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)

namespace test2
{
    using System;
    using System.Collections.Generic;

    internal class Program
    {
        private static bool IsPrime(long k)
        {
            for (var i = 2; i * i <= k; ++i)
            {
                if (k % i == 0)
                {
                    return false;
                }
            }

            return true;
        }

        private static long GetPowerOfPrime(long num, long power)
        {
            if (power == 0)
                return 1;

            if ((power & 1) == 1)
                return num * GetPowerOfPrime(num, power - 1);

            var b = GetPowerOfPrime(num, power / 2);
            return b * b;
        }

        static bool IsPowerOfPrime(long num)
        {
            var primes = new List<long>();

            for (long i = 2; i * i <= num; ++i)
            {
                if (IsPrime(i))
                    primes.Add(i);
            }

            for (var i = 0; i < primes.Count; ++i)
            {
                var k = 2;
                long res;
                while ((res = GetPowerOfPrime(primes[i], k)) <= num)
                {
                    primes.Add(res);
                    k++;
                }
            }

            return primes.Contains(num) || num == 2 || num == 3;
        }
        private static void Main()
        {
            var n = long.Parse(Console.ReadLine());

            var d = 2;
            var counter = 0;

            while (n > 0 && d <= n)
            {
                if (n % d == 0 && IsPowerOfPrime(d))
                {
                    counter++;
                    n /= d;
                }

                d++;
            }

            Console.WriteLine(counter);

            Console.ReadLine();
        }
    }
}