#include<iostream>
#include<cstdio>
#include<cmath>
#include<cassert>
#include<chrono>
#include<random>
#include<vector>
#include<functional>
#include<iomanip>
#include<algorithm>
using namespace std;
namespace Geometry
{
    const double eps=1e-12;
    const double PI=acos(-1);
    const double INF=1e18;
    bool equal(double a,double b)
    {
        return abs(a-b)<eps;
    }
    bool less(double a,double b)
    {
        return b-a>=eps;
    }
    bool greater(double a,double b)
    {
        return a-b>=eps;
    }
    bool less_equal(double a,double b)
    {
        return less(a,b)||equal(a,b);
    }
    bool greater_equal(double a,double b)
    {
        return greater(a,b)||equal(a,b);
    }
    class Point
    {
    public:
        double x,y;
        Point(){x=0,y=0;}
        Point(const double &_x,const double &_y):x(_x),y(_y) {}
        friend Point operator * (const Point &a,const double &b)
        {
            return Point(a.x*b,a.y*b);
        }
        friend Point operator * (const double &a,const Point &b)
        {
            return Point(a*b.x,a*b.y);
        }
        friend Point operator / (const Point &a,const double &b)
        {
            return Point(a.x/b,a.y/b);
        }
        friend Point operator + (const Point &a,const Point &b)
        {
            return Point(a.x+b.x,a.y+b.y);
        }
        Point operator += (const Point &b)
        {
            x+=b.x,y+=b.y;
            return *this;
        }
        friend Point operator - (const Point &a,const Point &b)
        {
            return Point(a.x-b.x,a.y-b.y);
        }
        Point operator -= (const Point &b)
        {
            x-=b.x,y-=b.y;
            return *this;
        }
        friend double cross(const Point &a,const Point &b)
        {
            return a.x*b.y-a.y*b.x;
        }
        friend double dot(const Point &a,const Point &b)
        {
            return a.x*b.x+a.y*b.y;
        }
        friend bool operator == (const Point &a,const Point &b)
        {
            return equal(a.x,b.x)&&equal(a.y,b.y);
        }
        friend bool operator != (const Point &a,const Point &b)
        {
            return (!equal(a.x,b.x))||(!equal(a.y,b.y));
        }
        friend bool operator < (const Point &a,const Point &b)
        {
            if(equal(a.x,b.x)) return less(a.y,b.y);
            else return less(a.x,b.x);
        }
        friend bool operator > (const Point &a,const Point &b)
        {
            if(equal(a.x,b.x)) return greater(a.y,b.y);
            else return greater(a.x,b.x);
        }
        friend bool operator <= (const Point &a,const Point &b)
        {
            if(equal(a.x,b.x)) return less_equal(a.y,b.y);
            else return less_equal(a.x,b.x);
        }
        friend bool operator >= (const Point &a,const Point &b)
        {
            if(equal(a.x,b.x)) return greater_equal(a.y,b.y);
            else return greater_equal(a.x,b.x);
        }
        Point operator - ()const
        {
            return Point(-x,-y);
        }
        double length()const
        {
            return sqrt(x*x+y*y);
        }
        Point unit()const
        {
            return *this/length();
        }
        double angle()const
        {
            return atan2(y,x);
        }
        int quadrant()const
        {
            if(x>0&&y>=0) return 1;
            else if(x<=0&&y>0) return 2;
            else if(x<0&&y<=0) return 3;
            else if(x>=0&&y<0) return 4;
            else return 0;
        }
