约数之和

#include <iostream>
#include <unordered_map>
using namespace std;
const int mod = 1e9 + 7;
unordered_map<int,int> primes;

void divide(int n){

    for(int i = 2; i <= n / i; i ++){
        if(n % i == 0){
            while(n % i == 0){
                n /= i;
                primes[i] ++;
            }
        }
    }
    if(n > 1) primes[n] ++;
}

int main(){
    int n;
    cin >> n;
    while(n--){
        int x;
        cin >> x;
        divide(x);
    }
    long long res = 1;
    for(unordered_map<int,int>::iterator it = primes.begin(); it != primes.end(); it ++){
        int p = it -> first,b = it -> second;
        long long t = 1;
        while(b--){
            t = (t * p + 1) % mod;
        }
        res = res * t % mod;
    }
    cout << res << endl;
    return 0;
}