#include #include using namespace std; namespace my{ #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define RDVL(T,n,...) vec__VA_ARGS__;resizes({n},__VA_ARGS__);lin(__VA_ARGS__) #define VL(n,...) RDVL(ll,n,__VA_ARGS__) #define jo(a,b) a##b #define FO_IMPL(n,c) for(ll jo(_i,c)=n;jo(_i,c)-->0;) #define FO(n) FO_IMPL(n,__COUNTER__) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i=i##stop;i+=i##step) #define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a) #define maybe(p,c) (p?c:remove_cvref_t{}) #define base_operator(op,type) auto operator op(const type&v)const{auto copy=*this;return copy op##=v;} #define entry void solve();void solve2();}int main(){my::io();my::solve();}namespace my{ #define use_ml998244353 using ml=atcoder::modint998244353; auto&operator>>(istream&i,atcoder::modint998244353&x){int t;i>>t;x=t;return i;} auto&operator<<(ostream&o,const atcoder::modint998244353&x){return o<<(int)x.val();} void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<=0);decltype(x)r=e;for(;n;x*=x,n>>=1)if(n&1)r*=x;return r;} constexpr auto pow(auto x,auto n){return pow(x,n,1);} auto max(auto...a){return max(initializer_list>{a...});} templatecommon_type_tgcd(T a,U b){return b?gcd(b,a%b):abs(a);} auto gcd(auto...a){common_type_tr=0;((r=gcd(r,a)),...);return r;} ll rand(){static ll x=495;x^=x<<7;x^=x>>9;return x;} ll rand(ll l,ll r=0){if(l>r)swap(l,r);return rand()%(r-l)+l;} templatestruct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair&p):a(p.first),b(p.second){} auto operator<=>(const pair&)const=default; pair operator+(const pair&p)const{return{a+p.a,b+p.b};} friend istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;} friend ostream&operator<<(ostream&o,const pair&p){return o<>auto&sort(auto&a,F f={}){ranges::sort(a,f);return a;} templateusing pack_back_t=tuple_element_t>; templateconcept vectorial=is_base_of_v::value_type>,remove_cvref_t>; templateconstexpr int rank(){if constexpr(vectorial)return rank()+1;else return 0;} templatestruct core_t_helper{using core_t=T;}; templatestruct core_t_helper{using core_t=typename core_t_helper::core_t;}; templateusing core_t=core_t_helper::core_t; templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateostream&operator<<(ostream&o,const vector&v){ll n=v.size();fo(i,n)o<ostream&operator<<(ostream&o,const vector&v){ll n=v.size();fo(i,n)o<struct vec; templatestruct hvec_helper{using type=vec::type>;}; templatestruct hvec_helper<0,T>{using type=T;}; templateusing hvec=typename hvec_helper::type; templatestruct vec:vector{ static constexpr int R=rank>(); using C=core_t; using vector::vector; vec(const vector&v){vector::operator=(v);} vec(const auto&...a)requires(sizeof...(a)>=3){resizes(a...);} void resizes(const auto&...a){*this=make(a...);} static auto make(ll n,const auto&...a){ if constexpr(sizeof...(a)==1)return vec(n,array{a...}[0]); else return vec(n,make(a...)); } vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec&operator+=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]+=u[i];return v;} vec&operator-=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]-=u[i];return v;} vec&operator+=(const C&c){fe(*this,e)e+=c;return*this;} vec&operator*=(const C&c){fe(*this,e)e*=c;return*this;} base_operator(^,vec) base_operator(+,vec) base_operator(-,vec) base_operator(+,C); base_operator(*,C); vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} ll size()const{return vector::size();} auto&emplace_back(auto&&...a){vector::emplace_back(std::forward(a)...);return*this;} auto scan(const auto&f)const{ pairr{}; fe(*this,e)if constexpr(!vectorial)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s; return r; } auto sum()const{return scan([](auto&a,const auto&b){a+=b;}).a;} auto max()const{return scan([](auto&a,auto b){if(a)fe(v,e)e=e.mobius();of(i,v.size()-1)v[i+1]-=v[i];return v;} template>auto sort(F f={})const{vec v=*this;ranges::sort(v,f);return v;} auto transform(const auto&f)const{ hvecres(size()); if constexpr(vectorial)fo(i,size())res[i]=(*this)[i].transform(f); else std::transform(this->begin(),this->end(),res.begin(),f); return res; } auto rle()const{vec>r;fe(*this,e)if(r.size()&&e==r.back().a)++r.back().b;else r.eb(e,1);return r;} auto rce()const{return sort().rle();} auto as()const{return transform([](const auto&e){return e.a;});} }; templaterequires(sizeof...(A)>=2)vec(const A&...a)->vec>>; vec(ll)->vec; templatevoid resizes(const array::R+1>&s,A&...a){(apply([&](const auto&...b){a.resizes(b...); },s),...);} auto pack_vec(const auto&...a){return vec>{a...};} void lin(auto&...a){(cin>>...