#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() using ll=long long int; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} #line 2 "library/Utility/fastio.hpp" #include class FastIO{ static constexpr int L=1<<16; char rdbuf[L]; int rdLeft=0,rdRight=0; inline void reload(){ int len=rdRight-rdLeft; memmove(rdbuf,rdbuf+rdLeft,len); rdLeft=0,rdRight=len; rdRight+=fread(rdbuf+len,1,L-len,stdin); } inline bool skip(){ for(;;){ while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++; if(rdLeft==rdRight){ reload(); if(rdLeft==rdRight)return false; } else break; } return true; } template::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft='0' and rdbuf[rdLeft]<='9' and rdLeft=rdRight)reload(); x=rdbuf[rdLeft++]; return true; } inline bool _read(string& x){ if(!skip())return false; for(;;){ int pos=rdLeft; while(pos' ')pos++; x.append(rdbuf+rdLeft,pos-rdLeft); if(rdLeft==pos)break; rdLeft=pos; if(rdLeft==rdRight)reload(); else break; } return true; } templateinline bool _read(vector& v){ for(auto& x:v){ if(!_read(x))return false; } return true; } char wtbuf[L],tmp[50]; int wtRight=0; inline void flush(){ fwrite(wtbuf,1,wtRight,stdout); wtRight=0; } inline void _write(const char& x){ if(wtRight>L-32)flush(); wtbuf[wtRight++]=x; } inline void _write(const string& x){ for(auto& c:x)_write(c); } template::value,int> =0>inline void _write(T x){ if(wtRight>L-32)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); if (__builtin_expect(x == std::numeric_limits::min(), 0)) { switch (sizeof(x)) { case 2: _write("32768"); return; case 4: _write("2147483648"); return; case 8: _write("9223372036854775808"); return; } } x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } templateinline void _write(const vector& v){ rep(i,0,v.size()){ if(i)_write(' '); _write(v[i]); } } public: FastIO(){} ~FastIO(){flush();} inline void read(){} template inline void read(Head& head,Tail&... tail){ assert(_read(head)); read(tail...); } templateinline void write(){if(ln)_write('\n');} template inline void write(const Head& head,const Tail&... tail){ if(space)_write(' '); _write(head); write(tail...); } }; /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Geometry/intCoord.hpp" struct Point{ ll X,Y; Point():X(0),Y(0){} Point(ll _X,ll _Y):X(_X),Y(_Y){} int pos()const{ if(Y<0)return -1; if(Y==0 and X>=0)return 0; return 1; } Point& operator+=(const Point& p){ X+=p.X; Y+=p.Y; return *this; } Point& operator-=(const Point& p){ X-=p.X; Y-=p.Y; return *this; } Point& operator*=(const ll& t){ X*=t,Y*=t; return *this; } Point& operator*=(const Point& p){ ll NX=X*p.X-Y*p.Y,NY=X*p.Y+Y*p.X; X=NX,Y=NY; return *this; } Point operator+(const Point &p) const { return Point(*this) += p; } Point operator-(const Point &p) const { return Point(*this) -= p; } Point operator*(const ll &p) const { return Point(*this) *= p; } Point operator*(const Point &p) const { return Point(*this) *= p; } Point operator-() const { return Point(-X, -Y); } bool operator==(const Point &p) const { return X == p.X && Y == p.Y; } bool operator!=(const Point &p) const { return X != p.X || Y != p.Y; } bool operator<(const Point &p) const { return X == p.X ? Y < p.Y : X < p.X; } }; struct Line{ Point a,b; Line(){} Line(Point _a,Point _b):a(_a),b(_b){} }; struct Segment:Line{ Segment(){} Segment(Point _a,Point _b):Line(_a,_b){} }; using Poly=vector; ll dot(const Point &a, const Point &b) { return a.X * b.X + a.Y * b.Y; } ll cross(const Point &a, const Point &b) { return a.X * b.Y - a.Y * b.X; } ll norm(const Point& a){return a.X*a.X+a.Y*a.Y;} bool cmp(const Point& a,const Point& b){ if(a.pos()!=b.pos())return a.pos()0)return 1; //ccw if(C<0)return -1; //cw if(dot(b,c)<0)return 2; //c,a,b if(dot(b,b)q.Y)swap(p,q); if(p.Y<=0 and q.Y>0 and cross(p,q)>0)res^=1; if(cross(p,q)==0 and dot(p,q)<=0)return 1; } return (res?2:0); } Poly ConvexHull(Poly& a){ int n=a.size(),k=0; if(n<=2)return a; sort(ALL(a),[](const Point& p,const Point& q){ return (p.Y==q.Y?p.X=2 and cross(res[k-1]-res[k-2],a[i]-res[k-1])<0)k--; } for(int i=n-2,t=k+1;i>=0;res[k++]=a[i--]){ while(k>=t and cross(res[k-1]-res[k-2],a[i]-res[k-1])<0)k--; } res.resize(k-1); return res; } /** * @brief Geometry(integer Coordinates) */ #line 2 "library/Utility/random.hpp" struct Random{ random_device rnd; unsigned x=123456789,y=362436069,z=521288629,w=rnd(); Random(){} unsigned get(){ unsigned t=x^(x<<11); x=y,y=z,z=w; return w=(w^(w<<19))^(t^(t>>8)); } unsigned get(unsigned L){ return get()%(L+1); } templateT get(T L,T R){ return get(R-L)+L; } double uniform(){ return double(get())/UINT_MAX; } string str(int n){ string ret; rep(i,0,n)ret+=get('a','z'); return ret; } templatevoid shuffle(Iter first,Iter last){ if(first==last)return; int len=1; for(auto it=first+1;it!=last;it++){ len++; int j=get(0,len-1); if(j!=len-1)iter_swap(it,first+j); } } templatevector select(int n,T L,T R){ set ret; while(ret.size() X(N),Y(N),C(N); rep(i,0,N)io.read(X[i],Y[i],C[i]); auto get=[&](auto& get,int k)->vector{ if(k>=N/2){ auto out=get(get,N-k); vector done(N); rep(i,0,N-k)done[out[i]]=1; vector ret; rep(i,0,N)if(!done[i])ret.push_back(i); return ret; } else{ vector ret,done(N); rep(_,0,k){ int x; for(;;){ x=gen.get(0,N-1); if(!done[x])break; } done[x]=1; ret.push_back(x); } return ret; } }; double start=clock(); while((double)(clock()-start)/CLOCKS_PER_SEC<2.5){ auto sample=get(get,K); vector R,B; for(auto& i:sample){ if(C[i]==1)R.push_back(Point(X[i],Y[i])); else B.push_back(Point(X[i],Y[i])); } R=ConvexHull(R); B=ConvexHull(B); rep(i,0,R.size())if(isContained(B,R[i])!=0){ io.write("Yes"); return 0; } rep(i,0,B.size())if(isContained(R,B[i])!=0){ io.write("Yes"); return 0; } rep(i,0,R.size())rep(j,0,B.size())if(isIntersect(Segment(R[i],R[(i+1)%R.size()]),Segment(B[j],B[(j+1)%B.size()]))){ io.write("Yes"); return 0; } } io.write("No"); return 0; }