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>
using namespace std;
int primary[1000];
int main(){
  int n;cin>>n;
  for(int j = n; 1 < j; j--){
    int nn = j;
    for(int i = 2; nn != 1; i++){
      if(nn % i == 0){
        primary[i]++;
        nn = nn / i;
        i--;
      }
    }
  }

  long long ans = 1;
  for(int i = 0; 1000 > i; i++){
    if(primary[i] == 0)continue;
    ans = ans*(primary[i]+1) % 1000000007;
  }
  cout << ans << endl;
}