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 std::str::FromStr;
use std::fmt::Debug;
use std::cmp;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()
}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn calc_primes(n: u64) -> Vec<(u64, u64)>{
    if n == 2{
        return vec![(2, 1)];
    }

    let mut n = n;
    let mut ans = vec![];
    for i in 2..=(n as f64).sqrt().ceil() as u64{
        let mut div_counter: u64 = 0;
        while n%i == 0{
            div_counter += 1;
            n /= i;
        }
        if div_counter > 0{
            ans.push((i, div_counter));
        }

    }
    if n > 1{
        ans.push((n, 1));
    }
    return ans;
}

fn main(){
    let n = read_as_vec::<u64>()[0];
    if n == 1{
        println!("0");
        return;
    }
    let primes = calc_primes(n);
    //println!("{:?}", primes);

    //let mut s_acc = 0;
    let mut ans = 0;
    for (prime, count) in primes{
        let mut num = ((count*2) as f64).sqrt().floor() as u64;
        if num*(num+1) == count*2{
            ans += num;

        }else{
            if num*(num+1) > count*2{
                num -= 1;
            }
            ans += num;
        }

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