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 INF=1e9+7;
int main(){
  int M;cin>>M;
  vector<int>A(M+1,1);
  for(int i=1;i<=M;i++){
    int s=i;
    for(int j=2;j<=M;j++){
      while(s%j==0){
        A[j]++;
        s/=j;
      }
    }
  }
  long long ans=1;
  for(int i=1;i<=M;i++){
    ans*=A[i];
    ans%=INF;
  }
  cout<<ans<<endl;
}