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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.Scanner;

public class Main {
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        sc.close();
        int zCount =0;
        int devisor =2;

        //ごり押しで素因数分解
        //2の時だけいったん計算
        int devideCount =0;
        while(true){
            if(n % devisor ==0){
                n = n/devisor;
                devideCount++;
            }
            else{
                break;
            }
        }
        for(int j=1; j<=devideCount; j++){
            if(devideCount<j){
                break;
            }
            devideCount = devideCount - j;
            zCount++;
        }
        devisor++;

        //奇数だけ調べるため3移行+2で回す
        while(n>1){
            devideCount=0;
            while(true){
                if(n % devisor ==0){
                    n = n/devisor;
                    devideCount++;
                }
                else{
                    break;
                }
            }
            for(int j=1; j<=devideCount; j++){
                if(devideCount<j){
                    break;
                }
                devideCount = devideCount - j;
                zCount++;
            }
            devisor += 2;
        }
        System.out.println(zCount);
    }
}