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;
using System.IO;

namespace ABC169D
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());

            int[] pList = PrimeNumbers(1000000);

            var fact = PrimeFactorization(N, pList.ToList());

            Dictionary<long, int> count = new Dictionary<long, int>();
            for (int i = 0; i < fact.Count(); i++)
            {
                if (count.ContainsKey(fact[i])) count[fact[i]]++;
                else count.Add(fact[i], 1);
            }

            long ans = 0;
            foreach (var c in count)
            {
                int a = 2;
                int val = c.Value;
                while (val > 0)
                {
                    ans++;
                    val -= a;
                    a++;
                }
            }

            if (N == 1) ans = 0;
            if (fact.Length == 1) ans = 1;

            Console.WriteLine(ans);
        }

        /// <summary>
        /// 自然数n以下の素数prime列挙 (NloglogN)
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        public static int[] PrimeNumbers(int n)
        {
            int max = n;
            var searchList = Enumerable.Range(2, max).ToList();

            var pList = new List<int>();
            while (searchList.Count > 0)
            {
                int cand = searchList.First();

                pList.Add(cand);

                searchList.RemoveAll(x => x % cand == 0);
            }

            return pList.ToArray();
        }

        /// <summary>
        /// 自然数nの素因数分解 
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        public static long[] PrimeFactorization(long n, List<int> pList)
        {
            long N = n;
            //var pList = PrimeNumbers((int)Math.Sqrt(n)).ToList();

            var ansList = new List<long>();
            for (int i = 0; i < pList.Count;)
            {
                if (N % pList[i] == 0)
                {
                    ansList.Add(pList[i]);
                    N /= pList[i];
                }
                else i++;
            }
            if (ansList.Count == 0 || N != 1) ansList.Add(N);

            return ansList.ToArray();
        }

    }


}