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;
using Int = long long;
signed main(){
  const Int MOD = 1e9+7;
  Int n;
  cin>>n;
  vector<Int> cnt(n+1);
  for(Int i=1;i<=n;i++){
    Int b=i;
    for(Int j=2;j<=n;j++)
      while(b%j==0) b/=j,cnt[j]++;
  }
  Int ans=1;
  for(Int i=2;i<=n;i++) ans=ans*(cnt[i]+1)%MOD;
  cout<<ans<<endl;
  return 0;
}
