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.Linq;
using System.Collections.Generic;

namespace AtCoder.Contests.ABC169
{
    /// <summary>
    /// 
    /// </summary>
    static class D
    {
        static void Main(string[] args)
        {
            var n = NextLong();

            var count = 0;

            var f = Math.Floor(Math.Sqrt((double)n));

            for (int i = 2; i <= f; i++)
            {
                if (n % i != 0)
                {
                    continue;
                }

                var p = i;
                while (n % p == 0)
                {
                    count++;
                    n = n / p;
                    p *= i;
                }

                while (n % i == 0)
                {
                    n = n / i;
                }
            }

            if (count == 0 && n > 1)
            {
                count++;
            }

            Console.WriteLine(count);
        }

        #region Console
        static int _index = 0;
        static string[] _buffer;

        static string Next()
        {
            if (_buffer == null || _index >= _buffer.Length)
            {
                _buffer = Console.ReadLine().Split();
                _index = 0;
            }

            return _buffer[_index++];
        }
        static int NextInt()
        {
            return int.Parse(Next());
        }
        static long NextLong()
        {
            return long.Parse(Next());
        }
        static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }
        static int[] ReadIntArray(int n)
        {
            var a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = ReadInt();
            }
            return a;
        }
        static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }
        static long[] ReadLongArray(int n)
        {
            var a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = ReadLong();
            }
            return a;
        }
        static List<T> ReadObjects<T>(int n, Func<int[], T> creator)
        {
            var l = new List<T>(n);

            for (int i = 0; i < n; i++)
            {
                var a = ReadIntArray();
                l.Add(creator(a));
            }

            return l;
        }

        static int[,] ReadMatrix(int n, int m)
        {
            var r = new int[n, m];
            for (int i = 0; i < n; i++)
            {
                var a = ReadIntArray();
                for (int j = 0; j < m; j++)
                {
                    r[i, j] = a[j];
                }
            }
            return r;
        }
        #endregion
    }
}