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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;


public class Main {
    static int answer;
    static int N;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = Integer.parseInt(sc.nextLine());
        String[] str = sc.nextLine().split("[\\s]+");
        int[] inputs = new int[N];
        answer = 0;

        for(int i = 0; i < N; i++) {
          inputs[i] = Integer.parseInt(str[i]);
        }
        hoge(inputs,0);
        System.out.println(answer);
    }

    public static void hoge(int[] inputs,int count) {
      int[] w = new int[N];
      boolean check = true;
      for(int i =0; i < N; i++) {
        w[i] = inputs[i] * 3;
      }
      for(int i = 0; i < N; i++) {
        if(inputs[i] % 2 == 0) {
          check = false;
          w[i] = inputs[i] / 2;
          hoge(w,count+1);
          return;
        }
      }
      if(check && answer < count) {
        answer = count;
      }
    }
}