//#define _GLIBCXX_DEBUG #include using namespace std; #define endl '\n' #define lfs cout<= (ll)(n); i--) using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair; template using PQ = priority_queue; template using QP = priority_queue,greater>; templatebool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} templatebool chmax(T1 &a,T2 b){if(avoid ans(bool x,T1 y,T2 z){if(x)cout<void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);}; templatevoid debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;ivoid debug(const T &v,ll n,string sv=" "){if(n!=0)cout<void debug(const vector&v){debug(v,v.size());} templatevoid debug(const vector>&v){for(auto &vv:v)debug(vv,vv.size());} templatevoid debug(stack st){while(!st.empty()){cout<void debug(queue st){while(!st.empty()){cout<void debug(deque st){while(!st.empty()){cout<void debug(PQ st){while(!st.empty()){cout<void debug(QP st){while(!st.empty()){cout<void debug(const set&v){for(auto z:v)cout<void debug(const multiset&v){for(auto z:v)cout<void debug(const array &a){for(auto z:a)cout<void debug(const map&v){for(auto z:v)cout<<"["<vector>vec(ll x, ll y, T w){vector>v(x,vector(y,w));return v;} ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;} vectordx={1,-1,0,0,1,1,-1,-1};vectordy={0,0,1,-1,1,-1,1,-1}; templatevector make_v(size_t a,T b){return vector(a,b);} templateauto make_v(size_t a,Ts... ts){return vector(a,make_v(ts...));} templateostream &operator<<(ostream &os, const pair&p){return os << p.first << " " << p.second;} templateostream &operator<<(ostream &os, const vector &v){for(auto &z:v)os << z << " ";os<<"|"; return os;} templatevoid rearrange(vector&ord, vector&v){ auto tmp = v; for(int i=0;ivoid rearrange(vector&ord,Head&& head, Tail&&... tail){ rearrange(ord, head); rearrange(ord, tail...); } template vector ascend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i) vector descend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);}); return ord; } template vector inv_perm(const vector&ord){ vectorinv(ord.size()); for(int i=0;i0);return n>=0?n/div:(n-div+1)/div;} ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;} ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;} ll modulo(ll n,ll d){return (n%d+d)%d;}; templateT min(const vector&v){return *min_element(v.begin(),v.end());} templateT max(const vector&v){return *max_element(v.begin(),v.end());} templateT acc(const vector&v){return accumulate(v.begin(),v.end(),T(0));}; templateT reverse(const T &v){return T(v.rbegin(),v.rend());}; //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); int popcount(ll x){return __builtin_popcountll(x);}; int poplow(ll x){return __builtin_ctzll(x);}; int pophigh(ll x){return 63 - __builtin_clzll(x);}; templateT poll(queue &q){auto ret=q.front();q.pop();return ret;}; templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;}; templateT poll(QP &q){auto ret=q.top();q.pop();return ret;}; templateT poll(stack &s){auto ret=s.top();s.pop();return ret;}; ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;} ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;} ll POW(ll x, ll k){ll ret=1;for(int i=0;i struct edge { int to; T cost; int id; edge():id(-1){}; edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){} operator int() const { return to; } }; template using Graph = vector>>; template Graphrevgraph(const Graph &g){ Graphret(g.size()); for(int i=0;i Graph readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){ Graph ret(n); for(int es = 0; es < m; es++){ int u,v; T w=1; cin>>u>>v;u-=indexed,v-=indexed; if(weighted)cin>>w; ret[u].emplace_back(v,w,es); if(!directed)ret[v].emplace_back(u,w,es); } return ret; } template Graph readParent(int n,int indexed=1,bool directed=true){ Graphret(n); for(int i=1;i>p; p-=indexed; ret[p].emplace_back(i); if(!directed)ret[i].emplace_back(p); } return ret; } using I = long long; struct Point{ I x, y; Point(): x(0), y(0){} Point(I x,I y):x(x),y(y){} 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*=(I v){ x *= v, y *= v; return *this; } Point &operator/=(I v){ assert(x % v == 0 && y % v == 0); x /= v, y /= v; return *this; } friend Point operator+(const Point &l, const Point &r){ return Point(l) += r; } friend Point operator-(const Point &l, const Point &r){ return Point(l) -= r; } friend Point operator*(const Point &l, I r){ return Point(l) *= r; } friend Point operator/(const Point &l, I r){ return Point(l) /= r; } bool operator<(const Point &p)const{ if(x == p.x)return y < p.y; return x < p.x; } bool operator>(const Point &p) const{ if(x == p.x)return y > p.y; return x > p.x; } 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;} friend ostream &operator<<(ostream &os, const Point &p) { return os << "(" << p.x << "," << p.y << ")"; } friend istream &operator>>(istream &is, Point &p) { is >> p.x >> p.y; return (is); } }; struct Line{ Point a,b; Line() = default; Line(Point a, Point b) : a(a), b(b){} }; I norm(const Point &p){ return p.x * p.x + p.y * p.y; } I dot(const Point &a, const Point &b){ return a.x * b.x + a.y * b.y; } I cross(const Point &a, const Point &b){ return a.x * b.y - a.y * b.x; } I distance(const Point &a, const Point &b){ return norm(a - b); } I area(const Point &a,const Point &b,const Point &c){ return abs(cross(b-a,c-a)); } constexpr int COUNTER_CLOCKWISE = +1; constexpr int CLOCKWISE = -1; constexpr int ONLINE_BACK = +2; // c-a-b constexpr int ONLINE_FRONT = -2; // a-b-c constexpr int ON_SEGMENT = 0; // a-c-b int ccw(const Point &a, Point b, Point c) { b = b - a, c = c - a; if(cross(b, c) > 0) return COUNTER_CLOCKWISE; if(cross(b, c) < 0) return CLOCKWISE; if(dot(b, c) < 0) return ONLINE_BACK; if(norm(b) < norm(c)) return ONLINE_FRONT; return ON_SEGMENT; } bool parallel(const Line &a, const Line &b){ return cross(a.b - a.a, b.b - b.a) == 0; } bool orthogonal(const Line &a, const Line &b){ return dot(a.a - a.b, b.a - b.b) == 0; } bool argument_compare(Point a, Point b){ if(a.x == 0 && a.y == 0)a.x = 1; if(b.x == 0 && b.y == 0)b.x = 1; if(a.y < 0 && b.y >= 0){ return true; } else if(a.y >= 0 && b.y < 0){ return false; } else if(a.y == 0 && b.y == 0){ return a.x >= 0 && b.x < 0; } return cross(a, b) > 0; } vectorconvex_hull(const vector&points, bool onEdge = false){ int n = points.size(), k = 0; auto p = points; const I limit = onEdge ? 0 : 1; if(n <= 2)return p; sort(p.begin(), p.end()); vector ch(2 * n); for(int i = 0; i < n; ch[k++] = p[i++]) { while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < limit) --k; } for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) { while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < limit) --k; } ch.resize(k - 1); return ch; } vectorlower_convex_hull(const vector&points, bool onEdge = false){ int n = points.size(), k = 0; auto p = points; const I limit = onEdge ? 0 : 1; if(n <= 2)return p; sort(p.begin(), p.end()); vector ch(2 * n); for(int i = 0; i < n; ch[k++] = p[i++]) { while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < limit) --k; } ch.resize(k); return ch; } //各b_jに対して、cross(a_i,b_j)の最大値を求める vectorget_cross_max(vectora,vectorb){ a = convex_hull(a, false); vectorord(b.size()); iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return argument_compare(b[i],b[j]);}); vectorret(b.size()); if(norm(b[ord[0]]) == 0 && norm(b[ord.back()]) == 0){ return ret; } int start = 0; while(norm(b[ord[start]]) == 0)start++; int max_arg = 0; for(int i = 1; i < a.size(); i++){ if(cross(a[max_arg], b[ord[start]]) < cross(a[i], b[ord[start]])){ max_arg = i; } } for(auto i:ord){ while(1){ I c0 = cross(a[(max_arg == 0 ? a.size() - 1 : max_arg - 1)],b[i]); I c1 = cross(a[max_arg],b[i]); I c2 = cross(a[(max_arg == a.size() - 1 ? 0 : max_arg + 1)],b[i]); if(c0 <= c1 && c1 >= c2)break; max_arg++; if(max_arg >= a.size())max_arg -= a.size(); } ret[i] = cross(a[max_arg], b[i]); } return ret; } vectorget_cross_min(vectora,vectorb){ for(auto &p:b)p *= -1; auto ret = get_cross_max(a, b); for(auto &r:ret)r *= -1; return ret; } vectorget_dot_max(vectora,vectorb){ for(auto &p:b){ p = Point(-p.y, p.x); } auto ret=get_cross_max(a,b); return ret; } // 多角形と点の包含判定 enum { OUT, ON, IN }; using Polygon=vector; int contains(const Polygon &Q, const Point &p) { bool in = false; for(int i = 0; i < Q.size(); i++) { Point a = Q[i] - p, b = Q[(i + 1) % Q.size()] - p; if(a.y > b.y) swap(a, b); if(a.y <= 0 && 0 < b.y && cross(a, b) < 0) in = !in; if(cross(a, b) == 0 && dot(a, b) <= 0) return ON; } return in ? IN : OUT; } bool segment_intersect(const Line &s, const Line &t) { return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0; } bool segmnent_point_intersect(const Line &s, const Point &p) { return ccw(s.a, s.b, p) == 0; } int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); ll res=0,buf=0; bool judge = true; int n,k;cin>>n>>k; vector>p(2); rep(i,0,n){ int x,y,c;cin>>x>>y>>c;c--; p[c].EB(x,y); } assert(k>=4); bool sw=false; { auto q=p; rep(i,0,2){ if(q[i].size()>=3)q[i]=convex_hull(q[i],false); } rep(i,0,q[0].size())rep(j,0,q[1].size()){ Line x(q[0][i],q[0][(i+1)%q[0].size()]); Line y(q[1][j],q[1][(j+1)%q[1].size()]); if(q[0].size()>=2&&q[1].size()>=2&&segment_intersect(x,y)){ sw=true; } if(q[0].size()>=2&&segmnent_point_intersect(x,q[1][j]))sw=true; if(q[1].size()>=2&&segmnent_point_intersect(y,q[0][i]))sw=true; } if(q[0].size()>=3){ rep(i,0,q[1].size())if(contains(q[0],q[1][i]))sw=true; } if(q[1].size()>=3){ rep(i,0,q[0].size())if(contains(q[1],q[0][i]))sw=true; } } ans1(sw); return 0; }