#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 eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define VV(n,...) vec__VA_ARGS__;setsize({n},__VA_ARGS__);vin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij--;) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i=i##stop;i-=i##step) #define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a) #define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{ void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<constexpr auto range(bool s,A...a){arrayr{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 nl=10; constexpr char sp=32; ll pwm1(ll n){return 1-2*(n&1);} template>auto&sort(auto&a,const F&f={}){ranges::sort(a,f);return a;} auto&unique(auto&a){sort(a).erase(ranges::unique(a).begin(),a.end());return a;} 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<?nl:sp);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++(){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 lower_bound(const V&x)const{return std::lower_bound(this->begin(),this->end(),x);} ll arglb(const V&x)const{return lower_bound(x)-this->begin();} }; 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);}} templatevoid setsize(const ll(&l)[n],A&...a){((a=make_vec(l,core_t())),...);} void lin(auto&...a){(cin>>...>>a);} void vin(auto&...a){fo(i,(a.size()&...))(cin>>...>>a[i]);} templatevoid pp(const auto&...a){ll n=sizeof...(a);((cout<0,c)),...);cout<struct factorial{ ll M; vecfa,fa_inv; factorial(ll M):M(M),fa(M+1),fa_inv(M+1){ fa[0]=1; fo(i,1,M+1)fa[i]=fa[i-1]*i; fa_inv.back()=fa.back().inv(); of(i,M)fa_inv[i]=fa_inv[i+1]*(i+1); } T operator()(ll n)const{assert(n<=M);return fa[n];} T inv(ll n)const{assert(n<=M);return fa_inv[n];} }; templatestruct combination{ ll M; factorialfa; combination(ll M):M(M),fa(M){} T c(ll n,ll k){return n<0?pwm1(k)*c(-n+k-1,k):k<0||n>g(v.size()); fo(i,N){ g[a[i]].eb(i); g[b[i]].eb(~i); } combinationcomb(K); ml ans=1; ll choice=K; fo(x,v.size()){ ll c=0; fe(g[x],i){ if(i>=0)c++; else choice++; } ans*=(choice>=0?comb.p(choice,c):0); choice-=c; } pp(ml{K}.pow(N)-ans); }}