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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;

public class Main {
    static ArrayList<Integer> counter = new ArrayList<>();

    static {
        counter.add(1);
    }

    public static void main(String[] args) throws Exception {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        String line = bufferedReader.readLine();
        long N = Long.parseLong(line);
        int lim = (int) Math.sqrt(N) + 1;
        HashSet<Integer> pSet = new HashSet<>();
        int cnt = 0;
        for (int i = 2; i < lim; i++) {
            int tlim = (int) Math.sqrt(N) + 1;
            if (tlim < i) {
                break;
            }
            if (isP(i, pSet)) {
                Pair pair = div(N, i);
                if (pair.cnt != 0) {
                    cnt += count(pair.cnt);
                    N = pair.res;
                }
                pSet.add(i);
            }
        }
        if (N != 1) {
            cnt++;
        }
        System.out.println(cnt);
    }

    private static int count(int src) {
        int size = counter.size();
        for (int i = 0; i < size; i++) {
            int l = counter.get(i);
            if (src < l) {
                return i;
            }
        }
        int max = counter.get(size - 1);
        for (int i = size; ; i++) {
            max += i + 1;
            counter.add(max);
            if (src < max) {
                return i;
            }
        }
    }

    private static Pair div(long src, int p) {
        int cnt = 0;
        while (true) {
            if (src / p * p == src) {
                src = src / p;
                cnt++;
            } else {
                return new Pair(src, cnt);
            }
        }
    }

    private static boolean isP(int src, HashSet<Integer> pSet) {
        for (Integer p : pSet) {
            if (src / p * p == src) {
                return false;
            }
        }
        return true;
    }

    static class Pair {
        long res;
        int cnt;

        public Pair(long res, int cnt) {
            this.res = res;
            this.cnt = cnt;
        }
    }
}