#include<iostream>
#include<cstring>
#include<unordered_map>
#include<algorithm>
using namespace std;
int n, x;
long long res = 1;
int mod = 1e9 + 7;

int main() {
    cin >> n;
    unordered_map<int, int> h;
    while (n -- ) {
        cin >> x;
        //求质因子的指数
        for (int i = 2; i <= x / i; i ++ ) {
            while (x % i == 0) {
                h[i] ++ ;
                x = x / i;
            }
        }
        if (x > 1) h[x] ++ ;
    }

    for (auto i = h.begin(); i != h.end(); i ++ ) {
        res = res * (i -> second + 1) % mod;
    }

    cout << res;

}