#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include //#include #include #define bgn(a) begin(a) #define rbg(a) rbegin(a) #define fin(...) exit(pp(__VA_ARGS__)) #define done(...) rr vo(pp(__VA_ARGS__)) #define ep(...) emplace(__VA_ARGS__) #define ef(...) emplace_front(__VA_ARGS__) #define eb(...) emplace_back(__VA_ARGS__) #define pf(...) pop_front(__VA_ARGS__) #define pb(...) pop_back(__VA_ARGS__) #define ei(...) else if(__VA_ARGS__) #define iif if #define el else #define wh(...) while(__VA_ARGS__) #define lb(...) lower_bound(__VA_ARGS__) #define ub(...) upper_bound(__VA_ARGS__) #define itmax(...) max_element(al(__VA_ARGS__)) #define itmin(...) min_element(al(__VA_ARGS__)) #define srt(...) sort(al(__VA_ARGS__)) #define rv(...) reverse(al(__VA_ARGS__)) #define rsr(a) srt(a),rv(a) #define uq(a) srt(a),a.erase(unique(al(a)),end(a)) #define sw(a,b) swap(a,b) #define sb(...) substr(__VA_ARGS__) #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 al1(v) bgn(v),end(v) #define al2(v,b) bgn(v),bgn(v)+b #define al3(v,a,b) bgn(v)+a,bgn(v)+b #define al(...) ov3(__VA_ARGS__,al3,al2,al1)(__VA_ARGS__) #define fo1(b) for(ll ii=0;ii<(ll)(b);ii++) #define fo2(i,b) for(ll i=0;i<(ll)(b);i++) #define fo3(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++) #define fo4(i,a,b,c) for(ll i=(ll)(a);i<(ll)(b);i+=(ll)(c)) #define fo(...) ov4(__VA_ARGS__,fo4,fo3,fo2,fo1)(__VA_ARGS__) #define of1(a) fo(a) #define of2(i,a) for(ll i=(ll)(a)-1;i>=0;i--) #define of3(i,a,b) for(ll i=(ll)(a)-1;i>=(ll)(b);i--) #define of4(i,a,b,c) for(ll i=(ll)(a)-1;i>=(ll)(b);i-=(ll)(c)) #define of(...) ov4(__VA_ARGS__,of4,of3,of2,of1)(__VA_ARGS__) #define fe1(a) fo(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__;li(__VA_ARGS__) #define DD(...) dd __VA_ARGS__;li(__VA_ARGS__) #define ST(...) str __VA_ARGS__;li(__VA_ARGS__) #define MI(...) mint __VA_ARGS__;li(__VA_ARGS__) #define UL2(n,a) u1 a(n);li(a) #define UL3(n,a,b) u1 a(n),b(n);li(a,b) #define UL4(n,a,b,c) u1 a(n),b(n),c(n);li(a,b,c) #define UL5(n,a,b,c,d) u1 a(n),b(n),c(n),d(n);li(a,b,c,d) #define UL6(n,a,b,c,d,e) u1 a(n),b(n),c(n),d(n),e(n);li(a,b,c,d,e) #define UL(...) ov6(__VA_ARGS__,UL6,UL5,UL4,UL3,UL2)(__VA_ARGS__) #define UV2(n,a) u1 a(n);vi(a) #define UV3(n,a,b) u1 a(n),b(n);vi(a,b) #define UV4(n,a,b,c) u1 a(n),b(n),c(n);vi(a,b,c) #define UV5(n,a,b,c,d) u1 a(n),b(n),c(n),d(n);vi(a,b,c,d) #define UV6(n,a,b,c,d,e) u1 a(n),b(n),c(n),d(n),e(n);vi(a,b,c,d,e) #define UV(...) ov6(__VA_ARGS__,UV6,UV5,UV4,UV3,UV2)(__VA_ARGS__) #define DL2(n,a) v1
