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;
using System.Collections.Generic;
using System.IO;
using System.IO.Pipes;
using System.Linq;
using System.Windows.Markup;

namespace AtCoder
{
	public class ABC
	{
		static public void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
			Solve(args);
			Console.Out.Flush();
		}

		private const int mod = 1000000007;  // 10^9+7

		static public void Solve(string[] args)
		{
			//int n = int.Parse(Console.ReadLine());
			//string s = Console.ReadLine();
			//string[] vs = Console.ReadLine().Split();
			long n = long.Parse(Console.ReadLine());
			//int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();

			long[] a = PrimeFactorization(n);
			System.Diagnostics.Debug.WriteLine(string.Join(" ", a));

			long ans = 0;
			int c = 0;
			for (int i = 0; i < a.Length; i++) {
				c++;
				if (i == a.Length - 1 || a[i] != a[i + 1]) {
					//System.Diagnostics.Debug.WriteLine($"{a[i]},{c}");
					int j = 0, sum = 0;
					while (sum < c) {
						j++;
						sum += j;
					}
					if (sum == c) {
						ans += j;
					} else {
						ans += j - 1;
					}
					c = 0;
				}
			}
			Console.WriteLine(ans);

		}

		#region 素因数分解 long[] PrimeFactorization(long a)
		public static long[] PrimeFactorization(long a)
		{
			if (a < 2) { return new long[] { }; }

			List<long> ans = new List<long>();
			while (a % 2 == 0) {
				ans.Add(2);
				a /= 2;
			}
			for (int i = 3; i <= Math.Sqrt(a); i += 2) {
				while (a % i == 0) {
					ans.Add(i);
					a /= i;
				}
			}
			if (a > 1) {
				ans.Add(a);
			}
			return ans.ToArray();
		}
		#endregion

	}
}