#include "bits/stdc++.h" using namespace std; #if __has_include() #include using namespace atcoder; #endif using ll=long long; using dd=double; using vll=vector< ll>; using vdd=vector< dd>; using vvll=vector< vll>; using vvdd=vector; using vvvll=vector< vvll>; using vvvdd=vector; using vvvvll=vector; using pll=pair; using tll=tuple; using qll=tuple; using vpll=vector< pll>; using vtll=vector< tll>; using vqll=vector< qll>; using vvpll=vector; using vvtll=vector; using vvqll=vector; constexpr ll INF = 1LL << 60; struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<::max_digits10); } } fast; #define REPS(i, S, E) for (ll i = (S); i <= (E); i++) #define REP(i, N) REPS(i, 0, (N)-1) #define DEPS(i, S, E) for (ll i = (E); i >= (S); i--) #define DEP(i, N) DEPS(i, 0, (N)-1) #define EXPAND( x ) x//VS用おまじない #define overload3(_1,_2,_3,name,...) name #define overload4(_1,_2,_3,_4,name,...) name #define overload5(_1,_2,_3,_4,_5,name,...) name #define rep3(i, S, E) for (ll i = (S); i <= (E); i++) #define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t)) #define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,_,_)(__VA_ARGS__)) #define dep3(i, E, S) for (ll i = (E); i >= (S); i--) #define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t)) #define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__)) #define each2(e,v) for (auto && e:v) #define each3(a,b,v) for (auto &&[a,b]:v) #define each4(a,b,c,v) for (auto &&[a,b,c]:v) #define each5(a,b,c,d,v) for (auto &&[a,b,c,d]:v) #define each(...) EXPAND(overload5(__VA_ARGS__,each5,each4,each3,each2,_)(__VA_ARGS__)) #define ALL1(v) (v).begin(), (v).end() #define ALL2(v,E) (v).begin(), (v).begin()+((E)+1) #define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1) #define ALL(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__)) #define all ALL #define RALL1(v) (v).rbegin(), (v).rend() #define RALL2(v,E) (v).rbegin(), (v).rbegin()+((E)+1) #define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1) #define RALL(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__VA_ARGS__)) #define rall RALL template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; } template inline T MaxE(vector&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; } template inline T MinE(vector&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; } template inline T MaxE(vector &v) { return MaxE(v,0,(ll)v.size()-1); } template inline T MinE(vector &v) { return MinE(v,0,(ll)v.size()-1); } template inline auto maxe(T &&v,ll S,ll E){ return *max_element(ALL(v,S,E)); } template inline auto maxe(T &&v){ return *max_element(ALL(v)); } template inline auto mine(T &&v,ll S,ll E){ return *min_element(ALL(v,S,E)); } template inline auto mine(T &&v){ return *min_element(ALL(v)); } template inline T Sum(vector &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; } template inline T Sum(vector &v) { return Sum(v,0,v.size()-1); } template::type::value_type> inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());} template inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);} template inline ll sz(T &v){ return (ll)v.size(); } inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOK inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); } //負もOK //pair用テンプレート using vpll=vector< pll>; using vvpll=vector; template inline pair& operator+=(pair &a,const pair &b){ a.first+=b.first; a.second+=b.second; return a; } template inline pair& operator-=(pair &a,const pair &b){ a.first-=b.first; a.second-=b.second; return a; } template inline pair& operator*=(pair &a,const pair &b){ a.first*=b.first; a.second*=b.second; return a; } template inline pair& operator/=(pair &a,const pair &b){ a.first/=b.first; a.second/=b.second; return a; } template inline pair& operator%=(pair &a,const pair &b){ a.first%=b.first; a.second%=b.second; return a; } template inline pair& operator+=(pair &a,R b){ a.first+=b; a.second+=b; return a; } template inline pair& operator-=(pair &a,R b){ a.first-=b; a.second-=b; return a; } template inline