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.Linq;
public class Global{
    public static long a = long.Parse(Console.ReadLine());
    public static int ans = 0;
}

class program{
  static void Main(){
	divgame(2);
    divgame(3);
    divgame(5);
    for(int i=0;i<=Math.Sqrt(Global.a);i+=30){
      divgame(7+i);
      divgame(11+i);
      divgame(13+i);
      divgame(17+i);
      divgame(19+i);
      divgame(23+i);
      divgame(29+i);
      divgame(31+i);
    }
    if(Global.a != 1) Global.ans++;
    Console.Write(Global.ans);
  }
  
  static void divgame(long div){
    int meta = 0,ct = 0;
    while(Global.a%div == 0){
      Global.a/=div;
      ct++;
      if(ct > meta){
        meta++;
        Global.ans++;
        ct=0;
      }
    }
    return;
  }
}