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() {
  long N;
  cin>>N;
  long ans=1,mod=1e9+7;
  vector<int> b(1001);
  for(int i=1;i<=N;i++){
    int tmp=i;
    for(int j=2;j<=1000;j++){
      int count=1;
      while(tmp%j==0){
        b[j]++;
        tmp /=j;
      }
    }
  }
  for(int i=2;i<1001;i++){
      ans*=b[i]+1;
      ans%=mod;
  }

  cout<<ans<<endl;
  }
