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;
using System.Linq;

namespace AtCoder.Question
{
    public class QuestionD
    {
        public static void Main(string[] args)
        {
            var n = ReadValue<long>();
            var z = 2;
            var count = 0;

            while (n / 2 >= z)
            {
                if (n % z == 0)
                {
                    n /= z;
                    count++;
                }
                z++;
            }
            if (n > 1)
            {
                count++;
            }
            Console.WriteLine(count);
        }
        static T ReadValue<T>()
        {
            return (T)Convert.ChangeType(Console.ReadLine(), typeof(T));
        }
        static (T1, T2) ReadValue<T1, T2>()
        {
            var input = Console.ReadLine().Split(' ');
            return ((T1)Convert.ChangeType(input[0], typeof(T1)), (T2)Convert.ChangeType(input[1], typeof(T2)));
        }
        static (T1, T2, T3) ReadValue<T1, T2, T3>()
        {
            var input = Console.ReadLine().Split(' ');
            return ((T1)Convert.ChangeType(input[0], typeof(T1)), (T2)Convert.ChangeType(input[1], typeof(T2)), (T3)Convert.ChangeType(input[2], typeof(T3)));
        }
        static (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>()
        {
            var input = Console.ReadLine().Split(' ');
            return ((T1)Convert.ChangeType(input[0], typeof(T1)), (T2)Convert.ChangeType(input[1], typeof(T2)), (T3)Convert.ChangeType(input[2], typeof(T3)), (T4)Convert.ChangeType(input[3], typeof(T4)));
        }
        static T[] ReadValues<T>()
        {
            var input = Console.ReadLine().Split(' ');
            return input.Select(x => (T)Convert.ChangeType(x, typeof(T))).ToArray();
        }
    }
}