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: Wrong Answer)

import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
//    printTestValue();
    // abc170_d();
    // abc169_b();
    // abc169_c();
     abc169_d();
  }

  // int 2147483648 [ 2 * 10(9)]
  // long 9223372036854775808 [ 9 * 10(18)]

  public static void abc169_d() {
    try (Scanner sc = new Scanner(System.in)) {

      long n = Long.parseLong(sc.next());
      long m = n;

      long num1 = 2L;
      long num2 = 1L;
      int count = 0;

      while (num1 * num1 <= m) {
        long num = (long) Math.pow(num1, num2);
        if (n % num != 0) {
          num1++;
          num2 = 1L;
          continue;
        }
        n /= num;
        count++;
        num2++;
      }

      if (n == m && n != 1) {
        count = 1;
      }
      System.out.println(count);
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }
}