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 {

	static long bignum = 1000000000+7;

	public static void main(String[] args){

		Scanner sc = new Scanner(System.in);

		long n = sc.nextLong();

		int[] soin = new int[1000001];
		for(int i =0;i<soin.length;i++) {
			soin[i]=0;
		}
		int target = 2;
		boolean sosu  =true;
		long nn = n;
		while(target<n+1) {
			if(n%target==0) {
				n = n/target;
				soin[target]++;
				sosu =false;
			}else {
				target++;
				if(sosu&&target>Math.sqrt(nn)+3) {
					break;
				}
			}
		}
		int counter =0;
		for(int i=0;i<soin.length;i++) {
			int checker =1;
			while(checker<=soin[i]) {
				counter++;
				soin[i]-=checker;
				checker++;
			}
		}
		if(sosu&&(nn!=1)) {
			System.out.println(1);
		}else {
			System.out.println(counter);
		}
	}

	static long divn(int target, int times) {//10_9+7のあまり累乗版
		int sqtimes = (int)Math.sqrt(times);
		long ans = 1;
		for(int i =0;i<sqtimes;i++) {
			ans = (ans * target)%(1000000000+7);
		}
		long holder = ans;
		ans = 1;
		for(int i =0;i<sqtimes;i++) {
			ans = (ans*holder)%(1000000000+7);
		}
		for(int i=0;i<times - sqtimes*sqtimes;i++) {
			ans = (ans * target)%(1000000000+7);
		}
		return ans;
	}

	static long div(long a) {//10_9+7のあまり
		if(a<0)a+=1000000000+7;
		return a%(1000000000+7);
	}

}
/*
class City{
	int order;
	int prefecture;
	int year;
	int number;
	City(int order,int prefecture, int year){
		this.order = order;
		this.prefecture = prefecture;
		this.year = year;
	}
}
*/