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

namespace ABC169
{
    class D
    {
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());
            var Res = new long[100000000];
            var dict = new Dictionary<long, long>();
            long j;

            if (IsPrime(N)) { Console.WriteLine(1); return; }
            //Console.WriteLine("--- 1 --");
            j = 2;
            var Ntemp = N;
            while (j * j <= N)
            {
                while (Ntemp % j == 0)
                {
                    if (!dict.ContainsKey(j)) dict.Add(j, 1);
                    else dict[j]++;
                    //Res[j]++;
                    Ntemp /= j;
                }
                j++;
            }
            // Console.WriteLine("--- 2 --");


            var res = 0;
            if (Ntemp != 1) res = 1;

            foreach (var i in dict.Values)
            {
                var temp = i;
                var index = 1;
                while (index <= temp)
                {
                    temp -= index;
                    index++;
                    res++;
                }
            }
            Console.WriteLine(res);
        }

        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;
        }
    }
}