#include<iostream>
#include<cstdio>
#include<map>
using namespace std;
map<int,int> prime;
long long res=1;
const int Inf=1e9+7;
int main()
{
    int n,x;
    cin>>n;
    while(n--)
    {
        cin>>x;
        for(int i=2;i<=x/i;i++)
            while(x%i==0) prime[i]++,x=x/i;
        if(x>1) prime[x]++;
    }
    for(map<int,int>::iterator it=prime.begin();it!=prime.end();it++)
        res=res*(it->second+1)%Inf;
    cout<<res;
    return 0;
}