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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

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

class Program
{
    static void Main(string[] args)
    {
        var input = long.Parse(Console.ReadLine());

        var primeList = GetPrimeFactor(input);

        var ans = 0;

        foreach(var p in primeList)
        {
            var count = 1;
            var n = input;
            while (true)
            {
                if(n % Math.Pow(p, count) == 0)
                {
                    ans++;
                    n = n / (long)Math.Pow(p, count);
                    count++;
                }
                else
                {
                    break;
                }

            }
        }

        Console.WriteLine(ans);
        Console.Read();
    }

    public static List<long> GetPrimeFactor(long max)
    {
        var primeList = new List<long>();

        for (long i = 2; i * i <= max; i++)
        {
            while (max % i == 0)
            {
                primeList.Add(i);
                max /= i;
            }
        }
        if (max > 1)
        {
            primeList.Add(max);
        }
        return primeList.Distinct().ToList();
    }

}