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.math.BigDecimal;
import java.util.*;

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

        long n = scanner.nextLong();
        long count = 0;

        long v = getCommonDivisor(n, 2);
        if(v == 1){
            System.out.println(1);
            System.exit(0);
        }


        for(long i = 2 ; i <= n ; i++){
            long val = getCommonDivisor(n, i);
            if(val != i){
                continue;
            }
            n = n / val;
            count++;
        }
        System.out.println(count);
    }

    private static long getCommonDivisor(long x, long y) {
        long biggerNum = Math.max(x, y);
        long smallerNum = Math.min(x, y);

        long surplus = biggerNum % smallerNum;

        if (surplus == 0) {
            return smallerNum;
        }
        surplus = getCommonDivisor(smallerNum, surplus);

        return surplus;
    }
}