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 (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include<math.h>
#include<string.h>


int main() {
	int i, j, k;
	int  n = 0;
	long long int f = 0, m = 0;
	int g = 0;
	int x[110] = {0};
	int a, b, c, d;


	scanf("%lld", &m);
	
	if (m%2 == 0) {
		for (j = 0;m%2 == 0;j++) {
			m = m / 2;
		}
		for (k = 1;j >= 0;k++) {
			j = j - k;
			n++;
		}
		n--;
	}
	for (i=3;m>1;i=i+2) {
		
		if (m%i==0) {
			for (j=0;m%i == 0;j++) {
				m = m / i;
			}
			for (k = 1;j >= 0;k++) {
				j = j - k;
				n++;
			}
			n--;
		}
		
	}

	printf("%d", n);

	return 0;
}