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;

namespace ConsoleApp1
{

    class Program
    {
        public static IEnumerable<long> PrimeFactors(long n)
        {
            long i = 2;
            long tmp = n;

            while (i * i <= n) //※1
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;//最後の素数も返す
        }

        static void Main(string[] args)
        {
            long n = long.Parse(Console.ReadLine());
            var factors = PrimeFactors(n);
            Dictionary<long, int> factordict = new Dictionary<long, int> { };

            foreach (long factor in factors)
            {
                if (factordict.ContainsKey(factor))
                    factordict[factor]++;
                else
                    factordict.Add(factor, 1);
            }

            int res = 0;

            foreach (var factor in factordict)
            {
                int cnt = factor.Value;
                int step = 1;
                while (cnt >= step)
                {
                    res++;
                    cnt -= step;
                    step++;
                }
            }

            Console.WriteLine(res);

        }

    }
}