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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.At_Coder_Beginner_Contest_169
{
    class D
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());

            Console.WriteLine(Solve(N));
            //Console.ReadKey();
        }

        private static int Solve(long N)
        {
            // var sb = new StringBuilder();
            if (N == 1)
            {
                return 0;
            }

            var primeList = GeneratePrime((long)Math.Sqrt(N));
            int count = 0;
            for (int i = 0; i < primeList.Count; i++)
            {
                long p = primeList[i];
                int e = 1;
                while (true)
                {
                    long z = (long)Math.Pow(p, e);

                    if (N % z != 0)
                    {
                        if(N % p == 0)
                        {
                            N /= z;
                        }
                        break;
                    }

                    //sb.Append("p:").Append(p).Append(", e:").Append(e).Append(", z:").AppendLine(z.ToString());
                    count++;
                    e++;
                    N /= z;
                }

                if (N < p)
                {
                    break;
                }
            }

            if(IsPrime(N))
            {
                count++;
                //sb.AppendLine("last:" + N);
            }

            //Console.WriteLine(sb.ToString());

            return count;
        }

        public static bool IsPrime(long num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false;

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {
                    return false;
                }
            }

            return true;
        }

        public static List<long> GeneratePrime(long max)
        {
            long prime;
            double sqrtMax = Math.Sqrt(max);
            var primeList = new List<long>();

            var list = new List<long>();
            list.Add(2);
            for (int i = 3; i <= max; i += 2)
            {
                list.Add(i);
            }

            do
            {
                prime = list.First();
                primeList.Add(prime);
                list.RemoveAll(n => n % prime == 0);
            } while (prime < sqrtMax);

            primeList.AddRange(list);

            return primeList;
        }
    }
}