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

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

            var PrimeFactor = new List<long>();

            // 素因数分解する
            long sqrtN = (long)Math.Sqrt(N);
            long tmp = N;
            for(long i = 2; i <= sqrtN; i++)
            {
                if (tmp % i == 0)
                {
                    PrimeFactor.Add(i);
                    tmp = tmp / i;
                    i--;
                }
            }
            if (tmp > 1) PrimeFactor.Add(tmp);

            // 各素数が何個ずつあるか調べる(個数のみが重要)
            List<int> PrimeFactorCounts = new List<int>();
            long before = 0;
            int count = 0;
            foreach(var data in PrimeFactor)
            {
                if (before == 0)
                {
                    before = data;
                    count = 1;
                }
                else if (before == data)
                {
                    count++;
                }
                else
                {
                    before = data;
                    PrimeFactorCounts.Add(count);
                    count = 1;
                }
            }
            if (count > 0)PrimeFactorCounts.Add(count);
            // 素数の個数について、1,2,3,4,…と削りながらカウントする
            int ret = 0;
            foreach (var data in PrimeFactorCounts)
            {
                int next = 0;
                for (int i = data; i > next; i -= next)
                {
                    ret++;
                    next++;
                }
            }
            Console.WriteLine(ret);
        }
    }
}