pair& operator*=(pair &a,R b){ a.first*=b; a.second*=b; return a; } template inline pair& operator/=(pair &a,R b){ a.first/=b; a.second/=b; return a; } template inline pair& operator%=(pair &a,R b){ a.first%=b; a.second%=b; return a; } template inline pair operator+(const pair &a,R b){ pair c=a; return c+=b; } template inline pair operator-(const pair &a,R b){ pair c=a; return c-=b; } template inline pair operator*(const pair &a,R b){ pair c=a; return c*=b; } template inline pair operator/(const pair &a,R b){ pair c=a; return c/=b; } template inline pair operator%(const pair &a,R b){ pair c=a; return c%=b; } template inline pair operator-(R b,const pair &a){ pair c=-a; return c+=b; } template inline pair operator-(const pair &a){ pair c=a; return c*=(-1); } template inline ostream &operator<<(ostream &os,const pair &a){ return os << a.first << ' ' << a.second; } //vector用テンプレート template inline vector& operator+=(vector &a,const vector &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]+=b[i]; return a; } template inline vector& operator-=(vector &a,const vector &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]-=b[i]; return a; } template inline vector& operator*=(vector &a,const vector &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]*=b[i]; return a; } template inline vector& operator/=(vector &a,const vector &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]/=b[i]; return a; } template inline vector& operator%=(vector &a,const vector &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]%=b[i]; return a; } template inline vector& operator+=(vector &a,S b){ for (T &e: a) e+=b; return a; } template inline vector& operator-=(vector &a,S b){ for (T &e: a) e-=b; return a; } template inline vector& operator*=(vector &a,S b){ for (T &e: a) e*=b; return a; } template inline vector& operator/=(vector &a,S b){ for (T &e: a) e/=b; return a; } template inline vector& operator%=(vector &a,S b){ for (T &e: a) e%=b; return a; } template inline vector operator+(const vector &a,S b){ vector c=a; return c+=b; } template inline vector operator-(const vector &a,S b){ vector c=a; return c-=b; } template inline vector operator*(const vector &a,S b){ vector c=a; return c*=b; } template inline vector operator/(const vector &a,S b){ vector c=a; return c/=b; } template inline vector operator%(const vector &a,S b){ vector c=a; return c%=b; } template inline vector operator-(S b,const vector &a){ vector c=-a; return c+=b; } template inline vector operator-(const vector &a){ vector c=a; return c*=(-1); } template inline ostream &operator<<(ostream &os,const vector &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")< inline array& operator+=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i]; return a; } template inline array& operator-=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i]; return a; } template inline array& operator*=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i]; return a; } template inline array& operator/=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i]; return a; } template inline array& operator%=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i]; return a; } template inline array& operator+=(array &a,R b){ for (T &e: a) e+=b; return a; } template inline array& operator-=(array &a,R b){ for (T &e: a) e-=b; return a; } template inline array& operator*=(array &a,R b){ for (T &e: a) e*=b; return a; } template inline array& operator/=(array &a,R b){ for (T &e: a) e/=b; return a; } template inline array& operator%=(array &a,R b){ for (T &e: a) e%=b; return a; } template inline array operator+(const array &a,R b){ array c=a; return c+=b; } template inline array operator-(const array &a,R b){ array c=a; return c-=b; } template inline array operator*(const array &a,R b){ array c=a; return c*=b; } template inline array operator/(const array &a,R b){ array c=a; return c/=b; } template inline array operator%(const array &a,R b){ array c=a; return c%=b; } template inline array operator-(R b,const array &a){ array c=-a; return