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;
class DivGame
    {
        static void Main(string[] args)
        {
            ulong n = ulong.Parse(Console.ReadLine());
            ulong i = 2;
            ulong div = n;
            var PrimeList = new List<ulong>();

            while(i*i <= n)
            {
                if (div % i == 0)
                {
                    div /= i;
                    PrimeList.Add(i);

                }
                else
                {
                    i++;
                }
            }
            if (div != 1) PrimeList.Add(div);

            var PrimeListCount = new List<int>();
            ulong before = 0;
            int count = 0;

            foreach(var data in PrimeList)
            {
                if(before == 0)
                {
                    before = data;
                    count=1;
                }
                else if(before == data)
                {
                    count++;
                }
                else
                {
                    before = data;
                    PrimeListCount.Add(count);
                    count = 1;
                }
            }
            if (count > 0)
            {
                PrimeListCount.Add(count);
            }

            int x = 0;
            foreach(var data in PrimeListCount)
            {
                int next = 0;
                for(int j = data;j>next;j -= next)
                {
                    x++;
                    next++;
                }
            }
            Console.WriteLine(x);
        }

    }