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 <cstdio>
#include <cstring> 
#define max(a,b) a>b?a:b
#define min(a,b) a>b?b:a
#define N 200006
int n,a[N];char s[N];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)a[i]=1;
	for(int i=1;i<=n;i++){
		int x=i;
		for(int j=2;j<=n;j++)if(x%j==0){
			while(x%j==0)x/=j,a[j]++;
		}
	}
	for(int i=2;i<=n;i++)a[i]=1LL*a[i]*a[i-1]%1000000007;
	printf("%d",a[n]);
}