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;

class Program
{
	static void Main() => new Program().Solve();

	void Solve()
	{
		var n = ReadLong();
		var sqrt = (long)Math.Sqrt(n);
		var line = new int[sqrt + 1];

		for (var i = 2L; i <= sqrt; i++) {
			if (line[i] == 0) {
				if ((n % i) == 0) {
					n /= i;
					line[i] = 1;
					for (var a = i << 1; a <= sqrt; a += i) {
						line[a] = -1;
					}
				}
				while ((n % i) == 0) {
					n /= i;
					line[i]++;
				}
				if (n == 1) break;
			}
		}
		var cnt = 0L;
		for (var i = 2L; i <= sqrt; i++) {
			for (var a = 1; line[i] >= a; a++) {
				line[i] -= a;
				cnt++;
			}
		}
		if (n != 1) cnt++;
		Console.WriteLine(cnt);
	}

	#region Console.Read 関係
	long[] ReadLongArray() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
	long ReadLong() => long.Parse(Console.ReadLine());
	#endregion
}