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;

class ABC_169_D
{
    static void Main(string[] args)
    {
        long N = long.Parse(Console.ReadLine());

        List<long> ans = new List<long>();

        for (long i = 2; i < 1000000L; i++)
        {
            if (!primeExpCheck(i)) continue;

            if (N % i == 0)
            {
                ans.Add(i);
                N /= i;
            }
        }

        if(N>1 && !ans.Contains(N))
        {
            ans.Add(N);
        }

        Console.WriteLine(ans.Count);
    }

    // n>=2
    static bool primeExpCheck(long n)
    {
        long sqrt = (long) Math.Sqrt(n) + 1;
        for (long i = 2; i < sqrt; i++)
        {
            if(n%i == 0)
            {
                while(n>0)
                {
                    n /= i;
                    if (n == 1) return true;
                }
                return false;
            }
        }
        return true;
    }
}