>>a);} void pp(const auto&...a){ll n=sizeof...(a);((cout<0,space)),...);cout<struct montgomery64{ using modular=montgomery64; static inline ui64 N=998244353; static inline ui64 N_inv=996491785301655553ull; static inline ui64 R2=299560064; static int set_mod(ui64 N){ if(modular::N==N)return 0; assert(N<(1ull<<63)); assert(N&1); modular::N=N; R2=-ui128(N)%N; N_inv=N; fo(5)N_inv*=2-N*N_inv; assert(N*N_inv==1); return 0; } ui64 a; montgomery64(const i64&a=0):a(reduce((ui128)(a%(i64)N+N)*R2)){} static ui64 reduce(const ui128&T){ui128 r=(T+ui128(ui64(T)*-N_inv)*N)>>64;return r>=N?r-N:r;} auto&operator+=(const modular&b){if((a+=b.a)>=N)a-=N;return*this;} auto&operator-=(const modular&b){if(i64(a-=b.a)<0)a+=N;return*this;} auto&operator*=(const modular&b){a=reduce(ui128(a)*b.a);return*this;} auto&operator/=(const modular&b){*this*=b.inv();return*this;} friend auto operator+(const modular&a,const modular&b){return modular{a}+=b;} friend auto operator-(const modular&a,const modular&b){return modular{a}-=b;} friend auto operator*(const modular&a,const modular&b){return modular{a}*=b;} friend auto operator/(const modular&a,const modular&b){return modular{a}/=b;} friend bool operator==(const modular&a,const modular&b){return a.a==b.a;} auto operator-()const{return modular{}-modular{*this};} modular pow(ui128 n)const{return my::pow(*this,n);} modular inv()const{ui64 a=val(),b=N,u=1,v=0;assert(gcd(a,b)==1);while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return u;} ui64 val()const{return reduce(a);} friend istream&operator>>(istream&i,montgomery64&b){ll t;i>>t;b=t;return i;} friend ostream&operator<<(ostream&o,const montgomery64&b){return o<T one(T n){return n>0;} void sort(auto&...a){auto v=pack_vec(a...).sort();ll i=0;((a=v[i++]),...);} bool miller_rabin(ll n,vecas){ ll d=n-1; while(~d&1)d>>=1; using modular=montgomery64<1>; modular::set_mod(n); modular one=1,minus_one=n-1; fe(as,a){ if(a%n==0)continue; ll t=d; modular y=modular(a).pow(t); while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1; if(y!=minus_one&&~t&1)return 0; } return 1; } bool is_prime(ll n){ if(~n&1)return n==2; if(n<=1)return 0; if(n<4759123141LL)return miller_rabin(n,{2,7,61}); return miller_rabin(n,{2,325,9375,28178,450775,9780504,1795265022}); } ll pollard_rho(ll n){ if(~n&1)return 2; if(is_prime(n))return n; using modular=montgomery64<2>; modular::set_mod(n); modular R,one=1; auto f=[&](const modular&x){return x*x+R;}; while(1){ modular x,y,ys,q=one; R=rand(2,n),y=rand(2,n); ll g=1; constexpr ll m=128; for(ll r=1;g==1;r<<=1){ x=y; fo(r)y=f(y); for(ll k=0;g==1&&k0); vecres; auto f=[&](auto&f,ll m){ if(m==1)return; auto d=pollard_rho(m); if(d==m)res.eb(d); else f(f,d),f(f,m/d); }; f(f,n); return res.rce(); } auto radical(ll n){ll res=1;fe(factorize(n),p,q)res*=p;return res;} auto divisors(const vec>&prime_exponent){ vecr{1}; for(auto[p,e]:prime_exponent){ ll sz=size(r); for(ll t=p;e;--e,t*=p)fo(i,sz)r.eb(r[i]*t); } return sort(r); } auto divisors(ll n){return divisors(factorize(n));} ll mobius_prime_pow(ll,i8 k,ll){return-(k==1);} ll mobius(ll n){ll r=1;fe(factorize(n),p,q)r*=mobius_prime_pow(p,q,pow(p,q));return r;} templatestruct linear_sieve{ T n; veclpf; veclpf_ord; veclpf_pow; veclpf_pow_except; vecprimes; linear_sieve(T n):n(n),lpf(n+1,-1),lpf_ord(n+1),lpf_pow(n+1),lpf_pow_except(n+1){ lpf[1]=lpf_ord[1]=lpf_pow[1]=lpf_pow_except[1]=1; fo(i,2,n+1){ if(lpf[i]==-1)primes.eb(lpf[i]=i); fe(primes,p){ if(p*i>n||p>lpf[i])break; lpf[p*i]=p; } int j=i/lpf[i]; lpf_ord[i]=lpf_ord[j]*(lpf[i]==lpf[j])+1; lpf_pow[i]=((lpf_pow[j]-1)*(lpf[i]==lpf[j])+1)*lpf[i]; lpf_pow_except[i]=i/lpf_pow[i]; } } auto multiplicative_function_enumerate(const auto&f)const{ vecr(n+1); r[1]=1; fo(i,2,n+1)r[i]=f(lpf[i],lpf_ord[i],lpf_pow[i])*r[lpf_pow_except[i]]; return r; } auto mobius_enumerate()const{return multiplicative_function_enumerate(mobius_prime_pow);} auto factorize(T x)const{ assert(x<=n); vec>res; for(;x>1;x=lpf_pow_except[x])res.eb(lpf[x],lpf_ord[x]); return res; } auto radical(T x)const{ assert(x<=n); T res=1; for(;x>1;x=lpf_pow_except[x])res*=lpf[x]; return res; } auto divisors(ll x)const{ assert(x<=n); vecres{1}; fe(factorize(x),p,e){ ll m=res.size(); for(T t=p;e;--e,t*=p)fo(i,m)res.eb(res[i]*t); } return sort(res); } }; entry void solve(){ LL(N); VL(N,a); ll M=a.max()+1; linear_sievels(M); auto mobius=ls.mobius_enumerate(); use_ml998244353 ml su=0; // dp.sum() vecdp(M); vecg(M); fe(a,e){ e=ls.radical(e); ml f1=0; fe(ls.divisors(e),x)f1+=mobius[x]*g[x]; ml diff=1+su-f1; dp[e]+=diff; su+=diff; fe(ls.divisors(e),x)g[x]+=diff; } pp(su); }}