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 <stdio.h>

int main(void) {
  long long i, j, n, ans = 1;
  bool p[1010];
  for(i = 0; i < 1010; ++i) p[i] = true;
  p[0] = p[1] = false;
  for(i = 2; i < 33; ++i) if(p[i]) for(j = i * 2; j < 1010; j += i) p[j] = false;
  scanf("%lld", &n);
  for(i = 2; i <= n; ++i) if(p[i]) {
    long long cnt = 0, tmp = n;
    while(tmp) cnt += tmp / i, tmp /= i;
    ans *= cnt + 1, ans %= 1000000007;
  }
  printf("%lld", ans); 
  return 0;
}