        friend double angle(const Point &a,const Point &b)
        {
            return atan2(cross(a,b),dot(a,b));
        }
        Point rotate(const double &theta)const
        {
            return Point(x*cos(theta)-y*sin(theta),x*sin(theta)+y*cos(theta));
        }
        friend istream &operator>>(istream &in,Point &obj)
        {
            in>>obj.x>>obj.y;
            return in;
        }
        friend ostream &operator<<(ostream &out,const Point &obj)
        {
            out<<obj.x<<" "<<obj.y;
            return out;
        }
    };
    double distance(const Point &a,const Point &b)
    {
        return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
    }
    enum Direction
    {
        COUNTER_CLOCKWISE,
        CLOCKWISE,
        ONLINE_BACK,
        ONLINE_FRONT,
        ON_SEGMENT
    };
    istream& operator>>(istream& in,Direction& direction)
    {
        string value;
        in>>value;
        if(value=="COUNTER_CLOCKWISE") direction=COUNTER_CLOCKWISE;
        else if(value=="CLOCKWISE") direction=CLOCKWISE;
        else if(value=="ONLINE_BACK") direction=ONLINE_BACK;
        else if(value=="ONLINE_FRONT") direction=ONLINE_FRONT;
        else if(value=="ON_SEGMENT") direction=ON_SEGMENT;
        else in.setstate(ios::failbit);
        return in;
    }
    ostream& operator<<(ostream& out,const Direction& direction)
    {
        if(direction==COUNTER_CLOCKWISE) out<<"COUNTER_CLOCKWISE";
        else if(direction==CLOCKWISE) out<<"CLOCKWISE";
        else if(direction==ONLINE_BACK) out<<"ONLINE_BACK";
        else if(direction==ONLINE_FRONT) out<<"ONLINE_FRONT";
        else if(direction==ON_SEGMENT) out<<"ON_SEGMENT";
        return out;
    }
    class Line
    {
    public:
        Point a,b;
        Line(){}
        Line(const Point &_a,const Point &_b):a(_a),b(_b){}
        Point projection(const Point &p)const
        {
            return a+(b-a).unit()*(dot(p-a,b-a)/(b-a).length());
        }
        Point reflection(const Point &p)const
        {
            return projection(p)*2-p;
        }
        Direction direction(const Point &p)const
        {
            double t=cross(b-a,p-a);
            if(greater(t,0)) return COUNTER_CLOCKWISE;
            if(less(t,0)) return CLOCKWISE;
            double l1=dot(p-a,b-a);
            if(less(l1,0)) return ONLINE_BACK;
            double l2=dot(b-a,b-a);
            if(l1>l2) return ONLINE_FRONT;
            else return ON_SEGMENT;
        }
        double distance(const Point &p)const
        {
            Point u=projection(p);
            if(direction(u)==ON_SEGMENT) return Geometry::distance(u,p);
            else return min(Geometry::distance(a,p),Geometry::distance(b,p));
        }
        friend istream &operator>>(istream &in,Line &obj)
        {
            in>>obj.a>>obj.b;
            return in;
        }
        friend ostream &operator<<(ostream &out,const Line &obj)
        {
            out<<obj.a<<" "<<obj.b;
            return out;
        }
    };
    bool parallel(const Line &x,const Line &y)
    {
        return equal(cross(x.b-x.a,y.b-y.a),0);
    }
    bool orthogonal(const Line &x,const Line &y)
    {
        return equal(dot(x.b-x.a,y.b-y.a),0);
    }
    vector<Point> cross_point(const Line &x,const Line &y)
    {
        if(parallel(x,y)) return {};
        Point u=x.a-y.a,v=x.b-x.a,w=y.b-y.a;
        double t=cross(w,u)/cross(v,w);
        return {x.a+t*v};
    }
    int sign(double x)
    {
        return greater(x,0)-less(x,0);
    }
    bool intersection(const Line &x,const Line &y)
    {
