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: Runtime Error)

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

namespace ProconTemplate
{
    //https://atcoder.jp/contests/abc141/tasks/abc141_c
    class abc169_b
    {
        //private static int[] m_aiPrimes;
        //private static int m_iCurPrimeIdx;
        public static void Main(string[] args)
        {
            //string s = Console.ReadLine();

            //string[] asInput = Console.ReadLine().Split(' ');
            //long A = long.Parse(asInput[0]);
            //decimal B = decimal.Parse(asInput[1]);
            //Console.WriteLine(A * (long)(100 * B) / 100);

            long N = long.Parse(Console.ReadLine());

            int lPrime = 2;
            int iAns = 0;


            List<int> lsPrime = GeneratePrime((int)Math.Floor(Math.Sqrt(N)));

            for (int i = 0; i < lsPrime.Count; i++)
            {
                lPrime = lsPrime[i];
                int iDivCnt = 0;
                int iDivCntStep = 1;
                while (N % lPrime == 0)
                {
                    N /= lPrime;
                    iDivCnt++;
                    if (iDivCnt == iDivCntStep)
                    {
                        iAns++;
                        iDivCntStep++;
                        iDivCnt = 0;
                    }
                }
                if (N == 1) break;
            }
            if (N > 1)
            {
                //Nは素数
                iAns++;
            }
            Console.WriteLine(iAns);
            

        }

        //private static int GetNextPrime(int a_lStart, int a_lMax)
        //{
        //    int lCur;
        //    for (lCur = a_lStart; lCur <= a_lMax; lCur++)
        //    {
        //        if (IsNewPrime(lCur))
        //        {
        //            break;
        //        }
        //    }
        //    return lCur;
        //}

        //private static bool IsNewPrime(int a_lNum)
        //{
        //    if (a_lNum % 2 == 0) return false;
        //    for (int i = 0; i< m_iCurPrimeIdx; i++)
        //    {
        //        if (a_lNum % m_aiPrimes[i] == 0) return false;
        //    }
        //    m_aiPrimes[m_iCurPrimeIdx] = a_lNum;
        //    m_iCurPrimeIdx++;
        //    return true;
        //}

        //https://qiita.com/asksaito/items/8fe448d21b394eb35582 引用させていただきました...
        public static List<int> GeneratePrime(int max)
        {
            System.Diagnostics.Debug.Assert(max >= 2);  // maxは2以上の数

            int prime;
            double sqrtMax = Math.Sqrt(max);
            var primeList = new List<int>();

            // ■ステップ 1
            // 探索リストに2からxまでの整数を昇順で入れる。
            var searchList = Enumerable.Range(2, max - 1).ToList();

            do
            {
                // ■ステップ 2
                // 探索リストの先頭の数を素数リストに移動し、その倍数を探索リストから篩い落とす。
                prime = searchList.First();
                // 素数リストに追加
                primeList.Add(prime);
                // 倍数をふるい落とす
                searchList.RemoveAll(n => n % prime == 0);

                // ■ステップ 3
                // 上記の篩い落とし操作を探索リストの先頭値がxの平方根に達するまで行う。
            } while (prime < sqrtMax);

            // ■ステップ 4
            // 探索リストに残った数を素数リストに移動して処理終了。
            primeList.AddRange(searchList);

            return primeList;
        }
    }
}