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

pub 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")
}

use std::collections::HashMap;

fn factors(n: i64) -> HashMap<i64, i64> {
    let mut a = n;
    let mut f = 2;
    let mut map: HashMap<i64, i64> = HashMap::new();
    while a > 1 && f * f <= n {
        while a % f == 0 {
            let current = map.entry(f).or_insert(0);
            *current += 1;
            a /= f;
        }
        f += 1;
    }
    if a != 1 {
        let current = map.entry(a).or_insert(0);
        *current += 1;
    }
    return map;
}

fn main() {
    let n: i64 = read();
    let mut a: Vec<usize> = vec![1];
    let mut ans = 0;
    for i in 2..=50 {
        for j in 0..i - 1 {
            a.push(i - 1);
        }
        a.push(i)
    }

    let map = factors(n);
    // println!("{:?}", map);
    for (_, v) in map {
        ans += a[v as usize - 1];
    }
    println!("{}", ans);
    // println!("{:?}", factors(n));
}