        if(x.direction(y.a)==ON_SEGMENT||x.direction(y.b)==ON_SEGMENT||y.direction(x.a)==ON_SEGMENT||y.direction(x.b)==ON_SEGMENT) return true;
        return sign(cross(x.b-x.a,y.a-x.a))*sign(cross(x.b-x.a,y.b-x.a))<0&&sign(cross(y.b-y.a,x.a-y.a))*sign(cross(y.b-y.a,x.b-y.a))<0;
    }
    double distance(const Line &x,const Line &y)
    {
        if(intersection(x,y)) return 0;
        else return min({x.distance(y.a),x.distance(y.b),y.distance(x.a),y.distance(x.b)});
    }
    const int IN=2,ON=1,OUT=0;
    mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());
    class Polygon
    {
    private:
        vector<Point>g;
    public:
        Polygon(){}
        Polygon(const int &n){g.resize(n);}
        Polygon(const vector<Point> &f):g(f){}
        void clear()
        {
            g.clear();
        }
        void resize(int n)
        {
            g.resize(n);
        }
        void push_back(const Point &x)
        {
            return g.push_back(x);
        }
        void push_back(const vector<Point> &x)
        {
            for(const Point &p:x)
                g.push_back(p);
            return;
        }
        void pop_back()
        {
            return g.pop_back();
        }
        Point& front()
        {
            return g.front();
        }
        const Point& front()const
        {
            return g.front();
        }
        Point& back()
        {
            return g.back();
        }
        const Point& back()const
        {
            return g.back();
        }
        size_t size()const
        {
            return g.size();
        }
        Point& operator [](const int &i)
        {
            return g[i];
        }
        const Point& operator [](const int &i)const
        {
            return g[i];
        }
        vector<Point>::iterator begin()
        {
            return g.begin();
        }
        vector<Point>::iterator end()
        {
            return g.end();
        }
        vector<Point>::const_iterator begin()const
        {
            return g.begin();
        }
        vector<Point>::const_iterator end()const
        {
            return g.end();
        }
        vector<Point>::reverse_iterator rbegin()
        {
            return g.rbegin();
        }
        vector<Point>::reverse_iterator rend()
        {
            return g.rend();
        }
        vector<Point>::const_reverse_iterator rbegin()const
        {
            return g.rbegin();
        }
        vector<Point>::const_reverse_iterator rend()const
        {
            return g.rend();
        }
        double area()const
        {
            int n=g.size();
            double res=0;
            for(int i=0;i<n;i++)
                res+=cross(g[i],g[(i+1)%n]);
            res/=2;
            return abs(res);
        }
        double perimeter()const
        {
            int n=g.size();
            double sum=0;
            for(int i=0;i<n;i++)
                sum+=distance(g[i],g[(i+1)%n]);
            return sum;
        }
        bool is_convex()const
        {
            int n=g.size();
            for(int i=0;i<n;i++)
                if(less(cross(g[(i+1)%n]-g[i],g[(i-1+n)%n]-g[i]),0)) return false;
            return true;
        }
        int point_containment(const Point &a)const
        {
            int n=g.size();
            for(int i=0;i<n;i++)
                if(Line(g[i],g[(i+1)%n]).direction(a)==ON_SEGMENT) return ON;
            function<bool(const Line &)> check=[=](const Line &l)
            {
                for(int i=0;i<n;i++)
