#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #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 eb(...) emplace_back(__VA_ARGS__) #define ef(...) 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 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 rs(...) resize(__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 CH(...) chr __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 U23(h,w,a) u2 a(h,w);li(a) #define U24(h,w,a,b) u2 a(h,w),b(h,w);li(a,b) #define U25(h,w,a,b,c) u2 a(h,w),b(h,w),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 I template #define J typename #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 th this #define endl "\n" namespace my{void main();void solve();} int main(){my::main();} namespace my{ uu namespace std; uu namespace atcoder; uu vo=void; uu bo=bool; uu is=istream; uu os=ostream; uu mint=modint998244353; uu i128=__int128_t; uu ll=long long; uu dd=long double; uu ul=unsigned long long; uu chr=char; string sp=" ",nc="",nl="\n"; au nu=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 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;} Icp&O+=(cs T&x){a+=x,b+=x;rr*th;}Icp O+(cs T&x)cs{rr cp{*th}+=x;} Icp&O-=(cs T&x){a-=x;b-=x;rr*th;}Icp O-(cs T&x)cs{rr cp{*th}-=x;} Icp&O*=(cs T&x){a*=x;b*=x;rr*th;}Icp O*(cs T&x)cs{rr cp{*th}*=x;} au abs()cs{rr std::abs(a)+std::abs(b);}//manhattan au abs(cs cp&c)cs{rr (*th-c).abs();} bo O==(cs cp&c)cs{rr 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 a!=c.a?a>c.a:b>c.b;} friend 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 a!=t.a?a(cs tr&t)cs{rr a!=t.a?a>t.a:b!=t.b?b>t.b:c>t.c;} friend 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 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;} friend os&O<<(os&o,cs qu&q){rr o<uu v1=vector; Iss v2:v1>{uu v1>::v1;v2(ll a,ll b){th->rs(a,v1(b));}v2(ll a,ll b,T x){th->rs(a,v1(b,x));}}; Iss v3:v1>{uu v1>::v1;v3(ll a,ll b,ll c){th->rs(a,v2(b,c));}v3(ll a,ll b,ll c,T x){th->rs(a,v2(b,c,x));}}; Iss v4:v1>{uu v1>::v1;v4(ll a,ll b,ll c,ll d){th->rs(a,v3(b,c,d));}v4(ll a,ll b,ll c,ll d,T x){th->rs(a,v3(b,c,d,x));}}; uu u1=v1;uu u2=v2;uu u3=v3;uu u4=v4; uu m1=v1;uu m2=v2;uu m3=v3;uu m4=v4; ss str:v1{ uu v1::v1; str(cs string&s){fe(c,s)th->eb(c);} str(cs chr*s){fe(c,string(s))th->eb(c);} str(cs u1&a,cs chr&b='a'){fe(x,a)th->eb(x+b);} str(cs u1&a,cs string&b){ll n=a.size();th->rs(n);fo(i,n)fo(j,b.size())if(a[i]==j){(*th)[i]=b[j];bk;}} str&O+=(cs str&s){fe(c,s)th->eb(c);rr*th;}str O+(cs str&s){rr str{*th}+=s;} str&O+=(cs string&s){str t{s};rr*th+=t;}str O+(cs string&s){rr str{*th}+=s;} str&O+=(cs chr*s){str t{string(s)};rr*th+=t;}str O+(cs chr*s){rr str{*th}+=s;} str&O+=(cs chr&c){th->eb(c);rr*th;}str O+(cs chr&c){rr str{*th}+=c;} Istr&O+=(cs T&x){str t{to_string(x)};rr*th+=t;}Istr O+(cs T&x){rr str{*th}+=x;} u1 en(cs chr&b='a'){u1 r;fe(c,*th)r.eb(c-b);rr r;} u1 en(cs string&b){ll n=th->size();u1 r(n);fo(i,n)fo(j,b.size())if((*th)[i]==b[j]){r[i]=j;bk;}rr r;} friend is&O>>(is&i,str&s){string t;i>>t;s=str{t};rr i;} friend os&O<<(os&o,cs str&s){fe(c,s)o<{ uu v1::v1; u2 en(cs chr&b='a'){u2 r;fe(e,*th)r.eb(e.en(b));rr r;} u2 en(cs string&b){u2 r;fe(e,*th)r.eb(e.en(b));rr r;} }; Iuu