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: Accepted)

using System;
using System.Collections.Generic;

class Program
{
    static Dictionary<long, long> slist = new Dictionary<long, long>();
    static void Main () 
    {
        String[] inline = Console.ReadLine().Split(' ');
        long n = long.Parse(inline[0]);
        long ans = 0;
        var list = plen(n);

        foreach(long l in list)
        {
            long i = 1;
            long j = l;
            while(i <= j)
            {
                j -= i;
                i++;
                ans++;
            }
        }

        Console.WriteLine(ans == 0 ? n == 1 ? 0 : 1 : ans);
    }

    static List<long> plen (long n)
    {
        long i = 2;
        double tmp = Math.Sqrt(n);
        var list = new List<long>();

        while((double) i <= tmp)
        {
            long index = 0;
            while(true)
            {
                if(n % i == 0)
                {
                    index++;
                    n /= i;
                }
                else
                {
                    if(index != 0)
                    {
                        list.Add(index);
                    }
                    break;
                }
            }
            i++;
        }
        if(n > tmp)
        {
            list.Add(1);
        }
        return list;
    }
}