a(n);li(a) #define DL3(n,a,b) v1
a(n),b(n);li(a,b) #define DL4(n,a,b,c) v1
a(n),b(n),c(n);li(a,b,c) #define DL5(n,a,b,c,d) v1
a(n),b(n),c(n),d(n);li(a,b,c,d) #define DL(...) ov5(__VA_ARGS__,DL5,DL4,DL3,DL2)(__VA_ARGS__) #define DV2(n,a) v1
a(n);vi(a) #define DV3(n,a,b) v1
a(n),b(n);vi(a,b) #define DV4(n,a,b,c) v1
a(n),b(n),c(n);vi(a,b,c) #define DV5(n,a,b,c,d) v1
a(n),b(n),c(n),d(n);vi(a,b,c,d) #define DV(...) ov5(__VA_ARGS__,DV5,DV4,DV3,DV2)(__VA_ARGS__) #define U23(h,w,a) u2 a;rs(a,h,w);li(a) #define U24(h,w,a,b) u2 a,b;rs(a,h,w),rs(b,h,w);li(a,b) #define U25(h,w,a,b,c) u2 a,b,c;rs(a,h,w),rs(b,h,w),rs(c,h,w);li(a,b,c) #define U2(...) ov5(__VA_ARGS__,U25,U24,U23)(__VA_ARGS__) #define S22(h,a) strs a(h);li(a) #define S23(h,a,b) strs a(h),b(h);li(a,b) #define S2(...) ov3(__VA_ARGS__,S23,S22)(__VA_ARGS__) #define AND2(a,b) ((a)&&(b)) #define AND3(a,b,c) ((a)&&(b)&&(c)) #define AND4(a,b,c,d) ((a)&&(b)&&(c)&&(d)) #define AND5(a,b,c,d,e) ((a)&&(b)&&(c)&&(d)&&(e)) #define AND6(a,b,c,d,e,f) ((a)&&(b)&&(c)&&(d)&&(e)&&(f)) #define AND(...) ov6(__VA_ARGS__,AND6,AND5,AND4,AND3,AND2)(__VA_ARGS__) #define OR2(a,b) ((a)||(b)) #define OR3(a,b,c) ((a)||(b)||(c)) #define OR4(a,b,c,d) ((a)||(b)||(c)||(d)) #define OR5(a,b,c,d,e) ((a)||(b)||(c)||(d)||(e)) #define OR6(a,b,c,d,e,f) ((a)||(b)||(c)||(d)||(e)||(f)) #define OR(...) ov6(__VA_ARGS__,OR6,OR5,OR4,OR3,OR2)(__VA_ARGS__) #define I template #define J class #define O operator #define rr return #define ss struct #define uu using #define as assert #define au auto #define bk break #define cs const #define ct continue #define endl "\n" #define fd friend #define sc static #define th this namespace my{ uu vo=void; vo main(); vo solve(); } int main(){my::main();} namespace my{ uu namespace std; uu namespace atcoder; //uu namespace boost::multiprecision; uu mint=modint1000000007; //uu cint=cpp_int; uu ll=long long; uu dd=long double; uu