#include #include using namespace std; namespace my{ #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij--;) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);isync_with_stdio(0);cout<r{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;return r;} constexpr char newline=10; constexpr char space=32; constexpr auto zz(auto x){return x<0?-x:x;} bool amin(auto&a,const auto&b){return a>b?a=b,1:0;} auto min(const auto&...a){return min(initializer_list>{a...});} templatestruct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair&p):a(p.first),b(p.second){} auto operator<=>(const pair&)const=default; pair operator+(const pair&p)const{return{a+p.a,b+p.b};} friend ostream&operator<<(ostream&o,const pair&p){return o<ostream&operator<<(ostream&o,const std::pair&p){return o<concept vectorial=is_base_of_v,V>; templatestruct vec_attr{using core_type=T;static constexpr int d=0;}; templatestruct vec_attr{using core_type=typename vec_attr::core_type;static constexpr int d=vec_attr::d+1;}; templateusing core_t=vec_attr::core_type; templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateostream&operator<<(ostream&o,const vector&v){fe(v,e)o<?newline:space);return o;} templatestruct vec:vector{ using vector::vector; vec(const vector&v){vector::operator=(v);} vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec operator^(const vec&u)const{return vec{*this}^=u;} vec&operator+=(const vec&u){vec&v=*this;fo(i,v.size())v[i]+=u[i];return v;} vec&operator-=(const vec&u){vec&v=*this;fo(i,v.size())v[i]-=u[i];return v;} vec operator+(const vec&u)const{return vec{*this}+=u;} vec operator-(const vec&u)const{return vec{*this}-=u;} vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} vec operator-()const{vec v=*this;fe(v,e)e=-e;return v;} auto scan(const auto&f)const{pair,bool>r{};fe(*this,e)if constexpr(!vectorial)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;return r;} auto min()const{return scan([](auto&a,const auto&b){a>b?a=b:0;;}).a;} vec zeta()const{vec v=*this;if constexpr(vectorial)fe(v,e)e=e.zeta();fo(i,v.size()-1)v[i+1]+=v[i];return v;} auto rectangle_sum(ll a,ll b,ll c,ll d)const{ static_assert(is_same_v>>); assert(0<=a&&a<=b&&b<=(ll)this->size()); assert(0<=c&&c<=d&&d<=(ll)(*this)[0].size()); core_tr{}; if(b&&d)r+=(*this)[b-1][d-1]; if(a&&d)r-=(*this)[a-1][d-1]; if(b&&c)r-=(*this)[b-1][c-1]; if(a&&c)r+=(*this)[a-1][c-1]; return r; } auto&rectangle_imos(ll a,ll b,ll c,ll d,core_tx){ (*this)[a][c]+=x; if(b<(ll)this->size())(*this)[b][c]-=x; if(d<(ll)(*this)[0].size())(*this)[a][d]-=x; if(b<(ll)this->size()&&d<(ll)(*this)[0].size())(*this)[b][d]+=x; return*this; } }; templateauto make_vec(const ll(&s)[n],T x={}){if constexpr(n==i+1)return vec(s[i],x);else{auto X=make_vec(s,x);return vec(s[i],X);}} void lin(auto&...a){(cin>>...>>a);} auto sinen(const string&b="a"){string s;lin(s);vecr;fe(s,e)r.eb(b.size()==1?e-b[0]:b.find_first_of(e));return r;} auto sinen(ll n,const string&b="a"){vec>r;fo(n)r.eb(sinen(b));return r;} templatevoid pp(const auto&...a){ll n=sizeof...(a);((cout<0,c)),...);cout<1)(f((o+x)/2)?o:x)=(o+x)/2;return o;} namespace sgt{ templateT min(T a,T b){return a