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

namespace AtCoder.ABC169
{
    public class Problem4
    {
        public static void Main(string[] args)
        {
            var input = ulong.Parse(Console.ReadLine());

            var res = (ulong)0;

            if (input == 1)
            {
                res = 0;
            }
            else if (IsPrime(input))
            {
                res = 1;
            }
            else
            {
                var factors = PrimeFactors(input)
                    .GroupBy(x => x)
                    .Select(x => CountFactor((ulong)x.Count()));
                
                res = (ulong)factors.Sum(x => (decimal)x);
            }

            Console.WriteLine(res.ToString());
        }

        public static IEnumerable<ulong> PrimeFactors(ulong n)
        {
            ulong i = 2;
            ulong tmp = n;

            while (i * i <= n) //※1
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;//最後の素数も返す
        }

        public static bool IsPrime(ulong 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 (ulong 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;
        }

        public static ulong CountFactor(ulong num)
        {
            var con = (ulong)1;
            var i = (ulong)1;
            while (con <= num)
            {
                i++;
                con += i;
            }

            return i - 1;
        }
    }
}