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<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
const int MOD=1e9+7;
  long long ans=1,n,cnt[1005];
int main() {
  int i,j,k;
  cin >> n;
  for(i=2; i<=n; i++) {
    for(j=i,k=2; j>1;) {
      if(j%k==0) {
        j/=k,cnt[k]++;
      }
      else {
        k++;
      }
    }
  }
  for(i=2; i<=n; i++) {
    ans=ans*(cnt[i]+1)%MOD;
  }
  cout << ans << endl;
}
