#include <bits/stdc++.h>
using namespace std;
typedef int ll;
inline ll read()
{ll s=0; bool f=0; char ch=' ';while(!isdigit(ch))    {f|=(ch=='-'); ch=getchar();}while(isdigit(ch)) {s=(s<<3)+(s<<1)+(ch^48); ch=getchar();}return (f)?(-s):(s);
}
#define R(x) x=read()
inline void write(ll x)
{if(x<0) {putchar('-'); x=-x;}if(x<10) {putchar(x+'0'); return;}write(x/10); putchar((x%10)+'0');
}
#define W(x) write(x),putchar(' ')
#define Wl(x) write(x),putchar('\n')
const int Mod=1000000007;
int n;
map<int,int>Map;
int num[1000005],cnt[1000005];
int fac[15505],invf[15505];
inline int ksm(int x,int y)
{int ans=1;while(y){if(y&1) ans=1LL*ans*x%Mod;x=1LL*x*x%Mod;y>>=1;}return ans;
}
inline int C(int n,int m)
{int oo;oo=1LL*fac[n]*invf[m]%Mod*invf[n-m]%Mod;return oo;
}
int main()
{freopen("codeforces396A_data.in","r",stdin);int i,j,k,x;R(n);fac[0]=invf[0]=1;for(i=1;i<=15500;i++) fac[i]=1LL*fac[i-1]*i%Mod;invf[15500]=ksm(fac[15500],Mod-2);for(i=15499;i>=1;i--) invf[i]=1LL*invf[i+1]*(i+1)%Mod;for(i=1;i<=n;i++){R(x);for(j=2;j<=sqrt(x);j++) if(x%j==0){int oo=0;while(x%j==0) {x/=j; oo++;}if(!Map[j]){Map[j]=++(*num); num[*num]=j; cnt[*num]=oo;}else cnt[Map[j]]+=oo;}if(x>1){if(!Map[x]){Map[x]=++(*num); num[*num]=x; cnt[*num]=1;}else cnt[Map[x]]++;}}int ans=1;for(i=1;i<=*num;i++){ans=1LL*ans*C(cnt[i]+n-1,n-1)%Mod;}Wl(ans);return 0;
}