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.util.ArrayList;
import java.util.Scanner;
public class Main{
	static int counter=0;
	static void culsosu(int num) { //ある因数の数を受け取って割れる最大数をcounterに足す関数
		for(int k=1; num>0; k++) {
			counter++;
			num = num-k-1;
			
		}		
	}
	
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		long N = s.nextLong();
		ArrayList sosus = new ArrayList();

		for(long i=2; i*i<=N; i++) {
			while(N%i == 0 ) {
				sosus.add(i);
				N = N/i;
			}
		}
		if(N != 1) {
			sosus.add(N);
		}
		/*for(int i=0; i<sosus.size(); i++) {
			System.out.print(sosus.get(i));		
		}
		System.out.println(); */
		
	
		
		int num=1;
		for(int i=0; i<sosus.size()-1; i++) {
			
			if(sosus.get(i) == sosus.get(i+1)) {
				num++;
				if(i== sosus.size()-2) {
					culsosu(num);
					num=1;
				}
			}
			else {
				culsosu(num);
				num=1;
				if(i== sosus.size()-2) {counter++;}
				}
			    
		
			
		}
		if(sosus.size() ==1) {
			counter++;
		}

		/*for(int i=0; i<sosus.size(); i++) {
			System.out.print(sosus.get(i));
		} */


		System.out.println(counter);

	}

}