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_imports)]
#![cfg_attr(feature = "cargo-clippy", allow(redundant_field_names))]

use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{self, BufWriter, Read, Write};
use std::ops::{Add, Div, Mul, Sub};
use std::str::{self, FromStr};
use std::{cmp, fmt};

fn main() {
    let a_s: Vec<u64> = {
        let mut sc = InputScanOnce::new(io::stdin(), 1024);
        let n = sc.next();
        sc.vec(n)
    };
    let r = a_s.into_iter().map(|a| a.trailing_zeros()).sum::<u32>();
    println!("{}", r);
}

struct InputScanOnce {
    buf: Vec<u8>,
    pos: usize,
}

#[allow(dead_code)]
impl InputScanOnce {
    fn new<R: Read>(mut reader: R, estimated: usize) -> Self {
        let mut buf = Vec::with_capacity(estimated);
        let _ = io::copy(&mut reader, &mut buf).unwrap();
        InputScanOnce { buf: buf, pos: 0 }
    }

    #[inline]
    fn next<T: FromStr>(&mut self) -> T
    where
        T::Err: fmt::Debug,
    {
        let mut start = None;
        loop {
            match (self.buf[self.pos], start.is_some()) {
                (b' ', true) | (b'\n', true) => break,
                (_, true) | (b' ', false) | (b'\n', false) => self.pos += 1,
                (_, false) => start = Some(self.pos),
            }
        }
        let target = &self.buf[start.unwrap()..self.pos];
        unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where
        T::Err: fmt::Debug,
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<T1: FromStr, T2: FromStr>(&mut self, n: usize) -> Vec<(T1, T2)>
    where
        T1::Err: fmt::Debug,
        T2::Err: fmt::Debug,
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<T1: FromStr, T2: FromStr, T3: FromStr>(&mut self, n: usize) -> Vec<(T1, T2, T3)>
    where
        T1::Err: fmt::Debug,
        T2::Err: fmt::Debug,
        T3::Err: fmt::Debug,
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
    where
        T::Err: fmt::Debug,
    {
        (0..m).map(|_| self.vec(n)).collect()
    }

    fn strings_as_mat<T, F: FnMut(u8) -> T>(&mut self, h: usize, mut f: F) -> Vec<Vec<T>> {
        (0..h)
            .map(|_| {
                let l = self.next::<String>();
                l.as_bytes().iter().cloned().map(&mut f).collect()
            })
            .collect()
    }
}