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

int main() {
    cin >> n;
    unordered_map<int, int> h;

    //算质因子及其指数
    while (n -- ) {
        cin >> x;
        for (int i = 2; i <= x / i; i ++ ) {
            while (x % i == 0) {
                h[i] ++ ;
                x /= i;
            }
        }
        if (x > 1) h[x] ++ ;
    }

    //算和
    for (auto p : h) {
        long long a = p.first, b = p.second;
        long long t = 1;
        while (b -- ) {
            t = (t * a + 1) % mod;
        }
        res = res * t % mod;
    }

    cout << res << endl;
}