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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public class Hello
{
    public static void Main()
    {
        hoge();
        //System.Console.ReadLine();
    }

    public static void hoge()
    {
        var vars = System.Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var n = vars[0];

        if(n < 2)
        {
            System.Console.WriteLine(0);
            return;
        }

        int count = 0;

        var ans = new List<long>();
        var notuse  = new List<long>();

        while (n >= 2)
        {
            if (IsPrime(n))
            {
                if (!ans.Contains(n))
                {
                    count++;
                }
                
                break;
            }
            var limit = long.MaxValue;
            for (long v = 2; v <= limit; v++)
            {
                if(v >= limit)
                {
                    ans.Add(limit);
                    count++;
                    n /= limit;
                    limit = -1;
                    break;
                }
                if (!IsPrime(v))
                {
                    continue;
                }
                if(notuse.Contains(v))
                {
                    continue;
                }
                if (v > n)
                {
                    break;
                }
                if(n % v == 0)
                {
                    // 今まで回答に出てなければ割る
                    if (!ans.Contains(v))
                    {
                        ans.Add(v);
                        count++;
                        n /= v;
                        limit = -1;
                        break;
                    }
                    // 出てる場合、乗数で出てないものを探し、limitとする
                    var kai = v;
                    while(v <= n)
                    {
                        try
                        {
                            checked
                            {
                                kai *= v;
                                if(n % kai != 0)
                                {
                                    break;
                                }
                                if (!ans.Contains(kai))
                                {
                                    limit = kai;
                                    break;
                                }
                            }
                        }
                        catch
                        {
                            break;
                        }
                    }
                }
                else
                {
                    notuse.Add(v);
                }
            }
            if(limit != -1)
            {
                break;
            }
        }
        System.Console.WriteLine(count);
    }

    public static bool IsPrime(long num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

        double sqrtNum = Math.Sqrt(num);
        for (long i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                // 素数ではない
                return false;
            }
        }

        // 素数である
        return true;
    }

}