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;
  vector<bool> ip(N+1,true);
  long long ans=1;
  for (int i=2;i<N+1;i++){
    if (ip[i]){
      int count=1;
      int n=N;
      while (n>0){
        n=n/i;
        count+=n;
      }
      ans=ans*count%1000000007;
      for (int j=i;j<N+1;j+=i){
        ip[j]=false;
      }
    }
  }
  cout << ans << endl;
}