#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-->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; templatestruct 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;} 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_impl(index_sequence, const auto&...a){return array{get(forward_as_tuple(a...))...};} templateauto pack_slice(const auto&...a){return pack_slice_impl(make_index_sequence{},a...);} 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: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;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;} ll size()const{return vector::size();} }; templatestruct tensor_helper{using type=vec::type>;}; templatestruct tensor_helper<0,T>{using type=T;}; templateusing tensor=typename tensor_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{})),...);} 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 edge{ ll from,to; WT wt; ll id; edge()=default; edge(ll from,ll to,WT wt=1,ll id=-1):from(from),to(to),wt(wt),id(id){} auto operator<=>(const edge&e)const{return wt<=>e.wt;} friend ostream&operator<<(ostream&o,const edge&e){return o<<"(to "<struct graph{ vec>>edges; graph()=default; graph(ll n):edges(n){} decltype(auto)operator[](ll i){return edges[i];} decltype(auto)operator[](ll i)const{return edges[i];} ll size()const{return edges.size();} friend ostream&operator<<(ostream&o,const graph&g){ fo(u,g.size()){ o<<"from "<&p){fo(i,p.size())if(p[i]!=-1)edges[p[i]].eb(p[i],i,1,i);} void add_edges(const vec&a,const vec&b){fo(i,a.size())edges[a[i]].eb(a[i],b[i],1,i);} void add_edges(const vec&a,const vec&b,const vec&w){fo(i,a.size())edges[a[i]].eb(a[i],b[i],w[i],i);} void add_edges(const vec>&es){fe(es,e)edges[e.from].eb(e);} }; templatestruct rooted_tree:graph{ vec>rev_edge; ll r; rooted_tree(ll n,ll r):graph(n),rev_edge(n,{-1,-1,WT(),-1}),r(r){} ll root()const{return r;} void add_edge_and_set_rev_edge(const edge&e){ this->edges[e.from].eb(e); this->rev_edge[e.to]=e; } auto bfs_order()const{ vecord; queueq{r}; while(q.size()){ ll u=q.pop(); ord.eb(u); fe(this->edges[u],e)q.emplace(e.to); } return ord; } }; templateauto bfs_tree(const graph&g,ll s){ rooted_treetree(g.size(),s); vecused(g.size()); queue>q{{-1,s,WT{},-1}}; while(q.size()){ auto pu=q.pop(); ll u=pu.to; if(used[u])continue; used[u]=1; if(pu.from!=-1)tree.add_edge_and_set_rev_edge(pu); fe(g[u],e)if(!used[e.to])q.emplace(e); } return tree; } templateauto bfs_tree(const rooted_tree&g){return bfs_tree(g,g.root());} single_testcase void solve(){ LL(N); VV(N-1,a,b);dec(a,b); rooted_treeg(N,0); g.add_edges(a,b); g.add_edges(b,a); g=bfs_tree(g); vec dp(N,3,ml{}); // dp[u][k]:uの部分木について,uから伸びている辺がk本であるような場合の数. ef(g.bfs_order(),u){ dp[u][0]=1; fe(g[u],e){ ll v=e.to; ll n=dp[u].size(); ll m=dp[v].size(); vec nx(3,ml{}); fo(j,3){ fo(k,3){ ml X=dp[u][j]*dp[v][k]; // 頂点数1のグラフは無効なのでk>0のときのみ結ばない選択が可能. if(k>0)nx[j]+=X; // u-vを結ばない if(j==2||k==2)continue; // uから伸びている辺が2本,またはvから伸びている辺が2本ある場合,u-vを結ぶとパスグラフでなくなる. nx[j+1]+=X; // u-vを結ぶ } } swap(dp[u],nx); } } pp(dp[0][1]+dp[0][2]); // dp[0][0]は根0が孤立するので除外. }}