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::collections::HashMap;

fn main() {
    let n = read::<u64>();
    if n == 1 {
        println!("0");
        return;
    }

    let map = prime_factorize(n);

    // println!("{:?}", map);

    let mut ret = 0;
    for (_, v) in map.iter() {
        let mut i = 1;
        let mut cnt = *v;
        while i <= cnt {
            cnt -= i;
            i += 1;
            ret += 1;
        }
    }
    println!("{}", ret);
}

fn prime_factorize(mut n: u64) -> HashMap<u64, u64> {
    let mut map: HashMap<u64, u64> = HashMap::new();
    let mut i = 2;
    while i * i <= n {
        if n % i != 0 {
            i += 1;
            continue;
        }

        while n % i == 0 {
            let entry = map.entry(i).or_insert(0);
            *entry += 1;
            n /= i;
        }
        i += 1;
    }
    if n > 1 {
        let entry = map.entry(n).or_insert(0);
        *entry += 1;
    }
    map
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}