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 long n,ans=1,tmp,mod=1e9+7;
  cin >> n;
  map<long long,long long> mp;
  for(int i=1;i<=n;i++){
    tmp=i;
    for(int j=2;j<=i;j++){
      while(tmp%j==0){
        mp[j]++;
        tmp/=j;
      }
    }
  }
  for(int i=2;i<=n;i++){
    ans*=mp[i]+1;
    ans%=mod;
  }
  cout << ans << endl;
  return 0;
}
