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;
using System.Linq;
using System.Text;

namespace ABC169D
{
    class Program
    {
        static void Main(string[] args)
        {
            ulong N = ulong.Parse(Console.ReadLine().Trim());
            var prime = PrimeFactors(N);
            Dictionary<ulong, ulong> dic = new Dictionary<ulong, ulong>();
//            Console.WriteLine("{0} = {1}", N, string.Join(" x ", prime));
            foreach(var i in prime){
                if(!dic.ContainsKey(i)) dic.Add(i, 1ul); else dic[i]++;
            }
            ulong count = 0;
            foreach(var i in dic){
//                Console.WriteLine("Prime = {0} ^ {1}", i.Key, i.Value);
                count += tri(i.Value);
            }
            Console.WriteLine(count);
//            Console.WriteLine("{0} {1} {2} {3} {4}",tri(1ul), tri(2ul), tri(3ul), tri(5ul), tri(6ul));

        }

        static ulong tri(ulong x){
            ulong i = 0;
            ulong total = 0;
            while(total < x){
                i++; total += i; 
            }
            if(total == x) return i; else return i-1;
        }
        static IEnumerable<ulong> PrimeFactors(ulong n)
        {
            ulong i = 2;
            ulong tmp = n;

            while (i * i <= n) //※1
            {
                if(tmp % i == 0){
                    tmp /= i;
                    yield return i;
                }else{
                    i++;
                }
            }
            if(tmp != 1) yield return tmp;//最後の素数も返す
        }
    }
}