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

int a[1005];
const long long mod= 1e9 + 7;

int main()
{
	int n;
	
	long long res = 1;
	
	scanf("%d",&n);
	
	for (int i = 2;i <= n;i++)
	{
		int tmp = i;
		for (int j = 2;tmp != 1;j++)
		{
			if (tmp % j == 0)
			{
				a[j]++;
				tmp /= j;
				j--;
			}
		}
	}
	
	for (int i = 2;i <= n;i++)
	{
		if (a[i] != 0)
			res = ((res % mod) * ((a[i]+1) % mod)) % mod;
	}
	
	printf("%lld\n",res);
	
	return 0;
}
