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.Collections.Generic;
using System.Text;

namespace TaskD
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = ConsoleReader.Read<long>();
            var powers = new Dictionary<long, int>();
            var div = 2;
            while (Math.Sqrt(n) >= div)
            {
                if (n % div == 0)
                {
                    if (powers.ContainsKey(div))
                        powers[div] = powers[div] + 1;
                    else
                        powers[div] = 1;
                    n /= div;
                } else
                {
                    div++;
                }
            }

            if (n > 1)
            {
                if (powers.ContainsKey(n))
                    powers[n] = powers[n] + 1;
                else
                    powers[n] = 1;
            }

            var res = 0;
            foreach(var power in powers)
            {
                var exp = power.Value;
                var step = 1;
                while (exp >= step)
                {
                    res++;
                    exp -= step;
                    step++;
                }
            }

            Console.WriteLine(res);
        }
    }
}

public static class ConsoleReader
{
    public static T Read<T>()
    {
        var inputBuffer = new StringBuilder();
        int currChar;

        while ((currChar = Console.Read()) != -1)
        {
            if (!char.IsWhiteSpace((char)currChar))
            {
                inputBuffer.Append((char)currChar);
            }
            else if (inputBuffer.Length != 0)
            {
                break;
            }
        }

        return (T)Convert.ChangeType(inputBuffer.ToString(), typeof(T));
    }

    public static T[] ReadArray<T>(int count)
    {
        if (count < 0)
        {
            throw new ArgumentOutOfRangeException(nameof(count), $"'{nameof(count)}' must be >= 0");
        }

        var result = new T[count];

        for (var i = 0; i < count; i++)
        {
            result[i] = Read<T>();
        }

        return result;
    }
}