using System; using System.Collections.Generic; using System.Collections; using System.Collections.Specialized; using System.Linq; using System.Text; using System.IO; using System.Reflection; using static System.Math; using System.Numerics; using static Exg; static class Program{ const int mod=(int)1e9+7; const double eps=1e-11; static void Main(){ Sc sc=new Sc(); var n=sc.I; var hs=new Dictionary(); var pa=new Pair[n]; int ans=0; for(int i = 0;ix.ToString()+" "+y.ToString(); public static Pair operator+(Pair a,Pair b){a.x+=b.x;a.y+=b.y;return a;} public static Pair operator-(Pair a,Pair b){a.x-=b.x;a.y-=b.y;return a;} public static Pair operator*(Pair a,double n){a.x*=n;a.y*=n;return a;} public static Pair operator/(Pair a,double n){a.x/=n;a.y/=n;return a;} } static class Exg{ static public double Gp0(Pair a,Pair b){return Sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));} static public Tuple Gp1(Pair p1,Pair p2,Pair p3,Pair p4){ double t1=(p4.y-p3.y)*(p4.x-p1.x)-(p4.x-p3.x)*(p4.y-p1.y); double t2=(p2.x-p1.x)*(p4.y-p1.y)-(p2.y-p1.y)*(p4.x-p1.x); double t3=(p2.x-p1.x)*(p4.y-p3.y)-(p2.y-p1.y)*(p4.x-p3.x); if(t3==0){ if(Abs(Atan2(p2.y-p1.y,p2.x-p1.x))!=Abs(Atan2(p3.y-p1.y,p3.x-p1.x))){return Tuple.Create(p1.x==p3.x&&p1.y==p3.y?true:false,p1);} var a=new Tuple[]{Tuple.Create(p1,1),Tuple.Create(p2,2),Tuple.Create(p3,3),Tuple.Create(p4,4)}; Array.Sort(a,(d,e)=>{var c=d.Item1.x.CompareTo(e.Item1.y);return c==0?e.Item1.y.CompareTo(d.Item1.y):c;}); return Tuple.Create((Abs(a[0].Item2-a[1].Item2)!=1||Abs(a[2].Item2-a[3].Item2)!=1)||(a[1].Item1.x==a[2].Item1.x&&a[1].Item1.y==a[2].Item1.y)?true:false,a[1].Item1); } double t4=t1/t3,t5=t2/t3; if(t4<0||t4>1||t5<0||t5>1){return Tuple.Create(false,new Pair(0,0));} else{return Tuple.Create(true,new Pair(p1.x+t4*(p2.x-p1.x),p1.y+t4*(p2.y-p1.y)));} } static public double Gp2(Pair p1,Pair p2,Pair p0){return Abs((p2.y-p1.y)*p0.x-(p2.x-p1.x)*p0.y+p2.x*p1.y-p1.x*p2.y)/Sqrt((p2.y-p1.y)*(p2.y-p1.y)+(p2.x-p1.x)*(p2.x-p1.x));} static public double Gp3(Pair p1,Pair p2,Pair p0){return (p1.x-p2.x)*(p0.y-p1.y)+(p1.y-p2.y)*(p1.x-p0.x);} static public double Gp4(Pair a,Pair b,Pair c){ double a1=a.x-b.x,a2=a.y-b.y,c1=c.x-b.x,c2=c.y-b.y; return Acos((a1*c1+a2*c2)/Sqrt((a1*a1+a2*a2)*(c1*c1+c2*c2)))*180/PI; } static public Tuple Gp5(Pair p1,Pair p2,Pair p0){ double rx=p0.x,ry=p0.y; if(p1.x==p2.x){rx=p1.x;} else if(p1.y==p2.y){ry=p1.y;} else{ double m1=(p2.y-p1.y)/(p2.x-p1.x),b1=p1.y-(m1*p1.x),m2=-1.0/m1,b2=p0.y-(m2*p0.x); rx=(b2-b1)/(m1-m2); ry=(b2*m1-b1*m2)/(m1-m2); } return Tuple.Create(((p1.x>=rx&&p2.x<=rx)||(p2.x>=rx&&p1.x<=rx))&&((p1.y>=ry&&p2.y<=ry)||(p2.y>=ry&&p1.y<=ry)),new