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(void){
  int n, a[1010], wa=1000000007;
  long long int ans=1;
  for(int i=0;i<1010;++i){
    a[i] = 0;
  }
  cin >> n;
  for(int i=2;i<=n;++i){
    int k=i;
    for(int j=2;j<=i;++j){
      while(k%j==0){
        ++a[j];
        k/=j;
      }
    }
  }
  for(int i=2;i<=n;++i){
    if(a[i]==0) continue;
    ans *= (a[i]+1);
    ans %= wa;
  }
  cout << ans << endl;
}