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 AtCoder.Abc
{
    internal class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            long n = long.Parse(Console.ReadLine());

            var primeFactors = PrimeFactors.PrimeFactorsImpl(n);

            var a = primeFactors.GroupBy(v => v)
                .Select(x => new { Factor = x.Key, Count = x.Count() });
            string result = a.Select(v => {
                var i = 1;
                var count = v.Count;
                while (true) {
                    count -= i;
                    if (count >= i) {
                        i++;
                    } else {
                        break;
                    }
                }
                return i;
            }).Sum().ToString();

            Console.WriteLine(result);

            Console.Out.Flush();
        }
    }

    internal class PrimeFactors
    {
        /// <summary>
        /// 素因数分解。
        /// 出展：https://qiita.com/y_miyoshi/items/da814d96e8890224aad3
        /// </summary>
        public static IEnumerable<long> PrimeFactorsImpl(long n)
        {
            long i = 2;
            long 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
        }
    }
}