                    if(parallel(l,Line(g[i],g[(i+1)%n]))) return false;
                for(int i=0;i<n;i++)
                    if(l.direction(g[i])==ON_SEGMENT||l.direction(g[i])==ONLINE_FRONT||l.direction(g[i])==ONLINE_BACK) return false;
                return true;
            };
            Line l=Line(a,Point(rnd(),rnd()));
            while(!check(l))
                l=Line(a,Point(rnd(),rnd()));
            int s=0;
            for(int i=0;i<n;i++)
                if(intersection(l,Line(g[i],g[(i+1)%n]))) s++;
            if(s&1) return IN;
            else return OUT;
        }
        double convex_diamater()const
        {
            int n=g.size();
            double ans=0;
            for(int i=0,j=0;i<n;i++)
            {
                while(less(cross(g[i]-g[j],g[(i+1)%n]-g[j]),cross(g[i]-g[(j+1)%n],g[(i+1)%n]-g[(j+1)%n]))) j=(j+1)%n;
                ans=max(ans,max(distance(g[j],g[i]),distance(g[j],g[(i+1)%n])));
            }
            return ans;
        }
        pair<Polygon,Polygon> convex_cut(const Line &l)const
        {
            Polygon res1,res2;
            int n=g.size();
            for(int i=0;i<(int)g.size();i++)
            {
                Point u=g[i],v=g[(i+1)%n];
                if(greater_equal(cross(l.b-l.a,u-l.a),0))
                {
                    res1.push_back(u);
                    if(less(cross(l.b-l.a,v-l.a),0)) res1.push_back(cross_point(Line(u,v),l));
                }
                else if(greater(cross(l.b-l.a,v-l.a),0)) res1.push_back(cross_point(Line(u,v),l));
            }
            for(int i=0;i<(int)g.size();i++)
            {
                Point u=g[i],v=g[(i+1)%n];
                if(greater_equal(cross(l.a-l.b,u-l.b),0))
                {
                    res2.push_back(u);
                    if(less(cross(l.a-l.b,v-l.b),0)) res2.push_back(cross_point(Line(u,v),l));
                }
                else if(greater(cross(l.a-l.b,v-l.b),0)) res2.push_back(cross_point(Line(u,v),l));
            }
            return make_pair(res1,res2);
        }
        Polygon kernel()const;
    };
    Polygon convex_hull(const vector<Point> &_p)
    {
        vector<Point> p=_p;
        int n=p.size();
        if(n<=2)
        {
            sort(p.begin(),p.end(),[](const Point &a,const Point &b){return a.y==b.y?a.x<b.x:a.y<b.y;});
            Polygon res;
            for(const Point &q:p)
                res.push_back(q);
            return res;
        }
        sort(p.begin(),p.end(),[](const Point &a,const Point &b){return a.x==b.x?a.y<b.y:a.x<b.x;});
        vector<int>stk;
        int top=0;
        for(int i=0;i<n;i++)
        {
            while(top>=2&&less_equal(cross(p[stk[top-1]]-p[stk[top-2]],p[i]-p[stk[top-1]]),0)) stk.pop_back(),top--;
            stk.emplace_back(i),top++;
        }
        int tmp=top;
        for(int i=n-2;i>=0;i--)
        {
            while(top>tmp&&less_equal(cross(p[stk[top-1]]-p[stk[top-2]],p[i]-p[stk[top-1]]),0)) stk.pop_back(),top--;
            stk.emplace_back(i),top++;
        }
        stk.pop_back(),top--;
        vector<Point>hull;
        for(int i=0;i<top;i++)
            hull.emplace_back(p[stk[i]]);
        int t=min_element(hull.begin(),hull.end(),[](const Point &a,const Point &b){return a.y==b.y?a.x<b.x:a.y<b.y;})-hull.begin();
        Polygon res;
        for(int i=t;i<top;i++)
            res.push_back(hull[i]);
        for(int i=0;i<t;i++)
            res.push_back(hull[i]);
        return res;
    }
    Polygon non_strictly_convex_hull(const vector<Point> &_p)
