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 main(void){
  int N,n;
  cin>>N;
  int a[N+5];
  for(int i=0;i<=N;i++){
    a[i]=1;
  }
  for(int i=1;i<=N;i++){
    n=i;
    for(int j=2;j<=N;j++){
      while(n%j==0){
        if(n%j==0){
          a[j]+=1;
          n=n/j;
        }
      }
    }        
  }
  long long int ans=1;
  for(int i=1;i<=N;i++){
    ans*=a[i];
    ans=ans%1000000007;
  }
  cout<<ans<<endl;
  return 0;
}