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;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;
using System.IO;

namespace paiza
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = GetLong();
            var ans = new long();

            if (N == 1)
            {
                ans = 0;
                Console.WriteLine(ans);

                return;
            }

            var para = PrimeFactors(N);
            while (para.Count() > 0)
            {
                var p = para.First();
                var count = para.Count(value => value == p);
                for (int i = 1; i <= count; i++)
                {
                    ans++;
                    count -= i;
                }
                while (para.Count()>0 && para.First() == p)
                {

                    para.Remove(p);
                }

            }

            Console.WriteLine(ans);

            return;
        }

        public static List<long> PrimeFactors(long n)
        {
            long i = 2;
            var tmp = n;
            var list = new List<long>();

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

    }
}

public static class MyIO
{
    private static string[] args = null;
    private static int num = -1;
    private static int used = -1;

    private static string getArg()
    {
        if (used == num)
        {
            args = Console.ReadLine().Split(' ');
            num = args.Length;
            used = 0;
        }
        return args[used++];
    }

    public static int GetInt() => int.Parse(getArg());
    public static long GetLong() => long.Parse(getArg());
    public static double GetDouble() => double.Parse(getArg());
    public static string GetString() => getArg();
    public static char GetChar() => getArg()[0];
    public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
    public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
    public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
    public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}