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;

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

fn main() {
    let n: usize = read();
    let mut tmp = n;
    let mut cnt = 0;
    if is_prime(n) {
        println!("1");
    } else {
        for i in 2..=n {
            if i > tmp {
                break;
            }
            if tmp % i == 0 {
                if is_prime(i) {
                    tmp /= i;
                    cnt += 1;
                } else {
                    'middle: for j in 2..=i {
                        if is_prime(j) {
                            for k in 1..=i {
                                if j.pow(k as u32) > i {
                                    break;
                                } else if j.pow(k as u32) == i {
                                    tmp /= i;
                                    cnt += 1;
                                    break 'middle;
                                }
                            }
                        }
                    }
                }
            }
        }
        println!("{}", cnt);
    }
}

fn is_prime(x: usize) -> bool {
    match x {
        x if x == 2 => true,
        x if x < 2 || x % 2 == 0 => false,
        _ => {
            let mut i = 3;
            while i * i <= x {
                if x % i == 0 {
                    return false;
                }
                i += 2;
            }
            true
        }
    }
}