P6274 [eJOI2017]六

#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define W while
#define I inline
#define RI register int
#define LL long long
#define Cn const
#define CI Cn int&
#define gc getchar
#define D isdigit(c=gc())
#define pc(c) putchar((c))
#define min(x,y) ((x)<(y)?(x):(y))
#define max(x,y) ((x)>(y)?(x):(y))
using namespace std;
namespace Debug{
    Tp I void _debug(Cn char* f,Ty t){cerr<<f<<'='<<t<<endl;}
    Ts I void _debug(Cn char* f,Ty x,Ar... y){W(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
    Tp ostream& operator<<(ostream& os,Cn vector<Ty>& V){os<<"[";for(Cn auto& vv:V) os<<vv<<",";os<<"]";return os;}
    #define gdb(...) _debug(#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
namespace FastIO{
    Tp I void read(Ty& x){char c;int f=1;x=0;W(!D) f=c^'-'?1:-1;W(x=(x<<3)+(x<<1)+(c&15),D);x*=f;}
    Ts I void read(Ty& x,Ar&... y){read(x),read(y...);}
    Tp I void write(Ty x){x<0&&(pc('-'),x=-x,0),x<10?(pc(x+'0'),0):(write(x/10),pc(x%10+'0'),0);}
    Tp I void writeln(Cn Ty& x){write(x),pc('\n');}
}using namespace FastIO;
Cn int M=7,X=1e9+7,N=1e7+10;
LL n,p[M];
int f[1<<M],c[M],cnt,g[N],Ans;
map<__int128,int> mp;
I int DFS(__int128 x){
    if(mp.count(x)) return mp[x];
    RI i,j,k,S=1,o;for(i=1;i<(1<<cnt);i++) if((k=(x>>(i<<1))&3)<2){
        __int128 t=x;for(j=0;j<(1<<cnt);j++) i&j&&(x>>(j<<1)&3)<2&&(x+=((__int128)1<<(j<<1)),0);
        if(!f[i]) for(f[i]=1,j=1;j<=cnt;j++) i>>j-1&1&&(f[i]=1LL*f[i]*c[j]%X);
        S=(1LL*DFS(x)*f[i]%X+S)%X,x=t;
    }return mp[x]=S;
}
int main(){
    LL i;for(read(n),i=2;i*i<=n;i++) if(!(n%i)){
        p[++cnt]=i;W(!(n%i)) n/=i,++c[cnt];
    }n>1&&(p[++cnt]=n,c[cnt]=1);
    return writeln(DFS(0)-1),0;
}