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: Accepted)

import java.util.*;
import java.io.*;
 
public class Main{
    
	public static void main(String[] $){
		Scanner s = new Scanner(System.in);
		long N = s.nextLong();
		long N2 = N;
		int count = 0;
		int[] sosu = new int[1000000];
		int sosusount = 0;
		int i = 2;
		while(i <= 1000000){
			while(N%i == 0L){
				N = N/i;
				sosu[sosusount]++;
			}
			i++;
			sosusount++;
		}
		for(int j = 0; j < 1000000; j++){
			int aCount = 1;
			while(sosu[j] >= aCount){
				count++;
				sosu[j] = sosu[j] - aCount;
				aCount++;
			}
		}
		
		if(count == 0 && N == 1L){
			System.out.println(0);
		}else if(N != 1L){
			System.out.println(count+1);
		}else{
			System.out.println(count);
		}
		
	}
}