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: Runtime Error)

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

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 文字列の入力
            //string s = Console.ReadLine();

            // 整数の入力
            long n = long.Parse(Console.ReadLine());

            // 文字列配列の入力
            //string[] inputStrArray = Console.ReadLine().Split(' ');

            // 整数配列の入力
            //var inputlongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

            long N = n;
            long[] A = new long[N];
            var j = 0;

            for (long i = 2; i < n; i++)
            {
                while (N % i == 0)
                {
                    A[j] = i;
                    N = N / i;
                    j++;
                    //Console.Write("{0} ", i);
                    //Console.WriteLine();
                }
            }

            //for (long i = 0; i < n; i++)
            //{

            //  Console.Write("{0} ", A[i]);

            //}

            long cnt = 1;
            long cntB = 0;
            long cntC = 2;

            for(long i = 1; i < n; i++)
            {
                if (A[i] == 0) break;

                else if (A[i] != A[i - 1])
                {
                    cnt++;
                    cntB = 0;
                    cntC = 2;
                }

                else if (A[i] == A[i - 1])
                {
                    cntB++;
                    if (cntB >= cntC)
                    {
                        cnt++;
                        cntC++;
                        cntB = 0;
                    }

                }
            }

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


    }
}