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.util.*;

public class Main {

    public static void main(String[] args) {
        // write your code here
        Scanner sc = new Scanner(System.in);

        long x = sc.nextLong();
        PriorityQueue<Long> queue = new PriorityQueue<>();
        parent : for (int i = 2; i <= Math.sqrt(x); i++) {
            for (int j = 2; j < Math.sqrt(i); j++) {
                if (i % j == 0) {
                    continue parent;
                }
            }
            if (queue.contains((long)i)) {
                continue;
            }
            if (x % i == 0) { // 最小の因数を求める
                int v = i;
                while (x % v == 0) {
                    x /= v;
                    queue.add((long)v);
                    v *= i;
                }
                while (x % i == 0) {
                    x /= i;
                }
            }
        }
        if (x > 1 && !queue.contains(x)) {
            boolean isOK = true;
            for (int j = 2; j < Math.sqrt(x); j++) {
                if (x % j == 0) {
                    isOK = false;
                    break;
                }
            }
            if (isOK) {
                queue.add(x);
            }
        }

        System.out.println(queue.size());
    }
}