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 Microsoft.VisualBasic.CompilerServices;
using System;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel.DataAnnotations;
using System.Globalization;
using System.IO.Pipes;
using System.Linq;
using System.Text;
namespace AtC_169
{
    class Program
    {

        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            long rootN = (long)Math.Sqrt(N) + 1;

            long count = 0;
            for (long i = 2; i <= rootN; i++)
            {
                long tmp = 0;
                while (N % i == 0)
                {
                    N = N / i;
                    tmp++;
                   // Console.WriteLine($"{i} {N} {tmp}");
                }
                
                count += func(tmp);
            }
            if (N > 1) count++;
            Console.WriteLine(count);

        }
        static long func(long t)
        {
            long i = 1, ans = 0;
            while (t >= i)
            {
                t = t - i;
                i++;
                ans++;
            }
            return ans;
        }
    }

    
}