ui=unsigned int; uu ul=unsigned long long; uu chr=char; uu str=string; uu bo=bool; uu is=istream; uu os=ostream; str sp=" ",nc="",nl="\n"; au np=nullptr; Iss cp{ A a;B b; cp():a(A()),b(B()){} cp(A a,B b):a(a),b(b){} cp O+()cs{rr*th;} cp O-()cs{rr cp(-a,-b);} cp&O++(){a++,b++;rr*th;}cp O++(int){cp r=*th;++*th;rr r;} cp&O--(){a--,b--;rr*th;}cp O--(int){cp r=*th;--*th;rr r;} cp&O+=(cs cp&c){a+=c.a;b+=c.b;rr*th;}cp O+(cs cp&c)cs{rr cp(*th)+=c;} cp&O-=(cs cp&c){a-=c.a;b-=c.b;rr*th;}cp O-(cs cp&c)cs{rr cp(*th)-=c;} cp&O*=(cs cp&c){a*=c.a;b*=c.b;rr*th;}cp O*(cs cp&c)cs{rr cp(*th)*=c;} Icp&O+=(cs D&d){a+=d;b+=d;rr*th;}Icp O+(cs D&d)cs{rr cp(*th)+=d;} Icp&O-=(cs D&d){a-=d;b-=d;rr*th;}Icp O-(cs D&d)cs{rr cp(*th)-=d;} Icp&O*=(cs D&d){a*=d;b*=d;rr*th;}Icp O*(cs D&d)cs{rr cp(*th)*=d;} bo O==(cs cp&c)cs{rr AND(a==c.a,b==c.b);}bo O!=(cs cp&c)cs{rr!(*th==c);} bo O<(cs cp&c)cs{rr a!=c.a?a=(cs cp&c)cs{rr!(*th(cs cp&c)cs{rr a!=c.a?a>c.a:b>c.b;}bo O<=(cs cp&c)cs{rr!(*th>c);} fd is&O>>(is&i,cp&c){rr i>>c.a>>c.b;} fd os&O<<(os&o,cs cp&c){rr o<ss tr{ A a;B b;C c; tr():a(A()),b(B()),c(C()){} tr(A a,B b,C c):a(a),b(b),c(c){} bo O==(cs tr&t)cs{rr AND(a==t.a,b==t.b,c==t.c);} bo O!=(cs tr&t)cs{rr!(*th==t);} bo O<(cs tr&t)cs{rr a!=t.a?a(cs tr&t)cs{rr a!=t.a?a>t.a:b!=t.b?b>t.b:c>t.c;} fd is&O>>(is&i,tr&t){rr i>>t.a>>t.b>>t.c;} fd os&O<<(os&o,cs tr&t){rr o<ss qu{ A a;B b;C c;D d; qu():a(A()),b(B()),c(C()),d(D()){} qu(A a,B b,C c,D d):a(a),b(b),c(c),d(d){} bo O==(cs qu&q)cs{rr AND(a==q.a,b==q.b,c==q.c,d==q.d);} bo O!=(cs qu&q)cs{rr!(*th==q);} bo O<(cs qu&q)cs{rr a!=q.a?a(cs qu&q)cs{rr a!=q.a?a>q.a:b!=q.b?b>q.b:c!=q.c?c>q.c:d>q.d;} fd is&O>>(is&i,qu&q){rr i>>q.a>>q.b>>q.c>>q.d;} fd os&O<<(os&o,cs qu&q){rr o<uu v1=vector;uu u1=v1; Iuu v2=v1>;uu u2=v1; Iuu v3=v1>;uu u3=v1; Iuu v4=v1>;uu u4=v1; Iuu mset=multiset; Iuu fn=function; Iuu pqmax=priority_queue; Iuu pqmin=priority_queue,greater>; uu strs=v1; uu cl=cp; uu cd=cp; uu tl=tr; uu ql=deque; uu sl=set; uu msl=mset; uu ml=map; ss edg{ll t,w;edg(){}edg(ll t,ll w=1):t(t),w(w){}}; uu graph=v2; ll inf=3e18; dd ee=1e-10,pi=acosl(-1); u1 dx={-1,0,1,0,-1,1,1,-1},dy={0,-1,0,1,-1,-1,1,1}; 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 no(){rr