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;

class Program
{
    static Dictionary<long, long> slist = new Dictionary<long, long>();
    static void Main () 
    {
        String[] inline = Console.ReadLine().Split(' ');
        long n = long.Parse(inline[0]);
        long i = 2;
        long ans = 0;
        while(n >= i)
        {
            if (n % i == 0 && plen(i) != -1)
            {
                n /= i;
                ans++;
            }
            i++;
        }
        Console.WriteLine(ans);
    }

    static long plen (long n)
    {
        long len = 0;
        long i = 2;
        long tmp = n;
        long hit = 0;

        while(i <= n)
        {
            if (tmp % i == 0)
            {
                hit = i;
                tmp/=i;
                len++;
            }
            else
            {
                if (tmp == 1) { break; }
                if (hit != 0 ) { return -1; } else { i++; }
            }
        }
        return len;
    }
}