[0],ch[1]=p[1],ch[2]=p[2],s=i=3;i<n;ch[s++]=p[i++])
        for (;s>2&&xmult(ch[s-2],p[i],ch[s-1])<-eps;s--);
}

int wipesame_cp(const void *a, const void *b)
{
    if ((*(point *)a).y < (*(point *)b).y - eps) return -1;
    else if ((*(point *)a).y > (*(point *)b).y + eps) return 1;
    else if ((*(point *)a).x < (*(point *)b).x - eps) return -1;
    else if ((*(point *)a).x > (*(point *)b).x + eps) return 1;
    else return 0;
}

int _wipesame(point * p, int n)
{
    int i, k;
    qsort(p, n, sizeof(point), wipesame_cp);
    for (k=i=1;i<n;i++)
        if (wipesame_cp(p+i,p+i-1)!=0) p[k++]=p[i];
    return k;
}

//構造凸包接口函數,傳入原始點集大小n,點集p(p原有順序被打亂!)
//返回凸包大小,凸包的點在convex中
//參數maxsize為1包含共線點,為0不包含共線點,缺省為1
//參數clockwise為1順時針構造,為0逆時針構造,缺省為1
//在輸入僅有若干共線點時算法不穩定,可能有此類情況請另行處理!
int graham(int n,point* p,point* convex,int maxsize=1,int dir=1){
    point* temp=new point[n];
    int s,i;
    n = _wipesame(p,n);
    _graham(n,p,s,temp);
    for (convex[0]=temp[0],n=1,i=(dir?1:(s-1));dir?(i<s):i;i+=(dir?1:-1))
        if (maxsize||!zero(xmult(temp[i-1],temp[i],temp[(i+1)%s])))
            convex[n++]=temp[i];
    delete []temp;
    return n;
}