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 <iostream>
#include <cstring>
using namespace std;

int main() {
  int N;
  cin >> N;
  int a[N+1];
  memset(a,0,sizeof(a));
  for (int j=1; j<=N; j++) {
    int k=j;
    for (int i=2; k>1; ) {
      if (k%i==0) {
        k/=i;
        a[i]++;
      } else {
        i++;
      }
    }
  }
  const int mod=1e9+7;
  long long int ans=1;
  for (int i=2; i<=N; i++) {
    ans=ans*(a[i]+1)%mod;
  }
  cout << ans << endl;
  return 0;
}

