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(){
  int n;cin>>n;
  long int ans=1;
  map<int,int>prime;
  for(int i=2;i<=n;i++){
    int a=i;
    for(int j=2;j<=i;j++){
      for(;;){
        if(a%j==0){
          prime[j]++;
          a/=j;
        }
        else 
          break;
      }
    }
  }
  map<int,int>::iterator i=prime.begin();
  while(i!=prime.end()){
    ans*=i->second+1;
    ans%=1000000007;
    i++;
  }
  cout<<ans<<endl;
}
        