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;

public class AtCoderC
{
    static void Main()
    {
        var sc = new Scanner();

        long n = sc.NextLong();

        Dictionary<long, long> dic = new Dictionary<long, long>();

        if (IsPrime(n))
        {
            Console.WriteLine(1);
            return;
        }

        long now = n;
        long current = 2;
        double sqrt = Math.Sqrt(n);
        while (true)
        {
            if (now % current == 0)
            {
                now /= current;
                if (dic.ContainsKey(current))
                {
                    dic[current]++;
                }
                else
                {
                    dic.Add(current, 1);
                }
            }
            else
            {
                current++;
            }
            if (current > sqrt + 10)
            {
                break;
            }
        }

        long answer = 0;

        foreach (var item in dic)
        {
            long num = item.Value;

            long max = num;
            for (long i = 1; i <= max; i++)
            {
                if (num >= i)
                {
                    answer++;
                    num -= i;
                }
            }
        }

        Console.WriteLine(answer);
    }

    // 素数判定
    private static bool IsPrime(long num)
    {
        if (num < 2)
        {
            return false;
        }
        if (num == 2)
        {
            return true;
        }
        if (num % 2 == 0)
        {
            return false;
        }

        double sqrt = Math.Sqrt(num);
        for (long i = 3; i <= sqrt + 10; i += 2)
        {
            if (num % i == 0)
            {
                return false;
            }
        }
        return true;
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}