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.Linq;
using System.Collections.Generic;

namespace ConsoleApp1 {
    public class Class {
        static void Main(string[] args) {
            var N = long.Parse(Console.ReadLine());
            var C = new List<long>();
            while (N != 1) {
                while (N % 2 == 0) {
                    C.Add(2);
                    N /= 2;
                }
                for (var i = 3; i <=Math.Sqrt(N); i += 2) {
                    while (N % i == 0) {
                        C.Add(i);
                        N /= i;
                    }
                }
            }
            var tmp = C.GroupBy(_ => _).Where(x => x.Count() > 0).Select(x => x.Count()).ToList();
            var ans = 0;
            for (var t = 0; t < tmp.Count(); t++) {
                for (var i = 1; i <= tmp[t]; i++) {
                    if (tmp[t] - i >= 0) {
                        ans++;
                        tmp[t] -= i;
                    }
                }
            }
            Console.Write(ans);
        }
    }
}