yes(0);} str Yes(bo t=1){rr t?"Yes":"No";}str No(){rr Yes(0);} str YES(bo t=1){rr t?"YES":"NO";}str NO(){rr YES(0);} 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";} ui rnd(){ sc ui x=123456789,y=362436069,z=521288629,w=88675123; ui t=(x^(x<<11));x=y,y=z,z=w; rr(w=(w^(w>>19))^(t^(t>>8))); } dd rnd_prb(){rr (dd)rnd()/UINT_MAX;} ll rnd_rng(ll r){rr rnd()%r;} ll rnd_rng(ll l,ll r){rr rnd()%(r-l)+l;} bo od(ll x){rr x&1;} bo ev(ll x){rr !od(x);} bo eqp(ll x,ll y){rr ev(x-y);} ll bit(ll a){rr 1LL<0;--b&=S)r.eb(b);srt(r);rr r;} Iau sum(T a,U d,V n){rr n*(a*2+(n-1)*d)/2;} Ill len(cs T&a){rr a.size();} Ibo yu(cs T&a){rr len(a);} Ibo mu(cs T&a){rr !yu(a);} IT sq(T a){rr a*a;} IT ab(T a){rr abs(a);} 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 U&b){rr sgn(a-b);} IT cei(T x,U y){as(y);rr(y<0?cei(-x,-y):(x>0?(x+y-1)/y:x/y));} IT flo(T x,U y){as(y);rr(y<0?flo(-x,-y):(x>0?x/y:x/y-!(x%y)));} str tos(cs chr&a){rr a+nc;} str tos(cs chr*a){rr a;} str tos(cs str&a){rr a;} Istr tos(cs T&a){rr to_string(a);} Istr tos(cs T&a,cs A&...b){rr tos(a)+tos(b...);} u1 tou(cs str&s,chr b='a'){u1 a;fe(c,s)a.eb(c-b);rr a;} u2 tou(cs strs&s,chr b='a'){u2 a;fe(t,s)a.eb(tou(t,b));rr a;} u1 tou(cs str&s,cs str&t){ ll n=len(s); u1 a(n); fo(i,n)fo(j,len(t))if(s[i]==t[j]){a[i]=j;bk;} rr a; } u2 tou(cs strs&s,cs str&t){ll h=len(s);u2 a(h);fo(i,h)a[i]=tou(s[i],t);rr a;} u1 tou(cs v1&b,cs str&t){ ll n=len(b); u1 a(n); fo(i,n)fo(j,len(t))if(b[i]==t[j]){a[i]=j;bk;} rr a; } u2 tou(cs graph&g){ll n=len(g);u2 a(n);fo(u,n)fe(v,w,g[u])a[u].eb(v);rr a;} graph tog(cs u2&a){ll n=len(a);graph g(n);fo(u,n)fe(v,a[u])g[u].eb(v);rr g;} ll rp(ll a,ll x=inf,ll y=-1){rr a==x?y:a;} u1 rp(u1 a,ll x=inf,ll y=-1){fo(i,len(a))a[i]=rp(a[i],x,y);rr a;} Iau&O^=(v1&v,cs v1&u){copy(al(u),back_inserter(v));rr v;} Iau O^(v1v,cs v1&u){rr v^=u;} Iau O+(v1v){rr v;} Iau O-(v1v){fe(x,v)x=-x;rr v;} Iau&O++(v1&v){fe(x,v)x++;rr v;} Iau&O--(v1&v){fe(x,v)x--;rr v;} Iau O++(v1&v,int){au r=v;++v;rr r;} Iau O--(v1&v,int){au r=v;--v;rr r;} Iau&O+=(v1&v,cs v1&u){fo(i,len(v))v[i]+=u[i];rr v;} Iau&O-=(v1&v,cs v1&u){fo(i,len(v))v[i]-=u[i];rr v;} Iau&O*=(v1&v,cs v1&u){fo(i,len(v))v[i]*=u[i];rr v;} Iau O+(v1v,cs v1&u){rr v+=u;} Iau O-(v1v,cs