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;
#define int long long
signed main(){
  int n;
  cin>>n;
  int a[n];
  for(int i=0;i<n;i++) a[i]=i+1;
  int ans=1,MOD=1000000007LL;
  for(int i=2;i<1000;i++){
    int tmp=1;
    for(int j=0;j<n;j++){
      while(a[j]%i==0){
	a[j]/=i;
	tmp++;
      }
    }
    (ans*=tmp)%=MOD;
  }
  cout<<ans<<endl;
  return 0;
}
