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>
using namespace std;
int main(){
  int n,b;
  long ans=1,a[1001];
  for(int i=0;i<=1000;i++)
    a[i]=1;
  scanf("%d",&n);
  for(int i=1;i<=n;i++){
    b=i;
    for(int j=2;j<=n;j++){
      while(b%j==0){
        a[j]++;
        b/=j;
      }
      if(b==1)
        break;
    }
  }
  for(int i=2;i<=n;i++){
    ans*=a[i];
    ans%=1000000007;
  }
  printf("%ld\n",ans);
}