v1&u){rr v-=u;} Iau O*(v1v,cs v1&u){rr v*=u;} Iau&O+=(v1&v,cs bitset<60>&a){fo(i,len(v))v[i]+=a[i];rr v;} Iau&O-=(v1&v,cs bitset<60>&a){fo(i,len(v))v[i]-=a[i];rr v;} Iau&O+=(v1&v,cs bitset<30>&a){fo(i,len(v))v[i]+=a[i];rr v;} Iau&O-=(v1&v,cs bitset<30>&a){fo(i,len(v))v[i]-=a[i];rr v;} Iau&O+=(v1&v,cs U&a){fe(x,v)x+=a;rr v;} Iau&O-=(v1&v,cs U&a){fe(x,v)x-=a;rr v;} Iau&O*=(v1&v,cs U&a){fe(x,v)x*=a;rr v;} Iau&O/=(v1&v,cs U&a){fe(x,v)x/=a;rr v;} Iau&O%=(v1&v,cs U&a){fe(x,v)x%=a;rr v;} Iau O+(v1v,cs U&a){rr v+=a;} Iau O-(v1v,cs U&a){rr v-=a;} Iau O*(v1v,cs U&a){rr v*=a;} Iau O/(v1v,cs U&a){rr v/=a;} Iau O%(v1v,cs U&a){rr v%=a;} Ibo amax(T&a,cs U&b){rr abo amin(T&a,cs U&b){rr a>b?a=b,1:0;} IT max(cs v1&a){rr *itmax(a);} IT min(cs v1&a){rr *itmin(a);} Iau max(cs v2&a){rr max(*itmax(a));} Iau min(cs v2&a){rr min(*itmin(a));} Iau max(T...a){rr max(initializer_list>{a...});} Iau min(T...a){rr min(initializer_list>{a...});} ll mex(cs sl&s){ll r=0;wh(s.count(r))r++;rr r;} ll mex(cs u1&v){rr mex(sl(al(v)));} Ill mex(cs T&...a){sl s;fe(x,{a...})s.insert(x);rr mex(s);} Ill argmax(cs v1&a){rr itmax(a)-bgn(a);} Ill argmin(cs v1&a){rr itmin(a)-bgn(a);} Iau gcd(cs T&a,cs U&b){rr std::gcd(a,b);} Iau gcd(cs T&a,cs A&...b){rr gcd(a,gcd(b...));} IT sum(cs set&s){T r=T();fe(x,s)r+=x;rr r;} IT sum(cs v1&a){rr accumulate(al(a),T());} Ill lbs(cs v1&a,cs U&b){rr lb(al(a),b)-bgn(a);} Ill ubs(cs v1&a,cs U&b){rr ub(al(a),b)-bgn(a);} Iau minmax(cs T&a,cs U&b){rr cp(min(a,b),max(a,b));} Iau minmax(cs cp&p){rr minmax(p.a,p.b);} Iau mp(cs fn&f,v1x){v1y;fe(a,x)y.eb(f(a));rr y;} Iau keys(cs map&m){v1r;fe(k,v,m)r.eb(k);rr r;} Iau vals(cs map&m){v1r;fe(k,v,m)r.eb(v);rr r;} u1 io(ll n,ll a=0){u1 i(n);iota(al(i),a);rr i;} Ivo emplace_front(v1&v,U x=U()){v.ep(bgn(v),x);} Ivo emplace_front(v1&v,T x=T()){v.ep(bgn(v),x);} Ivo pop_front(v1&v){v.erase(bgn(v));} Iau&bg(T&a){rr*bgn(a);} Iau&bg(cs T&a){rr*bgn(a);} Iau&rb(T&a){rr*rbg(a);} Iau&rb(cs T&a){rr*rbg(a);} IT bg(pqmax&q){rr q.top();} IT bg(pqmin&q){rr q.top();} IT pop(v1&v){T r=rb(v);v.pb();rr r;} IT pop_front(deque&q){T r=bg(q);q.pf();rr r;} IT pop_back(deque&q){T r=rb(q);q.pb();rr r;} IT pop(deque&q){rr pop_front(q);} IT pop(pqmax&q){T r=bg(q);q.pop();rr