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: Accepted)

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

int main(void)
{
	unsigned long long int a, b, c = 1, i, j, sq;
	long long int ret = 0;

	
	scanf("%lld", &a);

	sq = sqrt(a);

	for (i = 2; i <= sq; i++) {
		if (a % i == 0) {
			c = 1;
			while (1) {
				b = 0;
				for (j = 0; j < c; j++) {
					if (a % i != 0) {
						b = 1;
						break;
					}
					a = a / i;
				}

				if (b == 1) {
					break;
				}

				ret++;
				c++;
			}
			sq = sqrt(a) + 1;
		}
	}

	if (a != 1) {
		(ret)++;
	}

	printf("%d", ret);

	return 0;
}