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(non_snake_case)]
#![allow(unused_imports)]
 
use proconio::{input, fastout};
use proconio::marker::*;
use whiteread::parse_line;
use std::collections::*;

pub fn prime_factorize(mut n: usize) -> Vec<(usize, usize)> {
    let mut res: Vec<(usize, usize)> = Vec::new();

    let mut i: usize = 2;

    while i * i <= n {
        if n % i == 0 {
            let mut ex: usize = 0;

            while n % i == 0 {
                ex += 1;
                n = n / i;
            }
            res.push((i, ex));
        }
        i += 1;
    }

    if n != 1 {res.push((n, 1))}

    res
}



#[fastout]
fn main() {
    input!{
        n: usize,
    }
    if n == 1 {
        println!("0");
    } else {
        let map = prime_factorize(n);
        // dbg!(&map);
        let mut ans = 0;

        for v in map.iter() {
            let mut v_mut: isize = v.1 as isize;
            let mut cnt = 1;
            loop {
                // dbg!(&v_mut, &cnt);
                v_mut -= cnt;
                if v_mut > cnt {
                    cnt += 1;
                }  else {
                    break;
                }
                
            }
            // &dbg!(&cnt);
            ans += cnt;
        }

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