c+=b; } template inline array operator-(const array &a){ array c=a; return c*=(-1); } template inline ostream &operator<<(ostream &os,const array &a){ for (ll i=0; i<(ll)S; i++) os<<(i>0?" ":"")< struct mll_{ ll val; mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; } mll_ operator - () const { return -val; } mll_ operator + (const mll_ &b) const { return val + b.val; } mll_ operator - (const mll_ &b) const { return val - b.val; } mll_ operator * (const mll_ &b) const { return val * b.val; } mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; } mll_ operator + (ll b) const { return *this + mll_(b); } mll_ operator - (ll b) const { return *this - mll_(b); } mll_ operator * (ll b) const { return *this * mll_(b); } friend mll_ operator + (ll a,const mll_ &b) { return b + a; } friend mll_ operator - (ll a,const mll_ &b) { return -b + a; } friend mll_ operator * (ll a,const mll_ &b) { return b * a; } friend mll_ operator / (ll a,const mll_ &b) { return mll_(a)/b; } mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; } mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; } mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; } mll_ &operator /= (const mll_ &b) { ll c=b.val,d=MOD,u=1,v=0; while (d){ ll t = c / d; c -= t * d; swap(c,d); u -= t * v; swap(u,v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } mll_ &operator += (ll b) { return *this += mll_(b); } mll_ &operator -= (ll b) { return *this -= mll_(b); } mll_ &operator *= (ll b) { return *this *= mll_(b); } mll_ &operator /= (ll b) { return *this /= mll_(b); } bool operator == (const mll_ &b) const { return val == b.val; } bool operator != (const mll_ &b) const { return val != b.val; } bool operator == (ll b) const { return *this == mll_(b); } bool operator != (ll b) const { return *this != mll_(b); } friend bool operator == (ll a,const mll_ &b) { return mll_(a) == b.val; } friend bool operator != (ll a,const mll_ &b) { return mll_(a) != b.val; } friend ostream &operator << (ostream &os,const mll_ &a) { return os << a.val; } friend istream &operator >> (istream &is,mll_ &a) { return is >> a.val; } static mll_ Combination(ll a,ll b){ chmin(b,a-b); if (b<0) return mll_(0); mll_ c = 1; rep(i,0,b-1) c *= a-i; rep(i,0,b-1) c /= i+1; return c; } }; //using mll = mll_<1000000007LL>; using mll = mll_<998244353LL>; using vmll = std::vector; using vvmll = std::vector; using vvvmll = std::vector; using vvvvmll = std::vector; template struct view1d; template struct view1dIter{ view1d *vw=nullptr; ll idx=INF; view1dIter(){} view1dIter(view1d *vw_,ll idx_):vw(vw_),idx(idx_){} view1dIter(const view1dIter &it):vw(it.vw),idx(it.idx){} R &operator*() { return (*vw)[idx]; } R &operator*() const{ return (*vw)[idx]; } R &operator[](ll i) { return (*vw)[idx+i]; } R &operator[](ll i)const{ return (*vw)[idx+i]; } auto &operator++(){ idx++; return *this; } auto &operator--(){ idx--; return *this; } auto operator++(int){ auto it=*this; idx++; return it; } auto operator--(int){ auto it=*this; idx--; return it; } auto &operator+=(ll n){ idx+=n; return *this; } auto &operator-=(ll n){ idx-=n; return *this; } auto operator+(ll n){ auto it=*this; return it+=n; } auto operator-(ll n){ auto it=*this; return it-=n; } ll operator- (const view1dIter &it)const{ return idx- it.idx; } bool operator< (const view1dIter &it)const{ return idx< it.idx; } bool operator> (const view1dIter &it)const{ return idx> it.idx; } bool operator<=(const view1dIter &it)const{ return idx<=it.idx; } bool operator>=(const view1dIter &it)const{ return idx>=it.idx; } bool operator!=(const view1dIter &it)const{ return idx!=it.idx; } bool operator==(const view1dIter &it)const{ return idx==it.idx; } using iterator_category = random_access_iterator_tag; using value_type = R; using difference_type = ll; using pointer = R*; using reference = R&; }; template struct view1d{ using Sll=array; T &data; //参照先データ Sll dsize; //参照先データ各軸のサイズ Sll s=Sll(); //view先頭 Sll d=Sll(); //view方向 ll len; //view長さ R &dummy; //範囲外の値参照 R dummyj=R(); //範囲外の値実体 /*---- コンストラクタ ----*/ view1d(T &v): data(v),dummy(dummyj){ SetDsize(v,dsize); d[S-1]=1; len=dsize[S-1]; } //このコンストラクタは、マイナス座標指定を末尾にしない(暫定) //代入時Array{...