#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #define fin(...) exit(pp(__VA_ARGS__)) #define ep(...) emplace(__VA_ARGS__) #define eb(...) emplace_back(__VA_ARGS__) #define pb() pop_back() #define ef(...) emplace_front(__VA_ARGS__) #define pf(a) pop_front(a) #define ei(...) else if(__VA_ARGS__) #define el else #define wh(...) while(__VA_ARGS__) #define lb(...) lower_bound(__VA_ARGS__) #define ub(...) upper_bound(__VA_ARGS__) #define imx(...) max_element(al(__VA_ARGS__)) #define imn(...) min_element(al(__VA_ARGS__)) #define srt(...) sort(al(__VA_ARGS__)) #define rv(...) reverse(al(__VA_ARGS__)) #define un(a) srt(a);a.erase(unique(al(a)),end(a)) #define jo(a,b) copy(al(b),back_inserter(a)) #define ov3(a,b,c,d,...) d #define ov4(a,b,c,d,e,...) e #define ov5(a,b,c,d,e,f,...) f #define ov6(a,b,c,d,e,f,g,...) g #define bg begin #define rbg rbegin #define al1(v) bg(v),end(v) #define al2(v,b) bg(v),bg(v)+b #define al3(v,a,b) bg(v)+a,bg(v)+b #define al(...) ov3(__VA_ARGS__,al3,al2,al1)(__VA_ARGS__) #define rl1(v) rbg(v),rend(v) #define rl2(v,b) rbg(v),rbg(v)+b #define rl3(v,a,b) rbg(v)+a,rbg(v)+b #define rl(...) ov3(__VA_ARGS__,rl3,rl2,rl1)(__VA_ARGS__) #define rp1(b) for(ll ii=0;ii<(ll)(b);ii++) #define rp2(i,b) for(ll i=0;i<(ll)(b);i++) #define rp3(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++) #define rp4(i,a,b,c) for(ll i=(ll)(a);i<(ll)(b);i+=(ll)(c)) #define rp(...) ov4(__VA_ARGS__,rp4,rp3,rp2,rp1)(__VA_ARGS__) #define pr1(a) rp(a) #define pr2(i,a) for(ll i=(ll)(a)-1;i>=0;i--) #define pr3(i,a,b) for(ll i=(ll)(a)-1;i>=(ll)(b);i--) #define pr4(i,a,b,c) for(ll i=(ll)(a)-1;i>=(ll)(b);i-=(ll)(c)) #define pr(...) ov4(__VA_ARGS__,pr4,pr3,pr2,pr1)(__VA_ARGS__) #define fe1(a) rp(len(a)) #define fe2(a,v) for(au&&a:v) #define fe3(a,b,v) for(au&&[a,b]:v) #define fe4(a,b,c,v) for(au&&[a,b,c]:v) #define fe5(a,b,c,d,v) for(au&&[a,b,c,d]:v) #define fe(...) ov5(__VA_ARGS__,fe5,fe4,fe3,fe2,fe1)(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;ln(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;ln(__VA_ARGS__) #define ST(...) str __VA_ARGS__;ln(__VA_ARGS__) #define UL2(n,a) u1 a(n);ln(a) #define UL3(n,a,b) u1 a(n),b(n);ln(a,b) #define UL4(n,a,b,c) u1 a(n),b(n),c(n);ln(a,b,c) #define UL5(n,a,b,c,d) u1 a(n),b(n),c(n),d(n);ln(a,b,c,d) #define UL6(n,a,b,c,d,e) u1 a(n),b(n),c(n),d(n),e(n);ln(a,b,c,d,e) #define UL(...) ov6(__VA_ARGS__,UL6,UL5,UL4,UL3,UL2)(__VA_ARGS__) #define UV2(n,a) u1 a(n);vn(a) #define UV3(n,a,b) u1 