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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DDivGame solver = new DDivGame();
        solver.solve(1, in, out);
        out.close();
    }

    static class DDivGame {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            long n = in.nextLong();
            ArrayList<Integer> pr = Prime.eratosthenesSieve(2000000);
            int res = 0;
            for (long prime : pr) {
                int cnt = 0;
                while (n % prime == 0) {
                    //if(cnt == 0) out.println(prime);
                    n /= prime;
                    cnt++;
                }

                //if (cnt > 0) out.println(cnt);
                int plus = cnt < 1 ? 0 :
                        cnt < 3 ? 1 :
                                cnt < 6 ? 2 :
                                        cnt < 10 ? 3 :
                                                cnt < 15 ? 4 :
                                                        cnt < 21 ? 5 :
                                                                cnt < 28 ? 6 :
                                                                        cnt < 36 ? 7 :
                                                                                cnt < 45 ? 8 :
                                                                                        cnt < 55 ? 9 : 10;
                //if(plus > 0) out.println("p:" + plus);
                res += plus;
            }
            if (n != 1) res++;
            out.println(res);
        }

    }

    static class Prime {
        public static ArrayList<Integer> eratosthenesSieve(int n) {
            // n 以下の素数を列挙する, O(N*log(log N))
            ArrayList<Integer> prime = new ArrayList<>();
            ArrayList<Integer> nums = new ArrayList<>();
            for (int i = 2; i <= n; i++) {
                nums.add(i);
            }
            while (nums.get(0) <= Math.sqrt(n)) {
                int nxtPrime = nums.get(0);
                prime.add(nxtPrime);
                nums.removeIf(x -> (x % nxtPrime == 0));
            }
            prime.addAll(nums);
            return prime;
        }

    }
}