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.Collections;
using System.Linq;
namespace Atcoder_0404
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = GetInput_long()[0];
            var Nconst = N;
            int result = 0;
            for(long i = 2;true; i++)
            {
                if (i > N) break;
                if (i * i > Nconst) break;
                if (N % i == 0)
                {
                    N /= i;
                    result++;
                }
            }
            if (result == 0&&N!=1)
            {
                result++;
            }
            Console.WriteLine(result);
        }

        #region input


        static string[] GetInput_string()
        {
            var input = Console.ReadLine().Split(' ');
            return input;
        }

        static int[] GetInput_int()
        {
            var input = GetInput_string();
            var result = new int[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = int.Parse(input[i]);
            }
            return result;
        }
        static long[] GetInput_long()
        {
            var input = GetInput_string();
            var result = new long[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = long.Parse(input[i]);
            }
            return result;
        }
        #endregion
        #region sonota
        static void Swap_array<T>(T[] target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        static void Swap_list<T>(List<T> target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        /// <summary>
        /// 最大公約数
        /// </summary>
        public static int GCD(int a, int b)
        {

            /* 自然数 a > b を確認・入替 */
            if (a < b)
            {
                int tmp = a;
                a = b;
                b = tmp;
            }

            /* ユークリッドの互除法 */
            int r = a % b;
            while (r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }
            return b;
        }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        public static int LCM(int a, int b)
        {
            int x = a * b;
            b = GCD(a, b);
            return x / b;

        }
        #endregion
        
    }
}