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::{self, Read};

macro_rules! input {
    ($it: expr) => ($it.next().unwrap().parse().unwrap());
    ($it: expr, $T: ty) => ($it.next().unwrap().parse::<$T>().unwrap());
}

fn main() {
    let mut buf = String::new();
    io::stdin().read_to_string(&mut buf).unwrap();

    let mut it = buf.split_whitespace();

    let n: u64 = input!(it);

    let mut prime: Vec<bool> = vec![true; 1000000];
    prime[0] = false;
    prime[1] = false;
    for i in 2..prime.len() {
        if prime[i] {
            let mut j = i + i;
            while j < prime.len() {
                prime[j] = false;
                j += i;
            }
        }
    }

    let mut factors: Vec<u64> = Vec::new();
    let mut rem = n;
    for i in 0..prime.len() {
        if prime[i] {
            let mut count = 0;
            while rem % i as u64 == 0 {
                rem /= i as u64;
                count += 1;
            }
            if count > 0 {
                factors.push(count);
            }
        }
    }
    if rem != 1 {
        factors.push(1);
    }

    let mut ans = 0;
    for mut count in factors {
        let mut i = 0;
        while i + 1 <= count {
            count -= i + 1;
            i += 1;
        }
        ans += i;
    }

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