a(n),b(n);vn(a,b) #define UV4(n,a,b,c) u1 a(n),b(n),c(n);vn(a,b,c) #define UV5(n,a,b,c,d) u1 a(n),b(n),c(n),d(n);vn(a,b,c,d) #define UV6(n,a,b,c,d,e) u1 a(n),b(n),c(n),d(n),e(n);vn(a,b,c,d,e) #define UV(...) ov6(__VA_ARGS__,UV6,UV5,UV4,UV3,UV2)(__VA_ARGS__) #define DL2(n,a) v1a(n);ln(a) #define DL3(n,a,b) v1a(n),b(n);ln(a,b) #define DL4(n,a,b,c) v1a(n),b(n),c(n);ln(a,b,c) #define DL5(n,a,b,c,d) v1a(n),b(n),c(n),d(n);ln(a,b,c,d) #define DL(...) ov5(__VA_ARGS__,DL5,DL4,DL3,DL2)(__VA_ARGS__) #define DV2(n,a) v1a(n);vn(a) #define DV3(n,a,b) v1a(n),b(n);vn(a,b) #define DV4(n,a,b,c) v1a(n),b(n),c(n);vn(a,b,c) #define DV5(n,a,b,c,d) v1a(n),b(n),c(n),d(n);vn(a,b,c,d) #define DV(...) ov5(__VA_ARGS__,DV5,DV4,DV3,DV2)(__VA_ARGS__) #define I template #define J class #define oo operator #define rr return #define ss struct #define uu using #define au auto #define bk break #define cs const #define ct continue #define endl "\n" uu namespace atcoder; uu namespace std; uu namespace boost::multiprecision; uu ll=long long; uu ld=long double; uu str=string; uu bo=bool; uu vo=void; uu is=istream; uu os=ostream; vo abc(); int main(){abc();} str sp=" ",nc="",nl="\n"; Iuu v1=vector; Iuu v2=v1>; Iuu v3=v1>; Iuu v4=v1>; Iuu mset=multiset; Iuu fn=function; Iss cp{ T a;U b; cp():a(T()),b(U()){} cp(T a,U b):a(a),b(b){} cp oo+()cs{rr*this;} cp oo-()cs{rr cp(-a,-b);} cp&oo++(){a++,b++;rr*this;} cp&oo--(){a--,b--;rr*this;} cp oo++(int){cp r=*this;++*this;rr r;} cp oo--(int){cp r=*this;--*this;rr r;} cp&oo+=(cs cp&c){a+=c.a;b+=c.b;rr*this;} cp&oo-=(cs cp&c){a-=c.a;b-=c.b;rr*this;} cp&oo*=(cs cp&c){a*=c.a;b*=c.b;rr*this;} cp oo+(cs cp&c)cs{rr cp(*this)+=c;} cp oo-(cs cp&c)cs{rr cp(*this)-=c;} cp oo*(cs cp&c)cs{rr cp(*this)*=c;} cp&oo+=(cs T&d){a+=d;b+=d;rr*this;} cp&oo-=(cs T&d){a-=d;b-=d;rr*this;} cp&oo*=(cs T&d){a*=d;b*=d;rr*this;} cp oo+(cs T&d)cs{rr cp(*this)+=d;} cp oo-(cs T&d)cs{rr cp(*this)-=d;} cp oo*(cs T&d)cs{rr cp(*this)*=d;} bo oo==(cs cp&c)cs{rr a==c.a and b==c.b;} bo oo!=(cs cp&c)cs{rr!(*this==c);} bo oo<(cs cp&c)cs{rr a!=c.a?a(cs cp&c)cs{rr a!=c.a?a>c.a:b>c.b;} bo oo<=(cs cp&c)cs{rr!(*this>c);} bo oo>=(cs cp&c)cs{rr!