r;} IT pop(pqmin&q){T r=bg(q);q.pop();rr r;} ss z{z(){cin.tie(0);ios::sync_with_stdio(0);cout<>(is&i,mint&x){ll t;i>>t;x=t;rr i;} os&O<<(os&o,cs mint&x){rr o<is&O>>(is&i,pair&p){rr i>>p.first>>p.second;} Ios&O<<(os&o,cs pair&p){rr o<os&O<<(os&o,cs map&m){fe(p,m)o<os&O<<(os&o,cs set&s){fe(x,s)o<os&O<<(os&o,cs mset&s){fe(x,s)o<os&O<<(os&o,dequeq){wh(yu(q))o<os&O<<(os&o,pqmaxq){wh(yu(q))o<os&O<<(os&o,pqminq){wh(yu(q))o<is&O>>(is&i,v1&v){fe(x,v)i>>x;rr i;} Ios&O<<(os&o,cs v1&v){fe(x,v)o<os&O<<(os&o,cs v2&v){fe(x,v)o<ll pp(cs T&a,cs A&...b){cout<ll li(T&...a){(cin>>...>>a);rr 0;} Ivo vi(ll i,T&...a){(cin>>...>>a[i]);} Ivo vi(v1&a,A&...b){fo(i,len(a))vi(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);} au gi(u2&g,ll m,bo d=1){ u1 a(m),b(m); fo(i,m){ li(a[i],b[i]);a[i]--,b[i]--; g[a[i]].eb(b[i]); if(d)g[b[i]].eb(a[i]); } rr cp(a,b); } au gi(graph&g,ll m,bo w=1,bo d=1){ u1 a(m),b(m),c(m); fo(i,m){ li(a[i],b[i]);a[i]--,b[i]--; c[i]=1;if(w)li(c[i]); g[a[i]].eb(b[i],c[i]); if(d)g[b[i]].eb(a[i],c[i]); } rr tr(a,b,c); } au ti(u2&g,bo d=1){rr gi(g,len(g)-1,d);} au ti(graph&g,bo w=1,bo d=1){rr gi(g,len(g)-1,w,d);} Iss rcl:private F{ explicit rcl(F&&f):F(forward(f)){} Idecltype(au)O()(T&&...a)cs{rr F::O()(*th,forward(a)...);} }; vo pz(cs u1&v,u1&h){fe(x,h)x=lbs(v,x);} Ivo pz(cs u1&v,u1&h,T&...t){pz(v,h);pz(v,t...);} Iu1 zp(T&...a){u1 v;fe(e,{a...})v^=e;uq(v);pz(v,a...);rr v;} Ivo sv(cs u1&){} Ivo sv(cs u1&o,v1&a){au c=a;fo(i,len(a))a[i]=c[o[i]];} Ivo sv(cs u1&o,v1&a,A&...b){sv(o,a);sv(o,b...);} Iau vs(cs fn&f,v1&a){ ll n=len(a); u1 o=io(n),p(n); sort(al(o),f); fo(i,n)p[o[i]]=i; sv(o,a); rr cp(o,p); } Iau vs(cs fn&f,v1&a,A&...b){ ll n=len(a); u1 o=io(n),p(n); sort(al(o),f); fo(i,n)p[o[i]]=i; sv(o,a);sv(o,b...); rr cp(o,p); } ll bsl(cs fn&j,ll o,ll n){wh(ab(o-n)>1)(j((o+n)/2)?o:n)=(o+n)/2;rr o;} dd bsd(cs fn&j,dd o,dd n){wh(ab(o-n)>ee)(j((o+n)/2)?o:n)=(o+n)/2;rr o;} Iau zt(v1a){fo(i,1,len(a))a[i]+=a[i-1];rr a;} Iau mb(v1a){of(i,len(a),1)a[i]-=a[i-1];rr a;} Iau zt(v2a){fe(v,a)v=zt(v);fo(i,1,len(a))a[i]+=a[i-1];rr a;} Iau mb(v2a){fe(v,a)v=mb(v);of(i,len(a),1)a[i]-=a[i-1];rr a;} Iau ztdiv(v1a){ll n=len(a);fo(i,1,n)fo(j,i*2,n,i)a[i]+=a[j];rr a;} Iau mbdiv(v1a){ll