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.Scanner;


	public class Main {
		
		

		public static void main(String[] args) {

			Scanner sc = new Scanner(System.in);
	        
			long n = sc.nextLong();
			long m = n;
			long ans = 0;
			long p = 2;
			long c = 1;
			long div;
			
			while(true) {
				div = (long)Math.pow(p, c);
				
				if(n%div == 0) {
					ans++;
					n /= div;
					c++;
					continue;
				}
				
				while(n%p == 0) {
					n /=p;
				}
				
				p++;
				c = 1;
				
				if(p*p>n) {
					break;
				}
			}
			
			if(n!=1) {
				
				ans++;
			}
			
		    System.out.println(ans);
		}
	}