(*this>(is&i,cp&c){rr i>>c.a>>c.b;} friend os&oo<<(os&o,cs cp&c){rr o<; uu u2=v1; uu u3=v1; uu u4=v1; uu cl=cp; uu ql=queue; uu sl=set; uu msl=mset; uu ml=map; uu mnt=modint998244353; ss edg{ll t,w;edg(){}edg(ll t,ll w=1):t(t),w(w){}}; uu graph=v2; ll inf=3e18; ld pi=acosl(-1); ld ee=1e-10; str first(bo t=1){rr t?"first":"second";} str First(bo t=1){rr t?"First":"Second";} str yes(bo t=1){rr t?"yes":"no";} str Yes(bo t=1){rr t?"Yes":"No";} str YES(bo t=1){rr t?"YES":"NO";} str no(){rr "no";} str No(){rr "No";} str NO(){rr "NO";} str possible(bo t=1){rr t?"possible":"impossible";} str Possible(bo t=1){rr t?"Possible":"Impossible";} str POSSIBLE(bo t=1){rr t?"POSSIBLE":"IMPOSSIBLE";} vo as(bo t){assert(t);} ll bt(ll a){rr 1LL<ll len(cs T&a){rr size(a);} IT sq(T a){rr a*a;} Iuu hpmx=std::priority_queue; Iuu hpmn=std::priority_queue,greater>; ll at(ll S,ll i){rr S>>i&1;} IT at(cs v1&v,ll i){ll n=len(v);rr v[(i%n+n)%n];} Ill sgn(cs T&a){rr(a>ee)-(a<-ee);} Ill sgn(cs T&a,cs T&b){rr sgn(a-b);} Iau&oo+(v1&v){rr v;} Iau&oo-(v1&v){fe(x,v)x=-x;rr v;} Iau&oo++(v1&v){fe(x,v)x++;rr v;} Iau&oo--(v1&v){fe(x,v)x--;rr v;} Iau oo++(v1&v,int){au r=v;++v;rr r;} Iau oo--(v1&v,int){au r=v;--v;rr r;} Iau&oo+=(v1&v,cs U&a){fe(x,v)x+=a;rr v;} Iau&oo-=(v1&v,cs U&a){fe(x,v)x-=a;rr v;} Iau&oo*=(v1&v,cs U&a){fe(x,v)x*=a;rr v;} Iau&oo+=(v1&v,cs v1&u){rp(i,len(v))v[i]+=u[i];rr v;} Iau&oo-=(v1&v,cs v1&u){rp(i,len(v))v[i]-=u[i];rr v;} Iau&oo*=(v1&v,cs v1&u){rp(i,len(v))v[i]*=u[i];rr v;} Iau oo+(v1v,cs U&a){rr v+=a;} Iau oo-(v1v,cs U&a){rr v-=a;} Iau oo*(v1v,cs U&a){rr v*=a;} Iau oo+(v1v,cs v1&u){rr v+=u;} Iau oo-(v1v,cs v1&u){rr v-=u;} Iau oo*(v1v,cs v1&u){rr v*=u;} Ibo amx(T&a,cs U&b){rr abo amn(T&a,cs U&b){rr a>b?a=b,1:0;} IT mx(cs v1&a){rr *imx(a);} IT mn(cs v1&a){rr *imn(a);} Iau mx(cs v2&a){rr mx(*imx(a));} Iau mn(cs v2&a){rr mn(*imn(a));} Iau mx(T...a){rr max(initializer_list>{a...});} Iau mn(T...a){rr min(initializer_list>{a...});} Ill agmx(cs v1&a){rr imx(a)-bg(a);} Ill agmn(cs v1&a){rr imn(a)-bg(a);} IT gcd(cs T&a,cs A&...b){rr gcd(a,gcd(b...));} IT sm(cs v1&a){rr accumulate(al(a),T(0));} Ill lbs(cs v1&a,cs T&b){rr lb(al(a),b)-bg(a);} Ill ubs(cs v1&a,cs T&b){rr ub(al(a),b)-bg(a);} Iau mnmx(cs T&a,cs U&b){rr cp(mn(a,b),mx(a,b));} Iau mnmx(cs cp&p){rr mnmx(p.a,p.b);} Ivo emplace_front(v1&v,T x=0){v.ep(bg(v),x);} Ivo pop_front(v1&v){v.erase(bg(v));} Iau mp(cs fn&f,v1x){v1y;fe(a,x)y.eb(f(a));rr y;} Iau kys(cs map&m){v1r;fe(k,z,m)r.eb(k);rr r;} Iau vls(cs map&m){v1r;fe(z,v,m)r.eb(v);rr r;} u1 io(ll n,ll a=0){u1 i(n);iota(al(i),a);rr i;} ss z{z(){cin.tie(0);ios::sync_with_stdio(0);cout<>(is&i,mnt&x){ll t;i>>t;x=t;rr i;} os&oo<<(os&o,cs mnt&x){rr o<is&oo>>(is&i,pair&p){rr i>>p.first>>p.second;} Ios&oo<<(os&o,cs pair&p){rr o<is&oo>>(is&i,v1&v){fe(x,v)i>>x;rr i;} Ios&oo<<(os&o,cs v1&v){fe(x,v)o<os&oo<<(os&o,cs v2&v){fe(x,v)o<os&oo<<(os&o,cs set&s){fe(x,s)o<os&oo<<(os&o,cs mset&s){fe(x,s)o<os&oo<<(os&o,cs map&m){fe(p,m)o<os&oo<<(os&o,queueq){wh(len(q))o<os&oo<<(os&o,dequeq){wh(len(q))o<os&oo<<(os&o,hpmxq){wh(len(q))o<os&oo<<(os&o,hpmnq){wh(len(q))o<ll pp(cs T&a,cs A&...b){cout<vo ln(T&...a){(cin>>...