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: Wrong Answer)

using System;
class Program
{
    static void Main()
    {
        long n = long.Parse(Console.ReadLine());
        int cnt = 0;
        for (int i = 2; i <= (int)Math.Sqrt(n); i++)
        {
            if (n % i == 0)
            {
                n /= i;
                cnt++;
            }
        }
        if (cnt == 0) cnt++;//nが素数の時
        Console.WriteLine(cnt);
    }
    public static bool IsPrime(long x)
    {
        //素数判定
        if (x < 2) return false;
        if (x == 2) return true;
        if (x % 2 == 0) return false;
        double sqrt = Math.Sqrt(x);
        for (int i = 3; i < sqrt; i += 2)
        {
            if (x % i == 0) return false;
        }
        return true;
    }
}



//origina
//動くけど遅い
//class Program
//{
//    static void Main()
//    {
//        long n = long.Parse(Console.ReadLine());
//        int cnt = 0;
//        for(int i=2; i <= n; i++)
//        {
//            if (n % i == 0)
//            {
//                n /= i;
//                cnt++;
//            }
//        }
//        Console.WriteLine(cnt);
//    }
//    public static bool IsPrime(long x)
//    {
//        //素数判定
//        if (x < 2) return false;
//        if (x == 2) return true;
//        if (x%2 == 0) return false;
//        double sqrt = Math.Sqrt(x);
//        for(int i = 3; i < sqrt; i += 2)
//        {
//            if (x % i == 0) return false;
//        }
//        return true;
//    } 
//}