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: Time Limit Exceeded)

import java.util.Scanner;

class Main {
	
	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		long N = stdIn.nextLong();
		int count = 0;
		int z = 0;
		int p = 0;
		int sousa = 0;
		int muri=0;
		
		for(int i=1; i<=N; i++) {
			if(N % i == 0) {
				muri++;
			}
		}
		if(muri == 2) {
			System.out.println(muri - 2);
			System.exit(0);
		}
		
		for(int i=1; i<=N; i++) {
			count = 0;
			
			for(int j=1; j<=i; j++) {
				if(i%j == 0) {
					count++;
				}
			}
	
			if(i == 1) {
				count = 1;
			}
			
			if(count == 2) {
				p = i;
				for(int e=1; Math.pow(p,e) <= N; e++) {
					z = (int)Math.pow(p, e);
					if(N%z == 0) {
						N /= z;
						sousa++;
					}
				}
			}
		}
		
		System.out.println(sousa);
	}
}