n=len(a);of(i,n,1)fo(j,i*2,n,i)a[i]-=a[j];rr a;} au rle(u1 a){v1r;fe(x,a)yu(r)&&x==rb(r).a?rb(r).b++,0:(r.eb(x,1),0);rr r;} au rce(u1 a){v1r;ml m;fe(x,a)m[x]++;fe(k,v,m)r.eb(k,v);rr r;} IT esq(T x,ll n,T e){wh(n){if(n&1)e*=x;x*=x;n/=2;}rr e;} vo wafl(u2&d){ll n=len(d);fo(k,n)fo(i,n)fo(j,n)amin(d[i][j],d[i][k]+d[k][j]);} u1 divs(ll n){ml m;fo(i,1,n/i+1)if(n%i==0)m[i]++,m[n/i]++;rr keys(m);} ml fact(ll n){ml m;fo(i,2,n/i+1)wh(n%i==0)m[i]++,n/=i;if(n>1)m[n]++;rr m;} bo isp(ll n){ml fa=fact(n);rr len(fa)==1&&bg(fa).second==1;} ll inv(ll a,ll m){ a=(a%m+m)%m; ll b=m,u=1,v=0; wh(b)u-=a/b*v,sw(u,v),a-=a/b*b,sw(a,b); rr(u%m+m)%m; } ll pow(ll x,ll n,ll m=inf){ if(n<0)n=-n,x=inv(x,m); ll r=1;wh(n){if(n&1)r*=x,r%=m;x*=x,x%=m,n/=2;}rr r; } Iss tww{ v1fa,rf,bs; v2m; v2u; tww(ll n){ n++; rs(fa,n);rs(rf,n);rs(bs,n); fa[0]=rf[0]=bs[0]=1; fo(i,1,n)fa[i]=fa[i-1]*i,rf[i]=rf[i-1]/i; fo(i,1,n)bs[i]=bs[i-1]+rf[i]*pow(-1,i&1); if(n<=5000)rs(m,n,n),rs(u,n,n); } T c(ll n,ll k){rr n==k?1:n=0)rr u[n][k]=1,m[n][k]=p(n,k-1)+p(n-k,k); rr u[n][k]=1,m[n][k]=p(n,k-1); } }; ss ufin{ ll n; u1 d; ufin():n(0){} ufin(ll n):n(n),d(n,-1){} ll ldr(ll a){as(in(0,a,n));if(d[a]<0)rr a;rr d[a]=ldr(d[a]);} bo same(ll a,ll b){as(in(0,a,n)&&in(0,b,n));rr ldr(a)==ldr(b);} ll size(ll a){as(in(0,a,n));rr-d[ldr(a)];} ll mrg(ll a,ll b){ as(in(0,a,n)&&in(0,b,n)); ll x=ldr(a),y=ldr(b); if(x==y)rr x; if(-d[x]<-d[y])sw(x,y); d[x]+=d[y]; d[y]=x; rr x; } u2 groups(){ u1 l(n);u2 g(n); fo(i,n)l[i]=ldr(i);fo(i,n)g[l[i]].eb(i);fo(i,n)srt(g[i]);srt(g); g.erase(remove_if(al(g),[&](cs u1&v){rr mu(v);}),end(g)); rr g; } }; 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=bit(log); d=v1(A*2,e()); fo(i,n)d[i+A]=v[i]; of(i,A,1)upd(i); } ll size()cs{rr n;} vo upd(ll k){d[k]=op(d[k*2],d[k*2+1]);} vo set(ll i,S x){as(in(0,i,n));i+=A;d[i]=x;fo(j,1,log+1)upd(i>>j);} vo add(ll i,S x){set(i,get(i)+x);} S get(ll i)cs{as(in(0,i,n));rr d[i+A];} S aprd(){rr d[1];} S prd(ll l,ll r){ as(AND(0<=l,l<=r,r<=n)); S sml=e(),smr=e(); l+=A,r+=A; wh(lfa(N+1); fa[0]=1; fo(i,1,N+1)fa[i]=i*fa[i-1]; dd ans=0; fo(x,1,F+1){ dd t=0; fo(i,N+1){ fo(j,N+1){ if(i=K){ t+=fa[N]/fa[i]/fa[j]/fa[N-i-j] *std::pow(F-x,i)*std::pow(x-1,N-i-j)/std::pow(F,N); } } } ans+=x*t; } pp(ans); }}