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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        // 整数の入力
        long num = sc.nextLong();
        if(num == 1){
            System.out.println(0);
            return;
        }

        Map<Long, Long> map = devide(num);

        int count = 0;
        // 素数ごとにカウントする
        for(Map.Entry<Long, Long> entry : map.entrySet()){
            // 指数を順に減らしていく
            long sisu = entry.getValue();
            for(long i=1; i <= sisu; i++){
                sisu -= i;
                count++;
            }
            // 余った分は最後に足すので関係なし
        }
        System.out.println(count);
    }

    static Map<Long, Long> devide(long num){
        long tmpnum = num;
        Map<Long, Long> map = new HashMap<>();
        for(long i=2; i*i < num; i++){
            // <2, count>, <3, count>...
            long count = 0;
            while(tmpnum % i == 0){
                tmpnum = tmpnum / i;
                count++;
            }
            if(count != 0){
                map.put(i, count);
            }
        }
        if(tmpnum != 1L){
            map.put(tmpnum, 1L);
        }
        return map;
    }
}