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: Wrong Answer)

import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
import java.util.Scanner;

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

        long N = sc.nextLong();
        List<Integer> primeNumbers = new ArrayList<>();

        int devideNum = 2;
        while(N % devideNum == 0) {
            primeNumbers.add(devideNum);
            N /= 2;
        }

        devideNum++;
        while (N != 1) {
            if (N % devideNum == 0) {
                primeNumbers.add(devideNum);
                N /= devideNum;
            } else {
                devideNum +=2;
            }
        }

        //Debug
        for(int num: primeNumbers) {
            System.err.println(num);
        }

        Iterator<Integer> it = primeNumbers.iterator();
        int e = 1;
        int result = 0;
        int last = 0;

        main: for(int i=0; i<primeNumbers.size(); i++) {
            int current = primeNumbers.get(i);

            if(current == last) {
                e++;
            }else {
                e = 1;
            }

            for(int j=2; j<=e; j++) {
                if(i+j-1 >= primeNumbers.size()) {
                    continue main;
                }
                if(primeNumbers.get(i+j-1) != current) {
                    continue main;
                }
            }
            result++;
            last = current;
        }

        System.out.println(result);

    }
}