#line 2 "cpplib/util/template.hpp" #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx2") #include using namespace std; struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout< vec; typedef vector> mat; typedef vector>> mat3; typedef vector svec; typedef vector> smat; templateusing V=vector; templateusing VV=V>; templateinline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<inline void output2(T t){for(auto i:t)output(i);} templateinline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<inline void debug2(T t){for(auto i:t)output(i);} #define loop(n) for(long long _=0;_<(long long)(n);++_) #define rep(i,...) for(auto i:range(__VA_ARGS__)) #define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__))) #define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i) #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i) #define irep(i) for(lint i=0;;++i) inline vector range(long long n){if(n<=0)return vector();vectorv(n);iota(v.begin(),v.end(),0LL);return v;} inline vector range(long long a,long long b){if(b<=a)return vector();vectorv(b-a);iota(v.begin(),v.end(),a);return v;} inline vector range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector();vectorv((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;} templateinline T reversed(T v){reverse(v.begin(),v.end());return v;} #define all(n) begin(n),end(n) templatebool chmin(T& s,const E& t){bool res=s>t;s=min(s,t);return res;} templatebool chmax(T& s,const E& t){bool res=s(s,t);return res;} const vector dx={1,0,-1,0,1,1,-1,-1}; const vector dy={0,1,0,-1,1,-1,1,-1}; #define SUM(v) accumulate(all(v),0LL) templateauto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector(arg,x);else return vector(arg,make_vector(x,args...));} #define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__})) vector> __MAKE_MAT__(vector v){if(v.empty())return vector>(1,vector());long long n=v.back();v.pop_back();vector> ret;vector> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i>; templateusing graph_w=vector>>; templateostream& operator<<(ostream& out,pairv){out<<"("< p; std::vector prime_list(int n) { p.set(); p[0]=0; for(int i=2;i*i<=n;++i){ if(!p[i])continue; for(int j=2*i;j<=n;j+=i)p[j]=0; } std::vectorlist; for(int i=2;i<=n;++i)if(p[i])list.push_back(i); return list; } #line 2 "cpplib/math/is_prime.hpp" #include /** * @brief 素数判定(高速) */ bool is_prime(long long n){ if(n<=1)return 0; if(n==2)return 1; if(n%2==0)return 0; long long s=0,d=n-1; while(d%2)d/=2,s++; auto mod_pow=[](__int128_t a,__int128_t b,__int128_t n){ long long res=1; while(b){ if(b%2)res=res*a%n; a=a*a%n; b/=2; } return (long long)(res); }; for(long long e:{2,3,5,7,11,13,17,19,23,29,31,37}){ if(n<=e)break; if(mod_pow(e,d,n)==1)continue; bool b=1; for(int i=0;i>n; auto v=prime_list(20000001); vector>m(100000); mapmemo; auto dfs=[&](auto dfs,lint i,lint n)->lint{ if(n==0)return 0; if(m[i].count(n))return m[i][n]; if(n<=(v[i]-1)*(v[i]-1)){ lint res=n; lint l=v[i]-1,r=0; while(l<=n){ r=n/(n/l)+1; if(v[i]<=r&&(r<20000001?p[r]:is_prime(r))){ res++; } l=r; } m[i][n]=res; return res; } lint res=0; if(n/(v[i]-1)==n/v[i])res=dfs(dfs,i+1,n); else res=dfs(dfs,i+1,n)+dfs(dfs,i+1,n/(v[i]-1))-dfs(dfs,i+1,n/v[i]); m[i][n]=res; return res; }; cout<