    {
        vector<Point> p=_p;
        int n=p.size();
        if(n<=2)
        {
            sort(p.begin(),p.end(),[](const Point &a,const Point &b){return a.y==b.y?a.x<b.x:a.y<b.y;});
            Polygon res;
            for(const Point &q:p)
                res.push_back(q);
            return res;
        }
        sort(p.begin(),p.end(),[](const Point &a,const Point &b){return a.x==b.x?a.y<b.y:a.x<b.x;});
        vector<int>stk;
        int top=0;
        for(int i=0;i<n;i++)
        {
            while(top>=2&&less(cross(p[stk[top-1]]-p[stk[top-2]],p[i]-p[stk[top-1]]),0)) stk.pop_back(),top--;
            stk.emplace_back(i),top++;
        }
        int tmp=top;
        for(int i=n-2;i>=0;i--)
        {
            while(top>tmp&&less(cross(p[stk[top-1]]-p[stk[top-2]],p[i]-p[stk[top-1]]),0)) stk.pop_back(),top--;
            stk.emplace_back(i),top++;
        }
        stk.pop_back(),top--;
        vector<Point>hull;
        for(int i=0;i<top;i++)
            hull.emplace_back(p[stk[i]]);
        int t=min_element(hull.begin(),hull.end(),[](const Point &a,const Point &b){return a.y==b.y?a.x<b.x:a.y<b.y;})-hull.begin();
        Polygon res;
        for(int i=t;i<top;i++)
            res.push_back(hull[i]);
        for(int i=0;i<t;i++)
            res.push_back(hull[i]);
        return res;
    }
    Polygon minkowski_sum(const vector<Point> &a,const vector<Point> &b)
    {
        assert(a.size()!=0&&b.size()!=0);
        Polygon ca=convex_hull(a),cb=convex_hull(b);
        int na=ca.size(),nb=cb.size();
        vector<Point>la,lb;
        for(int i=0;i<na;i++)
            la.emplace_back(ca[(i+1)%na]-ca[i]);
        for(int i=0;i<nb;i++)
            lb.emplace_back(cb[(i+1)%nb]-cb[i]);
        int pa=0,pb=0;
        vector<Point> l;
        l.emplace_back(ca[0]+cb[0]);
        while(pa<(int)la.size()&&pb<(int)lb.size())
        {
            double val=cross(la[pa],lb[pb]);
            if(greater(val,0)) l.emplace_back(l.back()+la[pa]),pa++;
            else if(less(val,0)) l.emplace_back(l.back()+lb[pb]),pb++;
            else l.emplace_back(l.back()+la[pa]+lb[pb]),pa++,pb++;
        }
        while(pa<(int)la.size())
            l.emplace_back(l.back()+la[pa]),pa++;
        while(pb<(int)lb.size())
            l.emplace_back(l.back()+lb[pb]),pb++;
        Polygon res=convex_hull(l);
        return res;
    }
    Polygon half_plane_intersection(const vector<Line> &l,double x1=-INF,double y1=-INF,double x2=INF,double y2=INF)
    {
        vector<pair<double,Line>>f;
        for(int i=0;i<(int)l.size();i++)
            f.emplace_back((l[i].b-l[i].a).angle(),l[i]);
        f.emplace_back(0,Line(Point(x1,y1),Point(x2,y1)));
        f.emplace_back(PI/2,Line(Point(x2,y1),Point(x2,y2)));
        f.emplace_back(PI,Line(Point(x2,y2),Point(x1,y2)));
        f.emplace_back(-PI/2,Line(Point(x1,y2),Point(x1,y1)));
        int n=f.size();
        sort(f.begin(),f.end(),[](const pair<double,Line> &a,const pair<double,Line> &b){return !equal(a.first,b.first)?a.first<b.first:a.second.direction(b.second.a)==CLOCKWISE;});
        vector<Line>Ql(n);
        vector<Point>Qp(n);
        Polygon res;
        int head=0,tail=-1;
        Ql[++tail]=f[0].second;
        for(int i=1;i<n;i++)
            if(!equal(f[i].first,f[i-1].first))
            {
                while(head<tail&&f[i].second.direction(Qp[tail-1])==CLOCKWISE) tail--;
                while(head<tail&&f[i].second.direction(Qp[head])==CLOCKWISE) head++;
                Ql[++tail]=f[i].second;
                if(head<tail)
