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<stdio.h>
#include<string.h>
int mod=1e9+7;
int main()
{
	int n,i,x,j;
	int a[10005];
	scanf("%d",&n);
	memset(a,0,sizeof(a));
	for(i=2;i<=n;i++)
	{
		x=i;
		for(j=2;j<=x;j++)
		{
			while(x%j==0)
			{
				a[j]++;
				x/=j;
			}
		}
		if(x!=1) a[x]++;
	}
	long long sum;
	sum=1;
	for(i=1;i<=n;i++)
	{
		if(a[i]!=0)
		  sum=(sum*(a[i]+1))%mod;
	}
	printf("%lld\n",sum);
	return 0;
 } 
 
 