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)

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

#[allow(unused_macros)]
macro_rules! echo {
    ($($e:expr),+) => ( { $(println!("{}", $e))+ } );
}

fn prime_factors(n: usize) -> std::collections::HashMap<usize, usize> {
    let mut res = std::collections::HashMap::new();
    let mut n = n;

    for i in 2..(n as f32).sqrt() as usize + 1 {
        while n % i == 0 {
            *res.entry(i).or_insert(0) += 1;
            n /= i;
        }
    }

    if n > 1 {
        res.insert(n, 1);
    }

    res
}

fn main() {
    input! {
        n: usize,
    }

    if n == 1 {
        echo!(0);
        return;
    }

    let pf = prime_factors(n);
    let mut result = 0;

    for &k in pf.values() {
        let mut cnt = k;
        for i in 1..=k {
            if cnt >= i {
                cnt -= i;
                result += 1;
            }
        }
    }

    echo!(result);
}