fn=function; Iuu qmax=priority_queue; Iuu qmin=priority_queue,greater>; uu cl=cp;uu cd=cp;uu cls=v1; uu tl=tr;uu td=tr;uu tls=v1; uu ql=qu;uu qd=qu;uu qls=v1; uu ml=map;uu uml=unordered_map; uu sl=set;uu usl=unordered_set; uu msl=multiset; uu dl=deque; 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 Yes(bo b=1){rr b?"Yes":"No";}str No(){rr Yes(0);} ul xx=123456789,yy=362436069,zz=521288629,ww=88675123; ul rnd(){ul t=(xx^(xx<<11));xx=yy,yy=zz,zz=ww;rr(ww=(ww^(ww>>19))^(t^(t>>8)));} dd rnd_prb(){rr (dd)rnd()/ULLONG_MAX;} ll rnd_rng(ll r){rr rnd()%r;} ll rnd_rng(ll l,ll r){rr rnd()%(r-l)+l;} bo odd(ll x){rr x&1;} bo eve(ll x){rr !odd(x);} ll pm1(ll x){rr 1-2*odd(x);} ll bi(ll n){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(cs T&a){rr a*a;} IT cb(cs T&a){rr a*a*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)));} 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;} Ivo af(v1&v){v.ep(bgn(v),T{});} Ivo af(v1&v,U e=U{}){v.ep(bgn(v),e);} Ivo df(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 pof(deque&q){T r=bg(q);q.pop_front();rr r;} IT pob(deque&q){T r=rb(q);q.pop_back();rr r;} IT pop(v1&v){T r=rb(v);v.pop_back();rr r;} IT pop(qmax&q){T r=q.top();q.pop();rr r;} IT pop(qmin&q){T r=q.top();q.pop();rr r;} Iau&O^=(v1&v,cs v1u){copy(al(u),back_inserter(v));rr v;}Iau O^(v1v,cs v1&u){rr v^=u;} Iau O-(v1v){fe(x,v)x=-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){fe(x,v)x--;rr v;}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+(v1v,cs v1&u){rr v+=u;} 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+=(v1&v,cs U&a){fe(x,v)x+=a;rr v;}Iau O+(v1v,cs U&a){rr v+=a;} 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*=(v1&v,cs U&a){fe(x,v)x*=a;rr v;}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*max_element(al(a));} IT min(cs v1&a){rr*min_element(al(a));} Iau max(cs v2&a){T r=max(bg(a));fe(v,a)amax(r,max(v));rr r;} Iau min(cs v2&a){T r=min(bg(a));fe(v,a)amin(r,min(v));rr r;} Iau max(T...a){rr max(initializer_list>{a...});} Iau min(T...a){rr min(initializer_list>{a...});} Ill argmax(cs v1&a){rr max_element(al(a))-bgn(a);} Ill argmin(cs v1&a){rr min_element(al(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 v1&a){rr accumulate(al(a),T{});} IT sum(cs v2&a){T r{};fe(e,a)r+=sum(e);rr r;} IT sum(dequeq){T r{};wh(yu(q))r+=pop(q);rr r;} IT sum(cs set&s){T r{};fe(x,s)r+=x;rr r;} IT sum(qmaxq){T r{};wh(yu(q))r+=pop(q);rr r;} IT sum(qminq){T r{};wh(yu(q))r+=pop(q);rr r;} 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 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;} Iu1 inv(cs v1&a){ll n=len(a);u1 r(n);fo(i,n)r[a[i]]=i;rr r;} ss fio{fio(){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<os&O<<(os&o,cs pair&p){rr o<os&O<<(os&o,cs map&m){fe(p,m)o<os&O<<(os&o,cs unordered_map&m){fe(p,m)o<os&O<<(os&o,cs set&s){fe(x,s)o<os&O<<(os&o,cs unordered_set&s){fe(x,s)o<os&O<<(os&o,cs multiset&s){fe(x,s)o<os&O<<(os&o,dequeq){wh(yu(q))o<os&O<<(os&o,qmaxq){wh(yu(q))o<os&O<<(os&o,qminq){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...);} au mgi(u2&g,ll m){UV(m,a,b);a--,b--;fo(i,m)g[a[i]].eb(b[i]),g[b[i]].eb(a[i]);rr cp(a,b);} au ygi(u2&g,ll m){UV(m,a,b);a--,b--;fo(i,m)g[a[i]].eb(b[i]);rr cp(a,b);} au mgi(graph&g,ll m){UV(m,a,b,c);a--,b--;fo(i,m)g[a[i]].eb(b[i],c[i]),g[b[i]].eb(a[i],c[i]);rr tr(a,b,c);} au ygi(graph&g,ll m){UV(m,a,b,c);a--,b--;fo(i,m)g[a[i]].eb(b[i],c[i]);rr tr(a,b,c);} au ti(u2&g){rr mgi(g,len(g)-1);} au ti(graph&g){rr mgi(g,len(g)-1);} str ins(){ST(r);rr r;} strs ins2(ll n){S2(n,r);rr r;} Iss rcl:private F{explicit rcl(F&&f):F(forward(f)){}Idecltype(au)O()(T&&...a)cs{rr F::O()(*th,forward(a)...);}}; Iau tzp(A&...a){v1v;fe(e,{a...