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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO.Pipes;
using System.Linq;
using System.Security.Cryptography;
using System.Text;
using System.Numerics;
using System.Data.Common;
using System.Net.Sockets;

namespace cswork
{
    class Program
    {
        class Scanner
        {
            string[] s;
            int i;

            char[] cs = new char[] { ' ' };

            public Scanner()
            {
                s = new string[0];
                i = 0;
            }

            public string next()
            {
                if (i < s.Length) return s[i++];
                string st = Console.ReadLine();
                while (st == "") st = Console.ReadLine();

                s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                i = 0;
                return next();
            }

            public int nextInt()
            {
                return int.Parse(next());
            }

            public long nextLong()
            {
                return long.Parse(next());
            }

            public double nextDouble()
            {
                return double.Parse(next());
            }
        }

        public Program() { }

        static void Main(string[] args)
        {
            new Program().Omame();
        }

        Scanner cin;
        const int MAXIN = 1024;
        bool[] used = new bool[MAXIN];
        int[] perm = new int[MAXIN];

        List<int[]> permList = new List<int[]>();

        public void Permutation(int pos, int n, int length)
        {
            if (pos == n)
            {
                permList.Add((int[])perm.Clone());
            }

            for (int i = 0; i < n; i++)
            {
                if (!used[i])
                {
                    perm[pos] = i;
                    used[i] = true;
                    Permutation(pos + 1, n, length);
                    used[i] = false;
                }
            }
        }

        void Omame()
        {
            cin = new Scanner();
            long N = cin.nextLong();
            List<long> tmpList = divisor(N);
            List<long> list = new List<long>();
            tmpList.Sort();
            for (int i = 0; i < tmpList.Count; i++)
            {
                long num = tmpList[i];

                if (num == 1)
                {
                    continue;
                }

                list.Add(num);
                num *= tmpList[i];
                while (num <= Math.Pow(N, 0.5))
                {
                    list.Add(num);
                    num *= tmpList[i];
                }

            }
            list.Sort();

            long ans = 0;
            for (int i = 0; i < list.Count; i++)
            {
                long tmpN = N;
                long x = list[i];

                if (N % x == 0)
                {
                    N = N / x;
                    ans++;
                }
            }
            Console.WriteLine(ans);
        }

        List<long> divisor(long n)
        {
            List<long> list = new List<long>();
            for (long i = 1; i * i <= n; i++)
            {
                if (n % i == 0)
                {
                    list.Add(i);
                    if (i * i != n) list.Add(n / i);
                }
            }
            return list;
        }
    }
}