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 1.8.0) (judge verdict: Runtime Error)



import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);

		long n = sc.nextLong();

		if(n == 1){
			System.out.println(0);
			return;
		}

		//nが素数かどうか判定
		boolean isPrime = true;
		for(int i = 2; i <= Math.sqrt(n); i++){
			if(n % i == 0){
				isPrime = false;
				break;
			}
		}

		if(isPrime){
			System.out.println(1);
			return;
		}

		PrimeNumberGenerator pg = new PrimeNumberGenerator();

		long result = 0;
		for(int i = 2; i <= n ; i++){
			if(!pg.isPrime(i)){
				continue;
			}

			long j = 1;
			while(n % Math.pow(i, j) == 0){
				n /= Math.pow(i, j);
				j++;
				result++;
			}
		}

		System.out.println(result);
	}
}

class PrimeNumberGenerator {
    private boolean[] isPrime= new boolean[100001];

    public PrimeNumberGenerator() {
        Arrays.fill(isPrime, true);

        isPrime[0] = false;
        isPrime[1] = false;
        isPrime[2] = true;

        int limit = (int)Math.sqrt(isPrime.length);
        for(int i = 3; i <= limit; i+=2){
            if(isPrime[i] == false){
                continue;
            }

            for(int j = i * 2; j <= isPrime.length - 1; j += i){
                isPrime[j] = false;
            }
        }
    }

    public boolean isPrime(int index){
        if(index % 2 == 0 && index != 2){
            return false;
        }
        return isPrime[index];
    }
}