#include #include using namespace std; namespace my{ using ml=atcoder::modint998244353; auto&operator>>(istream&i,ml&x){int t;i>>t;x=t;return i;} auto&operator<<(ostream&o,const ml&x){return o<<(int)x.val();} #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<>(istream&i,ulll&x){ull t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<>(istream&i,lll&x){ll t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const lll&x){return o<0?x:-x);} constexpr auto range(bool s,auto...a){arrayr{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; templateconstexpr ll bit_sizeof(){return sizeof(T)*CHAR_BIT;} lll pow(lll x,ll n){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,n>>=1;return r;} constexpr auto at2(auto x,auto i){return x>>i&1;} 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<struct queue:std::queue{ queue(const initializer_list&a={}){fe(a,e)this->emplace(e);} queue(const vector&a){fe(a,e)this->emplace(e);} ll size()const{return std::queue::size();} T pop(){T r=this->front();std::queue::pop();return r;} T sum()const{T r{};fe(*this,e)r+=e;return r;} friend ostream&operator<<(ostream&o,queue q){while(q.size())o<0,space);return o;} }; templateauto pack_kth(const auto&...a){return get(make_tuple(a...));} templateauto pack_slice(const auto&...a){return[&](index_sequence){return array{get(forward_as_tuple(a...))...};}(make_index_sequence{});} templateconcept vectorial=is_base_of_v,V>; templatestruct vec_attr{using core_type=T;static constexpr int rank=0;}; templatestruct vec_attr{using core_type=typename vec_attr::core_type;static constexpr int rank=vec_attr::rank+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; templatestruct tensor_helper{using type=vec::type>;}; templatestruct tensor_helper<0,T>{using type=T;}; templateusing tensor=typename tensor_helper::type; 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;auto t=pack_slice(a...);ll s[n];fo(i,n)s[i]=t[i];*this=make_vec(s,pack_kth(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;assert(v.size()==u.size());fo(i,v.size())v[i]+=u[i];return v;} vec&operator-=(const vec&u){vec&v=*this;assert(v.size()==u.size());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&operator%=(auto M){vec&v=*this;fe(v,e)e%=M;return v;} vec operator%(auto M)const{return vec{*this}%=M;} ll size()const{return vector::size();} 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;} }; 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{})),...);} void lin(auto&...a){(cin>>...>>a);} template()>struct msb_first_binary_trie{ struct node{ ll elem_count; arraychild; node():elem_count(),child{nullptr,nullptr}{} }; using node_ptr=node*; node_ptr r; msb_first_binary_trie(const vec&a={}):r(nullptr){fe(a,e)emplace(e);} node_ptr root()const{return r;} ll size()const{return r?r->elem_count:0;} ll size(node_ptr p)const{return p?p->elem_count:0;} node_ptr inner_emplace(T x,node_ptr p,ll b=B-1){ if(!p)p=new node; p->elem_count++; if(b<0)return p; bool f=at2(x,b); p->child[f]=inner_emplace(x,p->child[f],b-1); return p; } void emplace(T x){r=inner_emplace(x,r);} }; void pp(auto&&...a){ll n=sizeof...(a);((cout<0,space)),...);cout<(); msb_first_binary_triembt(a); queue::node_ptr,ll>>q{{mbt.root(),0}}; vecis_branching(B); while(q.size()){ auto[p,d]=q.pop(); is_branching[d]|=(p->child[0]&&p->child[1]); fe(p->child,e)if(e)q.emplace(e,d+1); } pp(ml(2).pow(is_branching.sum())); }}