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

int main()
{
    int n;
    cin>>n;
    unordered_map<int,int>res;
    while(n--)
    {
        int a;
        scanf("%d",&a);
        for(int i=2;i<=a/i;i++)
        {
            while(a%i==0)
            {
                a/=i;
                res[i]++;
            }
        }
        if(a>1)res[a]++;
    }
    LL ans=1;
    for(auto it:res)
    {
        ans=ans*(it.second+1)%MOD;
    }
    cout<<ans<<endl;
    return 0;
}