Given is a positive integer N. Consider repeatedly applying the operation below on N:

* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer;
* z divides N;
* z is different from all integers chosen in previous operations.
* Then, replace N with N/z.



Find the maximum number of times the operation can be applied.

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:


N


Output

Print the maximum number of times the operation can be applied.

Examples

Input

24


Output

3


Input

1


Output

0


Input

64


Output

3


Input

1000000007


Output

1


Input

997764507000


Output

7
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    long n = sc.nextLong();
    if (n == 1) {
      System.out.println(0);
      return;
    }
    TreeSet<Long> set = getSet();

    long result = 0;
    for (long i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        int count = 0;
        while (n % i == 0) {
          n /= i;
          count++;
        }
        result += set.headSet((long) count, true).size();
      }
    }
    System.out.println(n > 1 ? result + 1 : result);
  }

  static TreeSet<Long> getSet() {
    TreeSet<Long> r = new TreeSet<>();
    long sum = 0;
    for (int i = 1; sum < 40; i++) {
      sum += i;
      r.add(sum);
    }
    return r;
  }
}