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)

package abc169.d;

import java.util.Scanner;

public class Main
{
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long nn = n;
		sc.close();
		int ans = 0;
		boolean endflag = false;
		for (long l = 2;l*l<=nn; l++) {
			if (n == 1) {
				break;
			}
			long l2 = l;
			while (true) {
				if (n % l2 == 0) {
					ans +=1;
					n = n / l2;
					l2 = l2 * l;
				} else if (n % l ==0 || n < l) {
					endflag = true;
					break;
				} else {
					break;
				}
			}
			if (endflag) break;
		}
		if (n >1 && !endflag) ans++;
		System.out.println(ans);
	}
}