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 (1.42.0) (judge verdict: Accepted)

use proconio::input;


fn factorize(mut base: i64) -> Vec<(i64, i64)> {
    let mut fs = Vec::<(i64, i64)>::new();
    let mut i: i64 = 2;

    while i*i <= base {
        if base % i == 0 {
            let mut cnt: i64 = 0;

            while base % i == 0 {
                base /= i;
                cnt += 1;
            }
            fs.push((i, cnt));
        }
        i += 1;
    }

    if base > 1 {
        fs.push((base, 1));
    }

    return fs;
}


fn main() {
    input! {
        n: i32,
        a: [i64; n],
    }

    let mut ans = 0;

    for ai in a {
        for (i, c) in factorize(ai) {
            if i == 2 {
                ans += c;
            }
        }
    }

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