                {
                    vector<Point> tmp=cross_point(Ql[tail],Ql[tail-1]);
                    if(!tmp.empty()) Qp[tail-1]=tmp[0];
                    else return res;
                }
            }
        while(head<tail&&Ql[head].direction(Qp[tail-1])==CLOCKWISE) tail--;
        while(head<tail&&Ql[tail].direction(Qp[head])==CLOCKWISE) head++;
        vector<Point> tmp=cross_point(Ql[tail],Ql[head]);
        if(tmp.empty()||tail-head+1<=2) return res;
        for(int i=head;i<tail;i++)
            res.push_back(Qp[i]);
        res.push_back(tmp[0]);
        return res;
    }
    Polygon Polygon::kernel()const
    {
        int n=g.size();
        vector<Line>l;
        for(int i=0;i<n;i++)
            l.emplace_back(Line(g[i],g[(i+1)%n]));
        return half_plane_intersection(l);
    }
    double closest_pair(const vector<Point> &_p)
    {
        vector<Point>p=_p;
        sort(p.begin(),p.end(),[](const Point &a,const Point &b){return a.x<b.x;});
        function<double(const int &,const int &)> solve=[&](const int &l,const int &r)
        {
            if(r-l+1<=1) return INF;
            if(r-l+1<=7)
            {
                double ans=INF;
                sort(p.begin()+l,p.begin()+r+1,[](const Point &a,const Point &b){return a.y<b.y;});
                for(int i=l;i<=r;i++)
                    for(int j=i+1;j<=r;j++)
                        ans=min(ans,distance(p[i],p[j]));
                return ans;
            }
            int mid=(l+r)/2;
            double w=p[mid].x;
            double d=min(solve(l,mid),solve(mid+1,r));
            inplace_merge(p.begin()+l,p.begin()+mid+1,p.begin()+r+1,[](const Point &a,const Point &b){return a.y<b.y;});
            vector<Point>q;
            for(int i=l;i<=r;i++)
                if(abs(w-p[i].x)<=d) q.emplace_back(p[i]);
            for(int i=0,j=0;i<(int)q.size();i++)
            {
                while(j<(int)q.size()&&q[j].y<=q[i].y+d) j++;
                for(int k=i+1;k<j;k++)
                    d=min(d,distance(q[i],q[k]));
            }
            return d;
        };
        return solve(0,p.size()-1);
    }
    class Circle
    {
    public:
        Point o;
        double r;
        Circle(){}
        Circle(const Point &_o,const double &_r):o(_o),r(_r){}
        friend istream &operator>>(istream &in,Circle &obj)
        {
            in>>obj.o>>obj.r;
            return in;
        }
        friend ostream &operator<<(ostream &out,const Circle &obj)
        {
            out<<obj.o<<" "<<obj.r;
            return out;
        }
        double area()const
        {
            return PI*r*r;
        }
        bool tangent(const Line &l)const
        {
            return equal(Geometry::distance(l.projection(o),o),r);
        }
        int point_containment(const Point &p)const
        {
            double d=distance(o,p);
            if(equal(d,r)) return ON;
            else if(less(d,r)) return IN;
            else return OUT;
        }
        vector<Point>cross_point(const Line &l)const
        {
            Point pr=l.projection(o),e=(l.b-l.a).unit();
            double d=distance(pr,o);
            if(greater(d,r)) return {};
            double t=sqrt(r*r-distance(pr,o)*distance(pr,o));
            if(equal(t,0)) return {pr};
            else return {pr-e*t,pr+e*t};
        }
        vector<Point>cross_point(const Circle &c)const
        {
            double d=distance(o,c.o);
            if(less(d,abs(r-c.r))||greater(d,r+c.r)) return {};
            double x=(r*r-c.r*c.r+d*d)/(d*2),h=sqrt(r*r-x*x);
