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.Text;
using System.Numerics;

public class MainClass
{
	public const long Giri = 1000000007;
	public const long DpInf = 99999999999999;
	
	public static void Main(string[] args)
	{
		var n = Console.ReadLine().ToLong();
		
		var o = new List<long>();
		var m = PrimeFact(n);
		var keys = m.Keys.ToArray();
		var arys = m.Values.ToArray();
		//foreach(var key in m.Keys)
		for(int i = 0; i < keys.Length; i++)
		{
			var max = arys[i];
			for(int j = 1; j <= max; j++)
			{
				if(arys[i] < j)
					break;
				o.Add((long)Math.Pow(keys[i], j));
				arys[i] -= j;
			}
			//break;
		}
		o.Sort();
		long wa = 0;
		for(int i = 0; i < o.Count; i++)
		{
			if(n<o[i])
				break;
			if(n%o[i] == 0)
			{
				wa++;
			}
			
		}
		Console.WriteLine(wa);
	}
	
	static SortedDictionary<long, int> PrimeFact(long n) {
		var dic = new SortedDictionary<long, int>();
		
	    for (long i = 2; i*i <= n; i++) {
	        if (n % i == 0) {
	        	int j = 0;
	            while (n % i == 0) {
	                n /= i;
	                j++;
	            }
	            dic.Add(i, j);
	        }
	    }
	    if (n > 1) 
	    {
	    	if(!dic.ContainsKey(n))
	    		dic.Add(n, 1);
	    	else
	    		dic[n]++;
	    }
	    return dic;
	}
	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str, int offset = 0)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt() + offset;
		return r;
	}
}