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


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        var n = long.Parse(Console.ReadLine());
        //long[] n = Console.ReadLine().Split().Select(long.Parse).ToArray();

        var ans = 0;
        var tmp = n;

        if (tmp % 2 == 0)
        {
            for (long k = 1; Math.Pow(2, k) <= n; k++)
            {
                long z = (long)Math.Pow(2, k);
                if (tmp % z == 0 || tmp == z)
                {
                    tmp = tmp / z;
                    ans++;
                }
                else
                {
                    break;
                }
            }
            if (tmp == 1 || IsPrime(tmp))
            {
                Console.WriteLine(ans);
                return;
            }
        }

        if (tmp % 3 == 0)
        {
            for (long k = 1; Math.Pow(3, k) <= n; k++)
            {
                long z = (long)Math.Pow(3, k);
                if (tmp % z == 0 || tmp == z)
                {
                    tmp = tmp / z;
                    ans++;
                }
                else
                {
                    break;
                }
            }
            if (tmp == 1 || IsPrime(tmp))
            {
                Console.WriteLine(ans);
                return;
            }
        }

        if (tmp % 5 == 0)
        {
            for (long k = 1; Math.Pow(5, k) <= n; k++)
            {
                long z = (long)Math.Pow(5, k);
                if (tmp % z == 0 || tmp == z)
                {
                    tmp = tmp / z;
                    ans++;
                }
                else
                {
                    break;
                }
            }
            if (tmp == 1 || IsPrime(tmp))
            {
                Console.WriteLine(ans);
                return;
            }
        }

        if (IsPrime(tmp))
        {
            if (tmp % tmp == 0)
            {
                for (long k = 1; Math.Pow(n, k) <= n; k++)
                {
                    long z = (long)Math.Pow(n, k);
                    if (tmp % z == 0 || tmp == z)
                    {
                        tmp = tmp / z;
                        ans++;
                    }
                    else
                    {
                        break;
                    }
                }
                if (tmp == 1 || IsPrime(tmp))
                {
                    Console.WriteLine(ans);
                    return;
                }
            }
        }

        for (long i = 6; i < n; i++)
        {
            if (IsPrime(i))
            {
                for (long k = 1; Math.Pow(i, k) <= n; k++)
                {
                    long z = (long)Math.Pow(i, k);
                    if (tmp % z == 0 || tmp == z)
                    {
                        tmp = tmp / z;
                        ans++;
                    }
                    else
                    {
                        break;
                    }
                }
                if (tmp == 1 || IsPrime(tmp)) break;
            }
        }

        // 出力
        Console.WriteLine(ans);
    }

    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 (int 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;
    }
}