Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

24

Sample Output 1

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=12.)

Choose z=3 (=3^1). (Now we have N=4.)

Choose z=4 (=2^2). (Now we have N=1.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=32.)

Choose z=4 (=2^2). (Now we have N=8.)

Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

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);
        int n = sc.nextInt();
        Map<Integer, Integer> primeList = primeFactorizationAsMap(n);
        if (primeList.size() == 0) {
            System.out.println(0);
        } else {
            int result = primeList.values().stream()
                    .mapToInt(v -> {
                        int count = 0;
                        while (v > 0) {
                            v = v - count - 1;
                            if (v >= 0) {
                                count++;
                            }
                        }
                        return count;
                    })
                    .sum();
            System.out.println(result);
        }
    }

    private static Map<Integer, Integer> primeFactorizationAsMap(int num) {
        if (num < 2) {
            return new HashMap<>();
        } else {
            Map<Integer, Integer> result = new HashMap<>();
            int temp = num;
            double sqrt = Math.sqrt(num);
            for (int i = 2; i <= sqrt; i++) {
                int count = 0;
                while (temp % i == 0) {
                    count++;
                    temp = temp / i;
                }
                if (count != 0) {
                    result.put(i, count);
                }
            }
            if (result.size() == 0) {
                result.put(num, 1);
            }
            return result;
        }
    }
}