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 ConsoleApplication6
{
    class Program
    {
        static void Main(string[] args)
        {
            //var rl = spr(RL()).Select(x=>c2i(x)).ToList();
            var start=c2i(RL());
            var crrnt=3;
            var count = 0;
            var tw = 2;
            while (true)
            {
                if (start % tw == 0)
                {
                    start /= tw;
                    count++;
                    tw *= 2;
                }
                else
                {
                    break;
                }
            }
            var lst = new List<long>();
            if (start > 2)
            {
                long sqnum = (long)Math.Sqrt(start);
                while (true)
                {
                    if (start % crrnt == 0)
                    {
                        start /= crrnt;
                        lst.Add(crrnt);
                        sqnum = (long)Math.Sqrt(start);
                        count++;
                    }
                    if (sqnum < crrnt)
                    {
                        if(start!=1&&!lst.Any(x=>x==start))count++;
                        break;
                    }
                    crrnt++;
                }
            }
            
            


            Console.WriteLine(count);
            Console.ReadLine();
        
        }
        
        static string RL() { return Console.ReadLine().Trim(); }
        static IEnumerable<string> spr(string s) { return s.Split(' '); }
        static Int64 c2i(string c) { return Int64.Parse(c); }
        //static double c2d(string c) { return double.Parse(c); }
        static string bool2ret(bool b) { return b ? "Yes" : "No"; }
    }
}