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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace ProblemD
{
    class Program
    {
        static void Main()
        {
            long N = long.Parse(Console.ReadLine());
            var list = new List<long>();

            if (N == 1)
            {
                Console.WriteLine(0);
                return;
            }
            else
            {
                foreach (long factor in PrimeFactors(N))
                {
                    list.Add(factor);
                }
                var used = new List<long>();
                long count = 0;
                long number = 1;
                for (int i = 0; i < list.Count;)
                {
                    if (number == 1 || number % list[i - 1] == 0)
                    {
                        number *= list[i];
                    }
                    else
                    {
                        number = list[i];
                    }
                    if (used.Contains(number))
                    {
                        i++;
                    }
                    else
                    {
                        count++;
                        list.RemoveAt(i);
                        used.Add(number);
                        number = 1;
                    }
                }
                Console.WriteLine(count);
            }
            
        }

        public static IEnumerable<long> PrimeFactors(long n)
        {
            long i = 2;
            long tmp = n;

            while (i * i <= n) 
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;
        }
    }
}