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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

public class Program
{

    static void Main()
    {
        var n = long.Parse(Console.ReadLine());

        var result = FactorizeIntoPrimeFactor(n);
        var answer = result.Factors.Select(f => f.Degree)
                                  .Sum(d =>
                                  {
                                      var i = 1;
                                      while (d >= i)
                                      {
                                          d -= i;
                                          i++;
                                      }
                                      return i - 1;
                                  });


        Console.WriteLine(answer);
        
    }

    static PrimeFactorizationResult FactorizeIntoPrimeFactor(long n)
    {
        var result = new PrimeFactorizationResult();

        if(n == 1)
        {
            return result;
        }

        var i = 2L;
        while ((i * i) < n + 1)
        {
            if (n % i == 0)
            {
                result.Add(i);
                n /= i;
                i = 2;
            }
            else
            {
                i++;
            }
        }
        result.Add(n);

        return result;
    }

    class Factor
    {
        public long PrimeNumber { get; set; }
        public long Degree { get; set; }

    }

    class PrimeFactorizationResult
    {
        public List<Factor> Factors { get; set; } = new List<Factor>();

        public void Add(long primeNumber)
        {
            var factor = Factors.FirstOrDefault(f => f.PrimeNumber == primeNumber);
            if(factor == null)
            {
                factor = new Factor { PrimeNumber = primeNumber, Degree = 1 };
                Factors.Add(factor);
            }
            else
            {
                factor.Degree++;
            }
        }
    }
}