}等と書くため、使い勝手悪い。将来廃止するかも。 view1d(T &v,Sll s,Sll e,Sll d): data(v),s(s),d(d),len(Len(s,e,d)),dummy(dummyj){ SetDsize(v,dsize); } view1d(T &v,Sll s,Sll d,ll len,R &dmy_): data(v),s(s),d(d),len(len),dummy(dmy_){ SetDsize(v,dsize); } /*---- 演算 ----*/ template auto &operator =(const Q &b){ rep(i,0,len-1) (*this)[i] =b; return *this; } template auto &operator+=(const Q &b){ rep(i,0,len-1) (*this)[i]+=b; return *this; } template auto &operator-=(const Q &b){ rep(i,0,len-1) (*this)[i]-=b; return *this; } template auto &operator*=(const Q &b){ rep(i,0,len-1) (*this)[i]*=b; return *this; } template auto &operator/=(const Q &b){ rep(i,0,len-1) (*this)[i]/=b; return *this; } template auto &operator%=(const Q &b){ rep(i,0,len-1) (*this)[i]%=b; return *this; } auto &operator =(const string &b){ return CpSeq(b); } template auto &operator =(const char (&b)[Q]){ return *this=string(b); } template auto &operator =(const vector &b){ return CpSeq(b); } template auto &operator+=(const vector &b){ return PlSeq(b); } template auto &operator-=(const vector &b){ return MnSeq(b); } template auto &operator*=(const vector &b){ return PrSeq(b); } template auto &operator/=(const vector &b){ return DvSeq(b); } template auto &operator%=(const vector &b){ return RmSeq(b); } template auto &operator =(const view1d &b){ return CpSeq(b); } template auto &operator+=(const view1d &b){ return PlSeq(b); } template auto &operator-=(const view1d &b){ return MnSeq(b); } template auto &operator*=(const view1d &b){ return PrSeq(b); } template auto &operator/=(const view1d &b){ return DvSeq(b); } template auto &operator%=(const view1d &b){ return RmSeq(b); } template auto &CpSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i] =b[i]; return *this; } template auto &PlSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]+=b[i]; return *this; } template auto &MnSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]-=b[i]; return *this; } template auto &PrSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]*=b[i]; return *this; } template auto &DvSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]/=b[i]; return *this; } template auto &RmSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]%=b[i]; return *this; } //template static bool eq(const Q &a,const P &b){ // return equals(ALL(a),ALL(b)); //} template static bool eq(const Q &a,const P &b){ if ((ll)a.size()!=(ll)b.size()) return false; rep(i,0,(ll)a.size()-1){ if (a[i]!=b[i]) return false; } return true; } template static bool lt(const Q &a,const P &b){ ll n=min((ll)a.size(),(ll)b.size()); rep(i,0,n-1){ if (a[i]b[i])return false; } return (ll)a.size()<(ll)b.size(); } template bool operator==( const view1d &b){ return eq(*this,b); } template bool operator==( const Q &b){ return eq(*this,b); } template friend bool operator==(const Q &a,const view1d &b){ return eq( a,b); } template bool operator==( const char (&b)[Q]){ return eq(*this,string(b)); } template bool operator!=( const view1d &b){ return !(*this==b); } template bool operator!=( const Q &b){ return !(*this==b); } template friend bool operator!=(const Q &a,const view1d &b){ return !( a==b); } template bool operator< ( const view1d &b){ return lt(*this,b); } template bool operator< ( const Q &b){ return lt(*this,b); } template friend bool operator< (const Q &a,const view1d &b){ return lt( a,b); } template bool operator> ( const view1d &b){ return lt(b,*this); } template bool operator> ( const Q &b){ return lt(b,*this); } template friend bool operator> (const Q &a,const view1d &b){ return lt(b,a ); } template bool operator<=( const view1d &b){ return !(*this>b); } template bool operator<=( const Q &b){ return !(*this>b); } template friend bool operator<=(const Q &a,const view1d &b){ return !( a>b); } template bool operator>=( const view1d &b){ return !(*this bool operator>=( const Q &b){ return !(*this friend bool operator>=(const Q &a,const view1d &b){ return !