nrdivprod

#include<bits/stdc++.h>
using namespace std;

ifstream in("nrdivprod.in");
ofstream out("nrdivprod.out");

vector<int> prime(1000001),v(80000),w={2};

int cautare(int x)
{
    int st=0,dr=w.size()-1,mij;
    while(st<=dr)
    {
        mij=(st+dr)/2;
        if(w[mij]==x)
            return mij;
        else
        if(w[mij]>x)
            dr=mij-1;
        else
            st=mij+1;
    }
    return 0;
}

void init()
{
    int i;
    prime[0]=prime[1]=1;
    for(i=3;i*i<=1000000;i+=2)
        if(prime[i]==0)
        {
            w.push_back(i);
            for(int j=i*i;j<=1000000;j+=2*i)
            prime[j]=1;
        }
    for(;i<=1000000;i+=2)
        if(prime[i]==0)
            w.push_back(i);
}

void fact(int x)
{
    int ap=0,ok=0;
    for(int i=0;i<w.size() && i*i<=x;i++)
    {
        ap=0;
        while(x%w[i]==0)
            x/=w[i],ap++;
        if(ap)
            v[i]+=ap;
    }
    if(x>1)
        v[cautare(x)]++;
}

int main()
{
    init();
    unsigned long long n,x,p=1;
    in>>n;
    for(int i=1;i<=n;i++)
    {
        in>>x;
        if(!prime[x] && (x%2 && x!=2))
            v[cautare(x)]++;
        else
            fact(x);
    }
    for(int i=0;i<v.size();i++)
        p*=(v[i]+1),p%=1000000007;
    out<<p;
}