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.*;
import java.util.function.BiConsumer;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
		int ans = 0;

		for(int i=2; i <= Math.sqrt(N); i++) {
			int count = 0;
			while(N%i == 0) {
				N = N / i;
				count ++;
			}
			
			for(int j=1; count-j>=0; j++) {
				ans ++;
				count -= j;
			}
		}
		
		
		if(N > 1) {
			ans ++;
		}
		System.out.println(ans);

	}
}
