#include<iostream>
#include<algorithm>
#include<unordered_map>

using namespace std;

unordered_map<int,int> hsh;

int n,a;

int main()
{
    cin>>n;
    while(n--)
    {
        cin>>a;
        for(int i=2;i<=a/i;i++)
        {
            if(a%i==0)
            {
                int s=0;
                while(a%i==0)
                {
                    s++;
                    a/=i;
                }
                hsh[i]=hsh[i]+s;
            }
        }
        if(a>1) hsh[a]=hsh[a]+1;
    }
    long long ans=1,mod=1e9+7;
    for(auto x:hsh) ans=(ans*(x.second+1))%mod;
    cout<<ans<<endl;
}