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 ABC169
{
    class Program
    {
        static void Main(string[] args)
        {
            //b();
            //c();
            d();
        }

        public static void b()
        {
            long n = long.Parse(Console.ReadLine());
            long[] a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            long b = 1000000000000000000;
            long ans = 1;
            bool flg = true;
            foreach (var x in a)
            {
                ans *= x;
                if(ans == 0)
                {
                    Console.WriteLine(0);
                    return;
                }
                else if(ans < 0)
                {
                    flg = false;
                }
            }
            if (ans > b)
            {
                Console.WriteLine(-1);
            }
            else if (flg == false)
            {
                Console.WriteLine(-1);
            }
            else
            {
                Console.WriteLine(ans);
            }
        }

        public static void c()
        {
            double[] ab = Console.ReadLine().Split(' ').Select(double.Parse).ToArray();
            double a = ab[0], b = ab[1] * 100;
            long ans =  (long)(a * b) / 100;
            Console.WriteLine(ans);
        }

        public static void d()
        {
            long n = long.Parse(Console.ReadLine());
            if(n == 1)
            {
                Console.WriteLine(0);
                return;
            }
            int ans = 0;
            int i = 2;
            bool flg = true;
            while(flg)
            {
                if(n % i == 0)
                {
                    n /= i;
                    if(n == 1)
                    {
                        flg = false;
                    }
                }
                else
                {
                    i++;
                    continue;
                }
                i++;
                ans++;
            }
            Console.WriteLine(ans);
        }
    }
}