You are given an integer N. Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

* 1≤N≤10^3

Input

The input is given from Standard Input in the following format:


N


Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
#include<iostream>
#include<algorithm>
#include<map>
typedef long long lint;
using namespace std;

int main()
{
	const int mod=1e9+7;
	int N;
	map<int,int> m;
	int tmp;
	lint ans=1;
	
	cin >> N;
	
	for(int i=2;i<=N;i++)
	{
		tmp=i;
		for(int j=2;j<=tmp;j++)
		{
			while(tmp%j==0)
			{
				tmp/=j;
				m[j]++;
			}
		}
	}
	
	for(auto&& i:m)
	{
		ans*=(i.second+1);
		ans%=mod;
	}
	
	cout << ans << endl;
	return 0;
}