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, num;
  cin >> N;
  bool prime;
  long ans = 1;

  for(int i=2; i<=N; i++){
    prime = true;
    for(int j=2; j<i; j++){
      if(i%j==0){
        prime = false;
        break;
      }
    }
    if(prime){
      num = 0;
      for(int k=1; k<10; k++) num += N/pow(i,k);
      ans *= num+1;
      ans %= 1000000007;
    }
  }

  cout << ans << endl;

  return 0;
}
