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>
int main(void){
  int n,k,a[1001]={},t,i;
  long ans=1;
  scanf("%d",&n);
  for (i=2;i<=n;i++){
    t=2;
    k=i;
    while (k!=1){
      while (k%t==0){
        a[t]++;
        k/=t;
      }
      t++;
    }
  }
  for (i=2;i<=997;i++) ans=ans*(a[i]+1)%1000000007;
  printf("%ld\n",ans);
  return 0;
}