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: Wrong Answer)

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

namespace contest_Csharp
{
    class Program
    {
        

        static void Main(string[] args)
        {
            checked
            {
                var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
                //Console.ReadLine();
                var vals = Console.ReadLine().Split(' ')
                    .Select(x => long.Parse(x)).ToList();
                long N = vals[0];

                List<(long p, long index)> factring = new List<(long p, long index)>();
                long tmp = N;
                for (long i = 2; i * i <= N; i++)
                {
                    long dex = 0;
                    while (tmp % i == 0)
                    {
                        tmp = tmp / i;
                        dex++;
                    }
                    if (dex != 0)
                    {
                        factring.Add((i, dex));
                    }
                }
                if (!factring.Any() && N != 1)
                {
                    factring.Add((N, 1));
                }
                long ans = 0;
                foreach (var f in factring)
                {
                    long usd = 0;
                    for (long i = 0; usd + i + 1 <= f.index; i++)
                    {
                        usd += i + 1;
                        ans++;
                    }
                }



                Console.WriteLine(ans);
                Console.Out.Flush();
            }
        }



    }

}