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: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main
{
	public static void main(String args[])throws IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		long n = Long.parseLong(br.readLine());
		int arr[] = new int[(int)Math.sqrt(n)+1];
		for(int i=2;i<arr.length;i++)
		{
			if(arr[i]==0){
			for(int j=i*2;j<arr.length;j+=i)
			{
				arr[j] = -1;
			}}
		}
	//	for(int i=2;i<arr.length;i++)
	//		System.out.println(i);
		long ans=0;
		for(int i=2;i<arr.length;i++)
		{
			int temp=0;long copy=n;
			if(arr[i]!=-1&&n%i==0)
			{
				while(copy%i==0)
				{
					copy/=i;
					temp++;
				}
			}
			if(temp>0)
			{
				int sum=0,k=1;
				while((k*k+1)<=temp)
					k++;
				ans += k-1;
			//	System.out.println(i+" "+temp+)
			}

		}
		if(ans!=1)
			ans++;
		System.out.println(ans);
	}
}