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)

/*
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 * and open the template in the editor.
 */
//https://atcoder.jp/contests/abc169/tasks/abc169_d
//package pkg21.days.of.code;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.*;
/**
 *
 * @author Pravash Ranjan
 */
 class Main {
    static class FastReader{BufferedReader br;StringTokenizer st;public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}String next(){ while (st == null || !st.hasMoreElements()){try{st = new StringTokenizer(br.readLine());}
        catch (IOException  e){e.printStackTrace();}}return st.nextToken();}int nextInt(){return Integer.parseInt(next());}long nextLong(){return Long.parseLong(next());} 
        double nextDouble(){return Double.parseDouble(next());}String nextLine(){String str = ""; try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}}
    public static void main(String args[])
    {
        FastReader ob=new FastReader();
        ArrayList<Integer> prm=new ArrayList<>();
        int size=(int)1e6+2;
        boolean prime[]=new boolean[(int)1e6+2];
        for(int i=2;i*i<size;i++)
        {
            for(int j=i*i;j<size;j+=i)
                prime[j]=true;
        }
        for(int i=2;i<size;i++)
            if(!prime[i])
                prm.add(i);
        long n=ob.nextLong();
        long m=n;
        HashMap<Long,Integer> map=new HashMap<>();
        int c=0;int x;int cnt=0;
        while(n!=1)
        {
           x=prm.get(c);c++;cnt=0;
           while(n%x==0)
           {
               n/=x;cnt++;
           }
           if(cnt!=0)
               map.put((long)x,cnt);
           if(x*x>n)
               break;
        }
        if(n!=1)
            map.put(n,1);
        long ans=0;int sum=0;long j;
        for(long i:map.keySet())
        {
            for(j=1;(j*(j+1))/2<=map.get(i);j++);
            ans+=(j-1);            
        }
        if(m==1)
            System.out.println(0);
        else
            System.out.println(ans);
    }
}