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: Wrong Answer)

#![allow(unused_imports)]
use proconio::input;
use std::collections::HashMap;
use ascii::*;

fn main() {
    input!(mut n: i64);
    if n == 1 {
        println!("0");
        return;
    }
    let mut factor_list: Vec<(i64, i64)> = Vec::new();
    let initial_n = n;
    let mut n_is_prime = true;
    for i in 2..=(f64::sqrt(n as f64) as i64) {
        let mut count = 0;
        while n % i == 0 {
            n /= i;
            count += 1;
            n_is_prime = false;
        }
        if count > 0 {
            factor_list.push((i, count));
        }
    }
    if n_is_prime {
        factor_list.push((initial_n, 1));
    }
    let mut count = 0;
    for item in factor_list.as_mut_slice() {
        let mut a = 1;
        while item.1 - a >= 0 {
            item.1 -= a;
            count += 1;
            a += 1;
        }
    }
    println!("{}", count);
}