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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        sc.close();

        Map<Long, Integer> map = bunkai(n);
        int ans = 0;
        for (int v : map.values()) {
        	int sum = 0;
        	for (int i = 1; i < 50; i++) {
				sum += i;
				if (sum > v) {
					break;
				}
				ans++;
			}
        }
        System.out.println(ans);
    }

	static Map<Long, Integer> bunkai(long n) {
		Map<Long, Integer> soinsu = new HashMap<>();
		int end = (int) Math.sqrt(n);
		long d = 2;
		while (n > 1) {
			if (n % d == 0) {
				n /= d;
				if (soinsu.containsKey(d)) {
					soinsu.put(d, soinsu.get(d) + 1);
				} else {
					soinsu.put(d, 1);
				}
				end = (int) Math.sqrt(n);
			} else {
				if (d > end) {
					d = n - 1;
				}
				d++;
			}
		}
		return soinsu;
	}
}