#include #include using namespace std; namespace my{ #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define VL(n,...) vec__VA_ARGS__;setsize({n},__VA_ARGS__);lin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij-->0;) #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;if(s)r[2]*=-1;return r;} constexpr char newline=10; constexpr char space=32; bool amax(auto&a,const auto&b){return a>{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 istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;} friend ostream&operator<<(ostream&o,const pair&p){return o<>auto&sort(auto&a,F f={}){ranges::sort(a,f);return a;} auto crev(auto a){ranges::reverse(a);return a;} templateostream&operator<<(ostream&o,const std::pair&p){return o<ostream&operator<<(ostream&o,const array&a){fo(i,n)o<ostream&operator<<(ostream&o,const tuple&t){apply([&](const auto&...a){ll i=sizeof...(a);(((o<0,space))),...);},t);return o;} templateconcept 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);} templaterequires(sizeof...(A)>=3)vec(A...a){const ll n=sizeof...(a)-1;ll s[n];ll i=0;((i(tuple{a...}));} templatestatic auto make_vec(const ll(&s)[n],T x){if constexpr(i==n-1)return vec(s[i],x);else{auto X=make_vec(s,x);return vec(s[i],X);}} 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;} vec slice(ll l,ll r)const{return vec(this->begin()+l,this->begin()+r);} vec select(const vec&ids)const{vec r;fe(ids,i)r.eb((*this)[i]);return r;} 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 sum()const{return scan([](auto&a,const auto&b){a+=b;}).a;} auto min()const{return scan([](auto&a,const auto&b){a>b?a=b:0;;}).a;} }; templatestruct dvec_helper{using type=vec::type>;}; templatestruct dvec_helper<0,T>{using type=T;}; templateusing dvec=typename dvec_helper::type; templaterequires(sizeof...(A)>=2)vec(A...a)->vec(declval>()))>>>; vec(ll)->vec; templatevoid setsize(const ll(&l)[n],A&...a){((a=vec::make_vec(l,core_t{})),...);} templatestruct infinity{ templateconstexpr operator T()const{return numeric_limits::max()*(1-is_negative*2);} templateconstexpr operator T()const{return static_cast(*this);} templateconstexpr bool operator==(T x)const{return static_cast(*this)==x;} constexpr auto operator-()const{return infinity();} templateconstexpr operator array()const{arraya;fe(a,e)e=static_cast(*this);return a;} }; constexpr infinity oo; void lin(auto&...a){(cin>>...>>a);} templateauto iota(auto...a){arrayv{};ll I=0;((v[I++]=a),...);if(I==1)swap(v[0],v[1]);vecr;fo(i,v[0],v[1])r.eb(i);return r;} void sort(auto&...a){vec>v;(v.eb(a),...);sort(v);ll I=0;((a=v[I++]),...);} templateauto sort_index(const vec&a){ auto o=iota(a.size()); return sort(o,[&](ll i,ll j){return a[i]==a[j]?ivoid pp(const auto&...a){ll n=sizeof...(a);((cout<0,c)),...);cout<