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 javax.xml.stream.events.EntityReference;
import java.util.*;

class Main {
    final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Main().run();
    }

    private void run() {
        long n = sc.nextLong();
        Map<Long, Long> map = primeFactorization(n);

        int ans = 0;
        for (int i = 1; ; i++) {
            boolean isFound = false;
            for (Map.Entry<Long, Long> entry : map.entrySet()) {
                if (entry.getValue() >= i) {
                    ans++;
                    map.put(entry.getKey(), entry.getValue()-i);
                    isFound = true;
                }
            }
            if (!isFound) break;
        }
        System.out.println(ans);
    }

    static TreeMap<Long, Long> primeFactorization(long n) {

        TreeMap<Long, Long> map = new TreeMap<>();
        long sq = (long) Math.sqrt(n);

        //nが素数ならn^1の形で返す
        if (isPrime(n) == true) {
            map.put(n, 1L);
            return map;
        }

        for (int i = 2; i <= sq; i++) {
            //n<iなら明らかにnをiで除算できないので終了（ループを余計に回さない）
            if (n < i)
                break;

            //iが素数なら、nをiで何回除算できるか、その回数をmapに記録する
            if (isPrime(i) == true) {
                long count = 0;
                while (n % i == 0) {
                    n /= i;
                    count++;
                }
                if (count > 0) { //1回以上割れた場合のみ、mapに記録する
                    map.put((long)i, count);
                }
            }

        }

        //2～sqrt(n)で除算した結果、なお残った数をmapに追加する
        if (n != 1)
            map.put(n, 1L);

        return map;

    }

    //素数判定メソッド
    static boolean isPrime(long n) {
        if (n == 2)
            return true;
        if (n < 2 || n % 2 == 0)
            return false;
        int d = (int) Math.sqrt(n);
        for (int i = 3; i <= d; i += 2) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}