( a(OrgAt(s+d*i)); } const R &operator[](ll i) const { return OrgAt(s+d*i); } R &at(ll i){ if(i<0)i+=len; return (*this)[i]; } //vector tov(){ vector vvv(len); rep(i,0,len-1) vvv[i]=(*this)[i]; return vvv; } operator vector(){ vector v(len); rep(i,0,len-1) v[i]=(*this)[i]; return v; } bool contains(R a){ rep(i,0,len-1) if((*this)[i]==a)return true; return false; } auto begin(){ return view1dIter(this,0); } auto end(){ return view1dIter(this,len); } /*---- view設定 ----*/ view1d &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット template view1d &st(Q... s_){//始点set 負は末尾からの位置 this->s=RevIfNeg(SllD(s_...)); this->len=AutoLen(this->s,this->d,this->dsize); return *this; } template view1d &en(Q... e_){//終了条件再設定負は末尾から this->len=Len(s, RevIfNeg(SllD(e_...)), d); return *this; } template view1d &dir(Q... d_){//方向set、長さはdata端まで this->d=SllD(d_...); this->len=AutoLen(this->s,this->d,this->dsize); return *this; } template view1d &mv(Q... s_){ this->s+=SllD(s_...); return *this; }//平行移動 view1d &size(ll len_) { len=len_; return *this; }//長さset template view1d &size(Q &v){ len=(ll)v.size(); return *this; }//長さset view1d &rev() { s+=d*(len-1); d*=-1; return *this; }//反転 /*---- utility ----*/ template inline static ll sz(Q &v){ return (ll)v.size(); } Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換 rep(i,0,S-1) if (pos[i]<0) pos[i]+=dsize[i]; return pos; } static ll AutoLen(Sll s_,Sll d_,Sll dsz){//位置s_から方向d_ではみ出すまでの長さ Sll e=dsz-1; rep(i,0,S-1) e[i] *= (d_[i]>=0);//方向が負の軸を0にする return Len(s_,e,d_); } /*---- 先頭位置s、方向d、終了条件eから長さlen計算 ----*/ //template static ll Len(array s,array e,array d){ // ll ret=INF; // rep(i,0,Q-1) chmin(ret, Len1(s[i],e[i],d[i])); // return ret; //} static ll Len(Sll s,Sll e,Sll d){ ll ret=INF; rep(i,0,S-1) chmin(ret, Len1(s[i],e[i],d[i])); return ret; } static ll Len1(ll s,ll e,ll d){ if (d==0) return INF; if (d<0){ s=-s; e=-e; d=-d; } if (s>e) return 0; return (e-s)/d+1; } /*---- 可変長引数をSllに変換 ----*/ template static Sll SllD(Q... args){ return SllRec(0,args...); } template static Sll SllRec(ll i,ll first,Q... rest) { Sll sll = (i==S-1) ? Sll() : SllRec(i+1,rest...); sll[i]=first; return sll; } static Sll SllRec(ll i){ return Sll(); } /*---- dataの位置posの値取得 ----*/ const R &OrgAt(Sll pos) const { rep(i,0,S-1){ if (pos[i]<0 || dsize[i]<=pos[i]) return dummy; } return OrgAt_(data,pos); } template using V = vector; template using VV = V>; template using VVV = V>>; using Vs = V; using VVs = VV; using ll1 = array; using ll2 = array; using ll3 = array; auto &OrgAt_(V &dat,ll1 pos)const{ auto [i] =pos; return dat[i]; } auto &OrgAt_(string &dat,ll1 pos)const{ auto [i] =pos; return dat[i]; } auto &OrgAt_(VV &dat,ll2 pos)const{ auto [i,j] =pos; return dat[i][j]; } auto &OrgAt_(Vs &dat,ll2 pos)const{ auto [i,j] =pos; return dat[i][j]; } auto &OrgAt_(VVV &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; } auto &OrgAt_(VVs &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; } /*---- dataの各軸size取得 ----*/ static void SetDsize(V &dat,ll1 &dsz){ dsz={sz(dat)}; } static void SetDsize(string &dat,ll1 &dsz){ dsz={sz(dat)}; } static void SetDsize(VV &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; } static void SetDsize(Vs &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; } static void SetDsize(VVV &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; } static void SetDsize(VVs &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; } typedef view1dIter iterator; using value_type = R; }; template using V = vector; template using VV = V>; template using VVV = V>>; template view1d( VVV ) -> view1d< VVV,3,T>; template view1d( VV ) -> view1d< VV,2,T>; template view1d( V ) -> view1d< V,1,T>; ; view1d(VV ) -> view1d,3,char>; ; view1d( V ) -> view1d< V,2,char>; ; view1d( string ) -> view1d< string ,1,char>; template view1d( VVV,S,S,S) -> view1d< VVV,3,T>; template view1d( VV,S,S,S) -> view1d< VV,2,T>; template view1d( V,S,S,S) -> view1d< V,1,T>; template view1d(VV,S,S,S) -> view1d,3,char>; template view1d( V,S,S,S) -> view1d< V,2,char>; template