})v^=e;uq(v);rr v;} 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=tzp(a...);pz(v,a...);rr v;} u1 zp(u2&a){u1 v;fe(e,a)v^=e;uq(v);fe(e,a)fe(x,e)x=lbs(v,x);rr v;} 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...);} Iu1 vs(cs fn&f,v1&a){u1 o=io(len(a));sort(al(o),f);sv(o,a);rr o;} Iu1 vs(cs fn&f,v1&a,A&...b){u1 o=io(len(a));sort(al(o),f);sv(o,a);sv(o,b...);rr o;} ll bsl(cs fn&j,ll o,ll n){wh(abs(o-n)>1)(j((o+n)/2)?o:n)=(o+n)/2;rr o;} dd bsd(cs fn&j,dd o,dd n){wh(abs(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(cs u1&a){cls r;fe(x,a)yu(r)&&x==rb(r).a?rb(r).b++,0:(r.eb(x,1),0);rr r;} au rce(cs u1&a){cls r;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){if(n<=1)rr 0;fo(i,2,n/i+1)if(n%i==0)rr 0;rr 1;} au inv(i128 a,ll m){a=(a%m+m)%m;i128 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;} au pow(i128 x,ll n,ll m=inf){if(n<0)n=-n,x=inv(x,m);i128 r=1;wh(n){if(n&1)r*=x,r%=m;x*=x,x%=m,n/=2;}rr r;} au quot_rng(ll n){tls r;ll m=sqr(n),l=n/(m+1);fo(i,1,m+1)r.eb(n/i,i,i);of(i,l+1,1)r.eb(i,n/(i+1)+1,n/i);rr r;} 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=l2(n*2-1)-1,A=bi(log),d.rs(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 i){d[i]=op(d[i*2],d[i*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(0<=l&&l<=r&&r<=n); S sml=e(),smr=e(); l+=A,r+=A; wh(lss kazoeage{ v1fa,rf,bs; kazoeage(ll n):fa(n+1,1),rf(n+1,1),bs(n+1,1){ fo(i,1,n+1)fa[i]=fa[i-1]*i; rf[n]=fa[n].inv(); of(i,n)rf[i]=rf[i+1]*(i+1); fo(i,1,n+1)bs[i]=bs[i-1]+pm1(i)*rf[i]; } T c(ll n,ll k){rr n<0?pm1(k)*c(-n+k-1,k):k<0||n; ss spf{ ll n; u1 sp;//sp[i]:iを割り切る最小の素数 u1 ps; spf(ll n):n(n){//前処理 sp=io(n+1); fo(i,2,n/i+1)if(sp[i]==i)fo(j,i+i,n+1,i)sp[j]=i;//O(nloglog(n)) fo(i,2,n+1)if(sp[i]==i)ps.eb(i); } bo ispr(ll x){as(x<=n);rr sp[x]==x;} cls qv(ll x){//素因数分解クエリ as(x<=n); v1r; wh(x>1){//O(log(x)) if(yu(r)&&rb(r).a==sp[x])rb(r).b++; el r.eb(sp[x],1); x/=sp[x]; } rr r; } ml qm(ll x){//素因数分解クエリ as(x<=n); ml r; wh(x>1)r[sp[x]]++,x/=sp[x];//O(log(x)) rr r; } }; vo main(){ ll T=1; //li(T); fo(T)solve(); } vo solve(){ LL(N); UL(N,a); ll Amax=max(a); spf sp(Amax); u1 primes=sp.ps; u1 m(Amax+1); fe(x,a)m[x]++; u1 cnt(Amax+1); fe(p,primes){ fo(j,p,Amax+1,p){ cnt[p]+=m[j]; } } u1 small,large; fe(p,primes){ if(p<=sqr(Amax))small.eb(p); el large.eb(p); } ll n=len(small); u2 dp(n+1,Amax+1); dp[0][1]=1; fo(i,n){ fo(j,Amax+1){ dp[i+1][j]|=dp[i][j]; if(j*small[i]<=Amax)dp[i+1][j*small[i]]|=dp[i][j]; } } m1 su(Amax); fe(p,large)su[p]=mint(2).pow(cnt[p])-1-cnt[p]; su=zt(su); u1 V; fo(j,2,Amax+1)if(dp[n][j])V.eb(j); mint ans=0; fe(S,V){ u1 v; fe(p,small)if(S%p==0)v.eb(p); mint t=1; fe(p,v)t*=mint(2).pow(cnt[p])-1-cnt[p]; ans+=-pm1(len(v))*t; ans+=-pm1(len(v)+1)*(t*su[Amax/S]); } pp(ans+N); }}