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>

int main()
{
	long long n, ncp;
	scanf("%lld", &n);
	ncp = n;

	int i;
	int count = 0;
	if (n == 1) {
		printf("0\n");
	} else {
		for (i = 2; i * i <= ncp; i++) {
			int incount = 0;
			if (n % i == 0) {
				int j = 0;
				while (n % i == 0) {
					n = n / i;
					j++;
					if (j > incount) {
						incount++;
						j = 0;
					}
				}
				count += incount;
			}

//			fprintf(stderr, "%d %d %d\n", i, incount, count);
		}
		if (ncp == n) {
			printf("1\n");
		} else {
			printf("%d\n", count);
		}
	}
	return 0;
}