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 ConsoleApp15
{
    class Class362
    {
        static void Main()
        {
            long N = long.Parse(Console.ReadLine());
            var dic = new Dictionary<long, int>();
            for(int i = 2; i <= Math.Sqrt(N); i++)
            {
                while (N % i == 0)
                {
                    N /= i;
                    if (!dic.ContainsKey(i))
                    {
                        dic[i] = 1;
                    }
                    else
                    {
                        dic[i]++;
                    }
                }
            }
            if (N != 1) dic[N] = 1;
            int count = 0;
            foreach(int i in dic.Keys)
            {
                int s = 0;
                int c = 0;
                for(c = 1; s <= dic[i]; c++)
                {
                    s += c;
                }
                count += c - 2;
            }
            Console.WriteLine(count);
        }
    }
}