Problem:
Score: 300 points

Problem Statement

As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.

Snuke, an employee, would like to play with this sequence.

Specifically, he would like to repeat the following operation as many times as possible:

For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.

At most how many operations can be performed?

Constraints

N is an integer between 1 and 10 \ 000 (inclusive).

a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 a_3 ... a_N

Output

Print the maximum number of operations that Snuke can perform.

Sample Input 1

3
5 2 4

Sample Output 1

3

The sequence is initially {5, 2, 4}. Three operations can be performed as follows:

First, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {15, 6, 2}.

Next, multiply a_1 by 3, divide a_2 by 2 and multiply a_3 by 3. The sequence is now {45, 3, 6}.

Finally, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {135, 9, 3}.

Sample Input 2

4
631 577 243 199

Sample Output 2

0

No operation can be performed since all the elements are odd. Thus, the answer is 0.

Sample Input 3

10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776

Sample Output 3

39

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn rec(nums: Vec<i32>, n: i32, count: i32, odd_num: i32) -> i32 {
    if odd_num == n {
        count
    } else {
        let mut div_count = 0;
        let mut maybe_div_num = Option::None;
        let mut new_odd_num = 0;
        let new_nums: Vec<i32> = nums.into_iter().map(|num| {
            if num % 2 == 1 {
                new_odd_num += 1;
                num
            } else if div_count != 0 {
                num
            } else {
                div_count += 1;
                let div_num = num / 2;
                maybe_div_num = Option::Some(div_num);
                maybe_div_num.unwrap()
            }
        }).collect();
        if let Some(div_num) = maybe_div_num {
            if div_num % 2 == 1 { new_odd_num += 1 }
        }
        rec(new_nums, n, count + 1, new_odd_num)
    }
}

fn main() {
    let _n: i32 = read();
    let nums: Vec<i32> = read_vec();
    let filtered_nums: Vec<i32> = nums.into_iter().filter(|num| num % 2 == 0).collect();
    let n = filtered_nums.len() as i32;
    println!("{}", rec(filtered_nums, n, 0, 0));
}