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: Time Limit Exceeded)

use std::io::*;
use std::str::FromStr;
use std::collections::HashMap;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
struct Main {
    factors: Vec<u64>,
}

#[allow(dead_code)]
impl Main {
    fn find_factors(&mut self, num: u64) -> u64 {
        let mut new_num = num;
        while new_num % 2 == 0 {
            self.factors.push(2);
            new_num /= 2;
        }

        for i in 3..=num { // 他の素数で割っていく
            while new_num % i == 0 {
                self.factors.push(i);
                new_num /= i;
            }
        }
        return 0;
    }
}

fn main() {
    let n = read::<u64>();
    let mut a = Main {factors: vec![]};
    a.find_factors(n);
    // println!("{:?}", a.factors);
    let mut map: HashMap<u64, usize> = HashMap::new();
    for i in a.factors.into_iter() {
        match map.get_mut(&i) {
            Some(v) => {
                *v += 1;
            },
            None => {
                map.insert(i, 1);
            },
        }
    }
    let mut res = 0;
    for (k, v) in map.into_iter() {
        for i in 1..100000 {
            let sum = i * (i + 1) / 2;
            if v < sum {
                res += i - 1;
                break;
            }
        }
    }
    println!("{}", res);
    // for i in 1..100000 {
    //     let sum = i * (i + 1) / 2;
    //     for (k, v) in map.into_iter() {
    //         sum
    //     }
    // }
    // println!("{:?}", map);
}