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)

use input::Input;

fn main() {
    let mut input = Input::default();

    let n = input.parse();
    if n == 1 {
        println!("0");
        return;
    }

    let v = f(n);

    let mut ans = 0;
    for x in v.iter() {
        let mut y = 0;
        let mut z = 0;
        while z + y + 1 <= x.1 {
            y += 1;
            z += y;
        }
        ans += y;
    }

    println!("{}", ans);
}

fn f(mut x: u64) -> Vec<(u64, u64)> {
    let mut res = Vec::new();
    for i in 2..=x {
        if i * i > x {
            break;
        }
        let mut n = 0;
        while x % i == 0 {
            x /= i;
            n += 1;
        }
        if n > 0 {
            res.push((i, n));
        }
    }
    if x > 1 {
        res.push((x, 1));
    }
    res
}

#[allow(dead_code)]
pub mod input {
    #[derive(Default)]
    pub struct Input(Vec<String>);

    impl Input {
        pub fn read_line(&mut self) -> String {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).ok().expect("read error");
            s
        }
        pub fn parse<T: std::str::FromStr>(&mut self) -> T {
            let x = if let Some(x) = self.0.pop() {
                x
            } else {
                let s = self.read_line();
                self.0 = s.split_whitespace().map(String::from).rev().collect();
                self.0.pop().expect("reached EOF")
            };
            x.parse().ok().expect("parse error")
        }
    }
}