Pair(rx,ry)); } static public Pair Gp6(Pair a,Pair b,Pair c,int n){ double l1=Sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)); double l2=Sqrt((c.x-b.x)*(c.x-b.x)+(c.y-b.y)*(c.y-b.y)); double ex=(a.x+(b.x+(c.x-b.x)*(l1/l2)))/2,ey=(a.y+(b.y+(c.y-b.y)*(l1/l2)))/2; ex+=(ex-b.x)*n;ey+=(ey-b.y)*n; return new Pair(ex,ey); } static public Pair Gp7(Pair a,double k,double p){return new Pair(a.x+k*Cos(p),a.y+k*Sin(p));} static public bool Gp8(Pair a,Pair b,Pair c){return (c.x-a.x)*(b.y-a.y)==(b.x-a.x)*(c.y-a.y);} static public Pair Gp9(Pair a,Pair b,Pair c){ double d=a.x*a.x+a.y*a.y,e=b.x*b.x+b.y*b.y,f=c.x*c.x+c.y*c.y,g=2*(a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y)); return new Pair((d*(b.y-c.y)+e*(c.y-a.y)+f*(a.y-b.y))/g,(d*(c.x-b.x)+e*(a.x-c.x)+f*(b.x-a.x))/g); } static public Pair[] Gp10(Pair p0,double r,Pair p1,Pair p2){ double a=p2.y-p1.y,b=p1.x-p2.x; double d=p0.x*-a+p0.y*-b+a*p1.x+b*p1.y; double g=a*a+b*b; double k=g*r*r-d*d; if(k<0){return new Pair[]{};} if(k==0){return new Pair[]{new Pair((a*d)/g+p0.x,(b*d)/g+p0.y)};} k=Sqrt(k); return new Pair[]{new Pair((a*d-b*k)/g+p0.x,(b*d+a*k)/g+p0.y),new Pair((a*d+b*k)/g+p0.x,(b*d-a*k)/g+p0.y)}; } static public Pair[] Gp11(Pair p1,double r1,Pair p2,double r2){ p2-=p1; double a=(p2.x*p2.x+p2.y*p2.y+r1*r1-r2*r2)/2; double g=p2.x*p2.x+p2.y*p2.y; double k=g*r1*r1-a*a; if(k<0){return new Pair[]{};} if(k==0){return new Pair[]{new Pair((p2.x*a)/g,(p2.y*a)/g)+p1};} k=Sqrt(k); return new Pair[]{new Pair((p2.x*a+p2.y*k)/g,(p2.y*a-p2.x*k)/g)+p1,new Pair((p2.x*a-p2.y*k)/g,(p2.y*a+p2.x*k)/g)+p1}; } static Tuple Gp12(Pair[] pa){ int n=pa.Length; double sumx=0,sumy=0,sumxy=0,sumx2=0; for(int i = 0;i Gp98(Pair a,Pair b){ long d=(long)(b.y-a.y),e=(long)(a.x-b.x),f=(long)(d*a.x+e*a.y),v=1; d=-d;e=-e; if(d==0){v=f==0?e:Gcd(e,f);} else if(e==0){v=f==0?d:Gcd(d,f);} else{ v=Gcd(d,e); if(f!=0){v=Gcd(v,f);} } return Tuple.Create(d/v,e/v,f/v); } static long Gcd(long a,long b){ long c=Max(a,b)%(b=Min(a,b)); while(c!=0){a=b%c;b=c;c=a;} return b; } static public Tuple Gp99(Pair a,Pair b){ double d=b.y-a.y,e=a.x-b.x; return Tuple.Create(-d,-e,d*a.x+e*a.y); } static public Tuple[] Psort(Pair[] pa,Pair p){ var arr=new Tuple[pa.Length]; for(int i = 0;iu.Item2.CompareTo(v.Item2)); return arr; } static public Tuple[] Psort2(Pair[] pa,Pair p){ int n=pa.Length; var arr=new Tuple[n]; for(int i = 0;iu.Item2.CompareTo(v.Item2)); Array.Resize(ref arr,n<<1); for(int i = 0;i(int n,Func f){var a=new T[n];for(int i=0;i(int n,Func f){var a=new T[n];for(int i=0;i(int n,Func f){var a=new T[n];for(int i=0;i(int n,Func f){var a=new T[n];for(int i=0;i