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.Scanner;

public class Main {
        public static void main(String[] args) {
                Scanner scan = new Scanner(System.in);

                long N = scan.nextLong();
                long rootN = (long)Math.sqrt(N);
                int count = 0;
                int pcount;
                int ncount;
                
                for (long i = 2; i < rootN; i++) {
                	
                	pcount = 0;
                	
                	while (N%i == 0) {
                		pcount++;
                		N /= i;
                	}
                	
                	ncount = 1;
                	
                	while (pcount - ncount >= 0) {
                		pcount -= ncount;
                		count++;
                		ncount++;
                	}
                	
                }
                
                if (N != 1) {
                	count++;
                }
                
                System.out.println(count);
                
        }
}