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 p[1010];//n!を素因数分解したときiはp[i]乗
void prime(int n){
  for(int i=2; i<=n; i++){
    while(n%i==0){
      n /= i;
      p[i]++;
    }
  }
}
int main(){
  int n;
  cin >> n;
  for(int i=0; i<1010; i++){
    p[i] = 0;
  }
  for(int i=2; i<=n; i++){
    prime(i);
  }
  long long int ans=1;
  for(int i=2; i<=n; i++){
    ans = (ans*(p[i]+1))%1000000007;
  }
  cout << ans << endl;
}