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) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		List<Long> list = insu(n);
		Map<Long, Integer> map = new HashMap<>();
		for (Long key : list) {
    		Integer i = map.get(key);
    		map.put(key, i == null ? 1 : i + 1);
		}
		int ans = 0;
		for (Integer v: map.values()) {
			int hituyou = 1;
			int nokori = v;
			while(nokori >= hituyou){
				ans++;
				nokori -= hituyou;
				hituyou++;
			}
		}
		System.out.println(ans);
	}
	public static List<Long> insu(long n){
		List<Long> list = new ArrayList<>();
		if(n==1) return list;
		for(int i=2; i<=Math.sqrt(n); i++){
			if(n%i == 0){
				list.add((long)i);
				n = n/i;
				i = 1;
			}
		}
		list.add(n);
		return list;
	}
}
