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: Accepted)

#![allow(unused)]

use std::{cell, cmp, collections, convert, fmt, io, iter, ops, str};

use cell::{Cell, RefCell};
use cmp::Ordering::{Equal, Greater, Less};
use collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};
use io::{Read, Write};

#[cfg(feature = "debug")]
macro_rules! debug {
    ($($args: tt)*) => { eprint!($($args)*) };
}

#[cfg(feature = "debug")]
macro_rules! debugln {
    ($($args: tt)*) => { eprintln!($($args)*) };
}

#[cfg(not(feature = "debug"))]
macro_rules! debug {
    ($($args:tt)*) => {};
}

#[cfg(not(feature = "debug"))]
macro_rules! debugln {
    ($($args:tt)*) => {};
}

macro_rules! vmax {
    ($x: expr, $y: expr) => { cmp::max($x, $y) };
    ($x: expr, $($args: expr),*) => { cmp::max($x, vmax!($($args),*)) };
}

macro_rules! vmin {
    ($x: expr, $y: expr) => { cmp::min($x, $y) };
    ($x: expr, $($args: expr),*) => { cmp::min($x, vmin!($($args),*)) };
}

fn main() {
    let n = parse_line::<usize>();
    let a = parse_vec::<u32>();

    let pow2_cnt_sum = a.iter().map(|&e| pow2_cnt(e)).sum::<u32>();
    println!("{}", pow2_cnt_sum);
}

fn pow2_cnt(mut x: u32) -> u32 {
    let mut cnt = 0;

    while x != 0 && x % 2 == 0 {
        cnt += 1;
        x /= 2;
    }

    cnt
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test() {
        assert_eq!(pow2_cnt(0), 0);
        assert_eq!(pow2_cnt(2), 1);
        assert_eq!(pow2_cnt(5), 0);
        assert_eq!(pow2_cnt(12), 2);
        assert_eq!(pow2_cnt(65535), 0);
        assert_eq!(pow2_cnt(65536), 16);
    }
}

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_owned()
}

fn read_word() -> String {
    const CAPACITY: usize = 16;

    let mut stdin = io::stdin();
    let mut byte: [u8; 1] = [0];

    loop {
        let mut buf = Vec::with_capacity(CAPACITY);

        loop {
            let res = stdin.read(&mut byte);

            if res.unwrap_or(0) == 0 || byte[0] <= b' ' {
                break;
            } else {
                buf.push(byte[0]);
            }
        }

        if !buf.is_empty() {
            return String::from_utf8(buf).unwrap();
        }
    }
}

fn parse_line<T: str::FromStr>() -> T {
    read_line().parse().ok().unwrap()
}

fn parse_word<T: str::FromStr>() -> T {
    read_word().parse().ok().unwrap()
}

fn parse_vec<T: str::FromStr>() -> Vec<T> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn flush() {
    io::stdout().flush();
}

fn next_prime(x: i32) -> i32 {
    for i in (x + 1).. {
        if is_prime(i) {
            return i;
        }
    }

    panic!("attempt to add with overflow");
}

fn is_prime(x: i32) -> bool {
    let ceil = f64::from(x).sqrt().ceil() as i32;
    x == 2 || (2..(ceil + 1)).all(|i| x % i != 0)
}