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)

package app;
import java.util.Map.Entry;
import java.util.*;
import java.math.*;
import org.w3c.dom.css.Counter;
  
public class Main{
    public static void main(final String[] args){
 
        final Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        int ans=0;
        long q =2;
        long keep =N;
 
        if(N==1){
            System.out.println(0);
            return;
        }
 
        while(q*q<=N){
            if(N%q ==0){
                //N = N/q;
                //ans ++;
                for(int i = 1; N>=Math.pow(q,i);i++){
                    if(N%Math.pow(q, i)==0){
                        ans++;
                        N = (long) (N / Math.pow(q, i));
                    }
                }
                while(N%q ==0){
                    N = N/q;
                }
            }   
            q++;
        }
        if(N != 1){ans++;}
       
            System.out.println(ans);
    }
}