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)

struct Scanner {
	handle: std::io::Stdin,
	buffer: std::collections::VecDeque<String>
}

impl Scanner {
	fn new() -> Scanner {
		Scanner {
			handle: std::io::stdin(),
			buffer: std::collections::VecDeque::new()
		}
	}
	fn next<T: std::str::FromStr>(&mut self) -> Result<T, T::Err> {
		if self.buffer.len() == 0 {
			loop {
				let mut available = String::new();
				self.handle.read_line(&mut available).unwrap();
				self.buffer = available.split_whitespace().map(String::from).collect();
				if self.buffer.len() > 0 {
					break;
				}
			}
		}
		T::from_str(&self.buffer.pop_front().unwrap())
	}
}

fn main() {
	let mut scanner = Scanner::new();
	let mut n: i64 = scanner.next().unwrap();
	let mut total: i64 = 0;
	for p in 2i64.. {
		#[cfg(debug_assertions)] dbg!(n, p);
		if p * p > n {
			break;
		}
		if n % p != 0 {
			continue;
		}
		let mut e = 0;
		while n % p == 0 {
			n /= p;
			e += 1;
		}
		for i in 1.. {
			e -= i;
			if e < 0 {
				break;
			}
			total += 1;
		}
	}
	if n > 1 {
		total += 1;
	}
	println!("{}", total);
}