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: Time Limit Exceeded)

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

namespace ConsoleAppTest
{
    class DivGame
    {
        static void Main(string[] args)
        {

            ulong num = ulong.Parse(Console.ReadLine());
            ulong checkNum = num;
            ulong reNum = 0;
            ulong powNum = 0;
            ulong[] prime = new ulong[0];
            int primeNum = 0;
            ulong i;
            ulong methodNum = 0;

            for(i = 2; i <= checkNum; i++)
            {
                reNum = 0;
                powNum = 0;
                while (checkNum % i == 0)
                {
                    Array.Resize(ref prime, primeNum + 1);
                    prime[primeNum] = i;
                    primeNum++;
                    checkNum /= i;

                    reNum++;
                    if(reNum == powNum + 1)
                    {
                        methodNum++;
                        powNum++;
                        reNum = 0;
                    }
                }
            }

            Console.WriteLine(methodNum);

        }
    }
}