Mathematical knowledge: finding the number of divisors

 

#include<iostream>
#include<algorithm>
#include<unordered_map> 
using namespace std;

typedef long long ll;
const int N=1e9+7;


int main()
{
	int n;
	cin>>n;
	unordered_map<int,int>zheng;
	while(n--)
	{
		int x;
		cin>>x;
		for(int i=2;i<=x/i;i++)
			while(x%i==0)
			{
				x/=i;
				zheng[i]++;
			}
		if(x>1)zheng[x]++;
	}
	ll ans=1;
	for(unordered_map<int,int>::iterator i=zheng.begin();i!=zheng.end();i++)
		ans=ans*(i->second+1)%N;
	
	cout<<ans<<endl;
	
	return 0;
}