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 ABC169D
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            long num = N;
            long[] z = new long[20];
            int sousa = 0;
            int x = 0;
            int sosuu = 0;
            if (N != 1)
            {
                for (long i = 2; i*i<=num; i++)
                {
                    if (N >= i)
                    {
                        if (N % i == 0)
                        {
                            while (N % i == 0)
                            {
                                z[x] += 1;
                                N = N / i;
                                //Console.WriteLine(z[x]);
                            }
                            x += 1;
                            sosuu = -1;
                        }
                    }

                }
                //Console.WriteLine(z[3]);
                //Console.WriteLine(z[2]);
                for (long i = 0; i < 20; i++)
                {
                    int j = 1;
                    int kaisuu = 0;
                    while (z[i] > 0)
                    {
                        z[i] -= j;
                        j++;
                        if (z[i] >= 0)
                        {
                            kaisuu++;
                        }
                    }
                    //Console.WriteLine(kaisuu);
                    if (kaisuu != 0)
                    {
                        sousa += kaisuu;
                    }
                }
                if (sosuu == 0)
                {
                    sousa = 1;
                }
            }
            else
            {
                sousa = 0;
            }
            Console.WriteLine(sousa);
        }
    }
}