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 Rust (1.42.0) (judge verdict: Accepted)

fn main() {
	let mut s = String::new();
	std::io::stdin().read_line(&mut s).unwrap();
	let n: i64 = s.trim().parse().unwrap();
	let f = factorize(n);
	let mut ans = 0;
	for (_, mut e) in f {
		let mut a = 1;
		while e >= a {
			e -= a;
			a += 1;
			ans += 1;
		}
	}
	println!("{}", ans);
}

fn factorize(mut n: i64) -> Vec<(i64, u32)> {
	let mut r = vec![];
	for i in 2.. {
		if i * i > n {
			break;
		}
		let mut e = 0;
		while n % i == 0 {
			e += 1;
			n /= i;
		}
		if e > 0 {
			r.push((i, e));
		}
	}
	if n != 1 {
		r.push((n, 1));
	}
	r
}