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.Text;
using System.Threading.Tasks;

namespace ProconTemplate
{
    //https://atcoder.jp/contests/abc141/tasks/abc141_c
    class abc169_b
    {
        static List<long> m_ls_lPrimes;
        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());

            long lPrime = 2;
            int iAns = 0;

            m_ls_lPrimes = new List<long>();

            while (N >= lPrime)
            {
                int iDivCnt = 0;
                int iDivCntStep = 1;
                while (N % lPrime == 0)
                {
                    N /= lPrime;
                    iDivCnt++;
                    if (iDivCnt == iDivCntStep)
                    {
                        iAns++;
                        iDivCntStep++;
                        iDivCnt = 0;
                    }
                }
                if (N == 1) break;
                long lPrimeMax = (long)Math.Floor(Math.Sqrt(N));
                lPrime = GetNextPrime(lPrime, lPrimeMax);
                if (lPrime > Math.Sqrt(N))
                {
                    //Nは素数
                    iAns++;
                    break;
                }
            }
            Console.WriteLine(iAns);
            

        }

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

        private static bool IsNewPrime(long a_lNum)
        {
            if (a_lNum % 2 == 0) return false;
            for (int i = 0; i< m_ls_lPrimes.Count; i++)
            {
                if (a_lNum % m_ls_lPrimes[i] == 0) return false;
            }
            m_ls_lPrimes.Add(a_lNum);
            return true;
        }
    }
}