约数个数

#include<iostream>
#include<algorithm>
#include<unordered_map>
using namespace std;
typedef long long LL;
const int N=1e9+7;
unordered_map<int,int>primes;
int n;

int main(void){
    cin>>n;
    for(int i=0,a;i<n;i++){
        cin>>a;
        for(int i=2;i<=a/i;i++)
            while(a%i==0){
                a/=i;
                primes[i]++;
            }
        if(a>1)primes[a]++;
    }
    LL res=1;
    for(auto x:primes)res=res*(x.second+1)%N;
    cout<<res%N<<endl;
    return 0;
}