#include<iostream>
#include<algorithm>
#include<unordered_map>
#include<vector>
using namespace std;
const int N=110,mod=1e9+7;
int main()
{
    int n,m,i;
    long long ans=1;
    scanf("%d",&n);
    unordered_map<int,int>prime;
    while(n--)
    {
        scanf("%d",&m);
        for(i=2;i<=m/i;i++)while(m%i==0)m/=i,prime[i]++;
        if(m>1)prime[m]++;
    }
    for(auto p:prime)ans=ans*(p.second+1)%mod;
    printf("%d\n",ans);
    return 0;
}