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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
class Program
{
    public static void Main()
    {
        long N = long.Parse(Console.ReadLine());
        var prime = PrimeFact(N);
        var prime2 = new Dictionary<long, long>();
        foreach(var p in prime)
        {
            if (prime2.ContainsKey(p))
            {
                prime2[p]++;
            }
            else
            {
                prime2[p] = 1;
            }
        }
        long ans = 0;
        foreach (var x in prime2.Values)
        {
            var temp = x;
            var count = 0;
            for(var i=1; ; i++)
            {
                temp = temp - i;
                if (temp >= 0) count++;
                else break;
            }
            ans += count;
        }
        Console.WriteLine(ans);
    }
    static IEnumerable<long> PrimeFact(long n)
    {
        var temp = n;
        long p = 2;
        while (p * p <= n)
        {
            if (temp % p == 0)
            {
                temp /= p;
                yield return p;
            }
            else
            {
                p++;
            }
        }
        if (temp != 1) yield return temp;
    }
}