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
int MOD=1e9+7,n,ans=1,v[1001];

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