#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <unordered_map>
using namespace std;
typedef long long LL;
const int mod = 1e9 + 7;
int main()
{
    int n,x;
    cin >> n;
    LL res = 1;
    unordered_map<int,int> mp;
    while(n --)
    {
        cin >> x;
        for(int i = 2;i <= x / i;i++)
        {
            while(x % i == 0)
            {
                x /= i;
                mp[i] ++;
            }
        }
        if(x > 1) mp[x]++;
    }
    for(auto i : mp) res = res * (i.second + 1) % mod;
    cout << res << endl;
    return 0;
}