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.lang.*; 


public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
                int cnt = 0;
                
                long N = scan.nextLong();
                if(N==1){
                   System.out.println(0);
                   System.exit(0);
               }
                
                ArrayList<Integer> a = new ArrayList<>();
                ArrayList<Integer> b = new ArrayList<>();
                
                a.add(2);
                b.add(2);
                a.add(3);
                b.add(3);
                
               for(int n=5; n<=1000000; n+=2){
                   boolean aru = false;
                   for(int i=0;a.get(i)*a.get(i)<=n; i++){
                       if(n % a.get(i)==0){
                           aru = true;
                           break;
                       }
                   }
                   if(aru==false){
                       a.add(n);
                       b.add(n);
                   }         
               }
               boolean OK = true;
               while(OK == true){
                    OK = false;
                    for(int i=0; i<a.size();i++){
                        if(N%a.get(i)==0){
                            N=N/a.get(i);
                            a.set(i,a.get(i) * b.get(i));
                            cnt++;
                            OK = true;
                            break;
                        }                        
                    }
               }
               if(N>1000000){
                   System.out.println(cnt+1);
               }else{
               System.out.println(cnt);
               }
        }
}