>>a);} Ivo vn(ll i,T&...a){(cin>>...>>a[i]);} Ivo vn(v1&a,A&...b){rp(i,len(a))vn(i,a,b...);} Ivo rs(v1&v,ll n){v.resize(n);} Ivo rs(v1&V,ll n,cs A&...a){rs(V,n);fe(v,V)rs(v,a...);} Ivo fl(T&x,cs U&a){x=a;} Ivo fl(v1&V,cs U&a){fe(v,V)fl(v,a);} vo gn(u2&g,ll m,bo d=1){rp(i,m){LL(a,b);a--;b--;g[a].eb(b);if(d)g[b].eb(a);}} vo gn(graph&g,ll m,bo w=1,bo d=1){ rp(i,m){ LL(a,b);a--,b--;ll c=1;if(w)ln(c); g[a].eb(b,c);if(d)g[b].eb(a,c); } } vo tn(u2&g,bo d=1){gn(g,len(g)-1,d);} vo tn(graph&g,bo w=1,bo d=1){gn(g,len(g)-1,w,d);} vo zzp(cs u1&v,u1&h){fe(x,h)x=lbs(v,x);} Ivo zzp(cs u1&v,u1&h,T&...t){zzp(v,h);zzp(v,t...);} Iu1 zp(T&...a){u1 v;fe(e,{a...})jo(v,e);un(v);zzp(v,a...);rr v;} Ivo zvs(cs u1&o,v1&a){au c=a;rp(i,len(a))a[i]=c[o[i]];} Ivo zvs(cs u1&o,v1&a,A&...b){zvs(o,a);zvs(o,b...);} Iau vs(cs fn&f,T&...a){ ll n=0;fe(e,{a...})n=len(e); u1 o=io(n),p(n); sort(al(o),f); rp(i,n)p[o[i]]=i; zvs(o,a...); rr cp(o,p); } IT bs(cs fn&j,T o,T n){ T d=(T)ee?ee:1; wh(abs(o-n)>d)(j((o+n)/2)?o:n)=(o+n)/2; rr o; } Iau zt(v1a){rp(i,1,len(a))a[i]+=a[i-1];rr a;} Iau mb(v1a){pr(i,len(a),1)a[i]-=a[i-1];rr a;} Iau zt(v2a){fe(v,a)v=zt(v);rp(i,1,len(a))a[i]+=a[i-1];rr a;} Iau mb(v2a){fe(v,a)v=mb(v);pr(i,len(a),1)a[i]-=a[i-1];rr a;} vo wf(u2&d){ll n=len(d);rp(k,n)rp(i,n)rp(j,n)amn(d[i][j],d[i][k]+d[k][j]);} IT exq(ll n,T r,T x){wh(n){if(n&1)r*=x;x*=x;n/=2;}rr r;} u1 dvs(ll n){ml m;rp(i,1,n/i+1)if(n%i==0)m[i]++,m[n/i]++;rr kys(m);} ml fct(ll n){ml m;rp(i,2,n/i+1)wh(n%i==0)m[i]++,n/=i;if(n>1)m[n]++;rr m;} ll mow(ll x,ll n,ll m=inf){ll r=1;wh(n){if(n&1)r*=x,r%=m;x*=x,x%=m,n/=2;}rr r;} ll mnv(ll a,ll m){ ll b=m,u=1,v=0; wh(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b); rr(u%m+m)%m; } ll sqr(ll x){ll r=sqrtl(x)-1;wh(r+1<=x/(r+1))r++;rr r;} ll lg2(ll n){ll r=0;wh(n){n/=2;r++;}rr r;} u1 dx={-1,0,1,0,-1,1,1,-1}; u1 dy={0,-1,0,1,-1,-1,1,1}; I&op,cs fn&e>ss sgt{ ll n,A,log; v1d; sgt(ll n):sgt(v1(n,e())){} sgt(cs v1&v):n(len(v)){ log=lg2(n*2-1)-1; A=bt(log); d=v1(A*2,e()); rp(i,n)d[i+A]=v[i]; pr(i,A,1)upd(i); } vo upd(ll k){d[k]=op(d[k*2],d[k*2+1]);} vo set(ll p,S x){as(0<=p and p>i);} vo add(ll p,S x){as(0<=p and p