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 proconio::{input, fastout};

fn is_prime(i: f64) -> bool {
    let i_int = i as i64;
    let end = i.sqrt() as i64;
    let mut flag = true;
    for j in 2..end {
        if i_int % j == 0 {
            flag = false;
            break;
        }
    }

    return flag;
}
fn prime_factorization(n: f64) -> i64 {
    let mut _n = n;
    let mut i = 2.0_f64;
    let mut count = 0;
    while _n.sqrt() > i {
        if _n % i == 0.0 && is_prime(i) {
            let mut c = 0;
            let mut thresh = 1;
            while _n % i == 0.0 {
                _n = _n / i;
                c += 1;

                if thresh == c {
                    thresh += 1;
                    count += 1;
                    c = 0;
                }

            }
        }
        i += 1.0;
    }

    if _n != 1.0 {
        count += 1;
    }

    return count;
}

#[fastout]
fn main() {
    input!{
        n: f64,
    }
    println!("{}", prime_factorization(n));

}