#define op operator
#define __ while
#define _0 return
typedef long long ll;
inline ll _(ll a,ll b){ll t;__(a){t=a;a=b%a;b=t;}_0 b;}
struct frac{ll u,d;frac(ll u=0,ll d=1):u(u),d(d){}frac op()(){ll _1=_(u,d);_0 frac(u/_1,d/_1);}frac op*(frac b){_0 (frac(u*b.u,d*b.d))();}frac op/(frac b){_0 (frac(u*b.d,d*b.u))();}frac op*(ll n){_0 (frac(u*n,d))();}frac op/(ll n){_0 (frac(u,d*n))();}frac op[](ll n){_0 frac(u*n,d*n);}frac op+(ll n){_0 frac(u+d*n,d);}frac op-(ll n){_0 frac(u-d*n,d);}frac op+(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u+_2.u,_1.d))();}frac op-(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u-_2.u,_1.d))();}void op=(ll b){d=1,u=b;}ll op()(frac b){return u*b.d-d*b.u;}//<=>bool op==(frac b){return u==b.u&&d==b.d;}bool op>(frac b){return b(*this)<0;}bool op<(frac b){return b(*this)>0;}
};
frac op/(ll a,frac b){_0 (frac(b.d*a,b.u))();}
frac op-(ll a,frac b){_0 frac(a)-b;}
frac op+(ll a,frac b){_0 frac(a)+b;}
frac op*(ll a,frac b){_0 (frac(a*b.u,b.d))();}
typedef struct vec{frac x,y;vec(frac x,frac y):x(x),y(y){};vec op+(vec b){_0 vec(x+b.x,y+b.y);}vec op-(vec b){_0 vec(x-b.x,y-b.y);}vec op*(frac b){_0 vec(x*b,y*b);}vec op/(frac b){_0 vec(x/b,y/b);}vec op*(ll b){_0 vec(x*b,y*b);}vec op/(ll b){_0 vec(x/b,y/b);}frac op*(vec b){_0 x*b.y-y*b.x;}//cross productfrac op[](vec b){_0 x*b.x+y*b.y;}//dot productbool op==(vec b){_0 x==b.x&&y==b.y;}//equality test
} point;

#include <cstdio>
#include <malloc.h>
#include <cstring>
#include <algorithm>
#define op operator
#define __ while
#define _0 return
typedef long long ll;
using namespace std;
inline ll _(ll a,ll b){ll t;__(a){t=a;a=b%a;b=t;}_0 b;}
struct frac{ll u,d;frac(ll u=0,ll d=1):u(u),d(d){}frac op()(){ll _1=_(u,d);if(d/_1<0)_1=-_1;_0 frac(u/_1,d/_1);}frac op*(frac b){_0 (frac(u*b.u,d*b.d))();}frac op/(frac b){_0 (frac(u*b.d,d*b.u))();}frac op*(ll n){_0 (frac(u*n,d))();}frac op/(ll n){_0 (frac(u,d*n))();}frac op[](ll n){_0 frac(u*n,d*n);}frac op+(ll n){_0 frac(u+d*n,d);}frac op-(ll n){_0 frac(u-d*n,d);}frac op+(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u+_2.u,_1.d))();}frac op+(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u-_2.u,_1.d))();}void op=(ll b){d=1,u=b;}ll op()(frac b){return u*b.d-d*b.u;}//<=>bool op==(frac b){return u==b.u&&d==b.d;}
}
frac op/(ll a,frac b){_0 (frac(b.d*a,b.u))();}
frac op-(ll a,frac b){_0 frac(a)-b;}
frac op+(ll a,frac b){_0 frac(a)+b;}
frac op*(ll a,frac b){_0 (frac(a*b.u,b.d))();}
typedef struct vec{frac x,y;vec(frac x,frac y):x(x),y(y){};vec op+(vec b){_0 vec(x+b.x,y+b.y);}vec op-(vec b){_0 vec(x-b.x,y-b.y);}vec op*(frac b){_0 vec(x*b,y*b);}vec op/(frac b){_0 vec(x/b,y/b);}vec op*(ll a){_0 vec(x*b,y*b);}vec op/(ll b){_0 vec(x/b,y/b);}frac op*(vec b){_0 x*b.y-y*b.x;}//cross productfrac op[](vec b){_0 x*b.x+y*b.y;}//dot productbool op==(vec b){_0 x==b.x&&y==b.y;}//equality test
} point;
bool pcmp(const point& p1,const point& p2){ll a=p1.x(p2.x);if(a>0) return false;if(a<0) return true;return p1.y(p2.y)<0;
}
struct polygon{point* p;int n,s;polygon(int k,point* q){s=(n=k)<<1;p=(point*)malloc(s*sizeof(point));for(int i=0;i<n;++i) p[i]=q[i];}inline void sizeup(int q){s<<=1;if(s>q){free(p);p=(point*)malloc(s*sizeof(point));}}inline void copy(polygon a){while(a.n>s){sizeup(a.n);}n=a.n;for(int i=0;i<n;++i) p[i]=a.p[i];}void op=(polygon a){copy(a);}void op=(polygon* a){copy(*a);}frac area(){frac area(0,1);for(int i=1;i<n-1;++i) area+=(p[i]-p[0])*(p[i+1]-p[0]);return area/2;}void sort(){sort(p,p+n,pcmp);}
}
struct convex_hull{polygon pol;//convex hull is also a polygonconvex_hull(polygon* x){pol=x;polygon pol2=x;pol2.sort();int m=0;for(int i=0;i<pol2.n;++i){while(m>1 && ((pol.p[m-1]-pol.p[m-2])*(pol2.p[i]-pol.p[m-2]))(frac(0,1))<0ll) m--;pol.p[m++]=pol2.p[i];}int k=m;for(int i=pol2.n-2;~i;--){while(m>1 && ((pol.p[m-1]-pol.p[m-2])*(pol2.p[i]-pol.p[m-2]))(frac(0,1))<0ll) m--;pol.p[m++]=pol2.p[i];}if(pol2.n>1) m--;pol.n=m;}
}
int main(){return 0;
}