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.Linq;

class Program
{
    static readonly long INF = 100100100100;
    static void Main(string[] args)
    {
        long n = long.Parse(Console.ReadLine());
        long count = 0;
        if (IsPrime(n))
        {
            Console.WriteLine(1);
            return;
        }
        for (long i = 2; i * i < n; i++)
        {
            if (!IsPrime(i)) continue;
            if (n % i == 0)
            {
                long n2 = n / i;
                long x = 1;
                for(long j = 2; j < INF; j++)
                {
                    if (n2 % i != 0) break;
                    n2 /= i;
                    x++;
                }
                for(long j = 1; j < INF; j++)
                {
                    x -= j;
                    if (x < 0) break;
                    count++;
                }
            }
        }
        Console.WriteLine(count);
    }

    static bool IsPrime(long n)
    {
        if (n == 1) return false;
        for (long i = 2; i * i <= n; i++)
            if (n % i == 0) return false;

        return true;
    }
}