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>

int main(void){
  int n, a[1010];
  long long ans=1;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    a[i] = i + 1;
  }
  for (int i = 2; i <= n; i++) {
    int cnt = 0;
    for (int j = 0; j < n; j++) {
      while (a[j]%i==0) {
        cnt++;
        a[j]/=i;
      }
    }
    ans = ans*(cnt + 1) % (1000000000 + 7);
  }
  printf("%lld", ans);

  return 0;
}