            Point p=o+(c.o-o).unit()*x;
            if(equal(d,abs(r-c.r))||equal(d,r+c.r)) return {p};
            Point v=(c.o-o).unit().rotate(PI/2)*h;
            return {p-v,p+v};
        }
        vector<Point>tangent(const Point &p)const
        {
            double d=distance(o,p);
            if(greater(r,d)) return {};
            if(equal(d,r)) return {p};
            return cross_point(Circle(p,sqrt(d*d-r*r)));
        }
        vector<Line>common_tangent(const Circle &c)const
        {
            vector<Line>f=common_tangent_out(c),g=common_tangent_in(c);
            for(const Line &l:g)
                f.emplace_back(l);
            g.clear();
            sort(f.begin(),f.end(),[](const Line &x,const Line &y){return x.a.x<y.a.x||(x.a.x==y.a.x&&x.a.y<y.a.y);});
            return f;
        }
        double intersection_area(const Point &a,const Point &b)const
        {
            bool ta=less_equal(distance(o,a),r),tb=less_equal(distance(o,b),r);
            if(ta&&tb) return cross(a-o,b-o)/2;
            vector<Point>t=cross_point(Line(b,a));
            if(ta&&!tb) return angle(t.front()-o,b-o)*r*r/2+cross(a-o,t.front()-o)/2;
            if(!ta&&tb) return angle(a-o,t.back()-o)*r*r/2+cross(t.back()-o,b-o)/2;
            double s=angle(a-o,b-o)*r*r/2;
            if(greater_equal(Line(a,b).distance(o),r)) return s;
            return s+angle(t.front()-o,t.back()-o)*r*r/2-cross(t.front()-o,t.back()-o)/2;
        }
        double intersection_area(const Polygon &g)const
        {
            int n=g.size();
            double s=0;
            for(int i=0;i<n;i++)
                s+=intersection_area(g[i],g[(i+1)%n]);
            return s;
        }
        double intersection_area(const Circle &c)const
        {
            double d=distance(o,c.o);
            if(greater(d,r+c.r)) return 0;
            if(less_equal(d,abs(r-c.r))) return min(area(),c.area());
            vector<Point>t=cross_point(c);
            double alpha=acos((d*d+r*r-c.r*c.r)/(2*d*r))*2,beta=acos((d*d+c.r*c.r-r*r)/(2*d*c.r))*2;
            double s1=alpha*r*r/2,s2=beta*c.r*c.r/2,s3=sin(alpha)*r*r/2+sin(beta)*c.r*c.r/2;
            return s1+s2-s3;
        }
        vector<Line>common_tangent_out(const Circle &c)const
        {
            if(equal(r,c.r))
            {
                Point p=(c.o-o).unit().rotate(PI/2)*r;
                return {Line(o-p,c.o-p),Line(o+p,c.o+p)};
            }
            double d=distance(o,c.o);
            if(less(d,abs(r-c.r))) return {};
            Point p((o.x*c.r-c.o.x*r)/(c.r-r),(o.y*c.r-c.o.y*r)/(c.r-r));
            vector<Point>p1=tangent(p),p2=c.tangent(p);
            vector<Line>res;
            for(const Point &u:p1)
                for(const Point &v:p2)
                    if(u!=v&&tangent(Line(u,v))) res.emplace_back(Line(u,v));
            return res;
        }
        vector<Line>common_tangent_in(const Circle &c)const
        {
            double d=distance(o,c.o);
            if(less_equal(d,abs(r-c.r))) return {};
            Point p((o.x*c.r+c.o.x*r)/(r+c.r),(o.y*c.r+c.o.y*r)/(r+c.r));
            vector<Point>p1=tangent(p),p2=c.tangent(p);
            vector<Line>res;
            for(const Point &u:p1)
                for(const Point &v:p2)
                    if(u!=v&&tangent(Line(u,v))) res.emplace_back(Line(u,v));
            return res;
        }
    };
    const int SEPARATED=4,CIRCUMSCRIBED=3,INTERSECTED=2,INSCRIBED=1,INCLUDED=0;
    int intersection(const Circle &a,const Circle &b)
    {
        double d=distance(a.o,b.o);
