#include <bits/stdc++.h>
using namespace std;
int n,x;
map<int,int>m;
typedef long long ll;
const int MOD=1e9+7; 
ll ans=1;
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++){
		scanf("%d",&x);
		for (int j=2;j<=sqrt(x);j++){
			while (x%j==0){
				m[j]++;
				x/=j;
			}
		}
		if (x>1)m[x]++;
	}
	for (const auto&it:m)ans=ans*(it.second+1)%MOD;
	printf("%d",ans);
	return 0;
}