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 static System.Math;
using System.Collections.Generic;
using System.Linq;
using System;

public class Hello
{
    public static void Main()
    {
        var n = long.Parse(Console.ReadLine().Trim());
        if (n == 1) { Console.WriteLine(0); goto exit; }
        if (IsPrime(n)) { Console.WriteLine(1); goto exit; }
        var a = GeneratePrime((int)Sqrt(n));
        var b = getPrime(n, a);
        getAns(b);
    exit:;
    }
    static void getAns(List<int> a)
    {
        var ans = 0;
        foreach (var x in a)
            ans += getN(x);
        Console.WriteLine(ans);
    }
    static int getN(int n)
    {
        var p = 1;
        while (true)
        {
            if (p * (p + 1) > 2 * n) return p - 1;
            else if (p * (p + 1) == 2 * n) return p;
            else p++;
        }
    }
    static bool IsPrime(long n)
    {
        if (n < 2) return false;
        else if (n == 2) return true;
        else if (n % 2 == 0) return false;
        double sqrtNum = Sqrt(n);
        for (int i = 3; i <= sqrtNum; i += 2)
            if (n % i == 0) return false;
        return true;
    }
    static List<int> getPrime(long n, List<int> a)
    {
        var ans = new List<int>();
        var t = n;
        for (int i = 0; i < a.Count(); i++)
        {
            if (a[i] > t) break;
            var count = 0;
            while (true)
            {
                if (t % a[i] == 0) 
                {
                    t /= a[i];
                    count++;
                    if (IsPrime(t) && t > a[i]) { t =1; ans.Add(1); }
                }
                else
                {
                    if (count > 0) ans.Add(count);
                    break;
                }
            }
        }
        return ans;
    }
    static List<int> GeneratePrime(int m)
    {
        var a = new List<int>();
        int p;
        var sqrtMax = Math.Sqrt(m);
        var s = Enumerable.Range(2, m - 1).ToList();
        do
        {
            p = s.First();
            a.Add(p);
            s.RemoveAll(n => n % p == 0);
        }
        while (p < sqrtMax);
        a.AddRange(s);
        return a;
    }
}