        if(greater(d,a.r+b.r)) return SEPARATED;
        else if(equal(d,a.r+b.r)) return CIRCUMSCRIBED;
        else if(greater(d,abs(a.r-b.r))) return INTERSECTED;
        else if(equal(d,abs(a.r-b.r))) return INSCRIBED;
        else return INCLUDED;
    }
    class Triangle
    {
    public:
        Point A,B,C;
        Triangle(){}
        Triangle(const Point &_A,const Point &_B,const Point &_C):A(_A),B(_B),C(_C){}
        friend istream &operator>>(istream &in,Triangle &obj)
        {
            in>>obj.A>>obj.B>>obj.C;
            return in;
        }
        friend ostream &operator<<(ostream &out,const Triangle &obj)
        {
            out<<obj.A<<" "<<obj.B<<" "<<obj.C;
            return out;
        }
        Circle inscribed_circle()const
        {
            double a=distance(B,C),b=distance(A,C),c=distance(A,B);
            double p=(a+b+c)/2;
            double s=abs(cross(B-A,C-A))/2;
            double r=s/p;
            Point o((a*A.x+b*B.x+c*C.x)/(a+b+c),(a*A.y+b*B.y+c*C.y)/(a+b+c));
            return Circle(o,r);
        }
        Circle circumscribed_circle()const
        {
            double t1=A.x*A.x+A.y*A.y;
            double t2=B.x*B.x+B.y*B.y;
            double t3=C.x*C.x+C.y*C.y;
            double t=A.x*B.y+B.x*C.y+C.x*A.y-A.x*C.y-B.x*A.y-C.x*B.y;
            Point o((t2*C.y+t1*B.y+t3*A.y-t2*A.y-t3*B.y-t1*C.y)/t/2,(t3*B.x+t2*A.x+t1*C.x-t1*B.x-t2*C.x-t3*A.x)/t/2);
            double a=distance(B,C),b=distance(A,C),c=distance(A,B);
            double s=abs(cross(B-A,C-A))/2;
            double r=a*b*c/(4*s);
            return Circle(o,r);
        }
    };
    Circle smallest_enclosing_circle(const vector<Point> &_p)
    {
        vector<Point>p=_p;
        shuffle(p.begin(),p.end(),rnd);
        int n=p.size();
        Circle c=Circle(Point(0,0),0);
        for(int i=0;i<n;i++)
            if(c.point_containment(p[i])==OUT)
            {
                c=Circle(p[i],0);
                for(int j=0;j<i;j++)
                    if(c.point_containment(p[j])==OUT)
                    {
                        c=Circle((p[i]+p[j])/2,distance(p[i],p[j])/2);
                        for(int k=0;k<j;k++)
                            if(c.point_containment(p[k])==OUT)
                                c=Triangle(p[i],p[j],p[k]).circumscribed_circle();
                    }
            }
        return c;
    }
}
using namespace Geometry;
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr),cout.tie(nullptr);
    int n;
    cin>>n;
    vector<Circle>c(n);
    for(int i=0;i<n;i++)
        cin>>c[i];
    Point q=Point(0,0);
    for(int i=0;i<n;i++)
        if(c[i].point_containment(q))
        {
            cout<<"Yes";
            return 0;
        }
    if(n==1)
    {
        cout<<"No";
        return 0;
    }
    vector<Point>p(n);
    for(int i=0;i<n;i++)
        p[i]=c[i].o;
    Polygon g=convex_hull(p);
    if(g.point_containment(q))
    {
        cout<<"Yes";
        return 0;
    }
    sort(c.begin(),c.end(),[=](const Circle &a,const Circle &b){return a.o.angle()<b.o.angle();});
    for(int i=0;i<n;i++)
    {
        vector<Line>l=c[i].common_tangent_out(c[(i+1)%n]);
        if(l.empty()) continue;
        Line l1=l[0],l2=l[1];
        Polygon gg(6);
        gg[0]=c[i].o,gg[1]=l1.a,gg[2]=l1.b,gg[3]=c[(i+1)%n].o,gg[4]=l2.b,gg[5]=l2.a;
        if(gg.point_containment(q))
        {
            cout<<"Yes";
            return 0;
        }
    }
    cout<<"No";
    return 0; 
}

/*
8
0 -8 3
9 -10 7
5 -7 1
4 -7 2
3 -7 5
0 -5 1
3 -7 2
2 -7 4
*/