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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<iostream>
#include<string>
#include<memory>
#include<cmath>
#include<algorithm>
#include<vector>
int main(){
    int length;
    std::cin>>length;

    
    std::vector<long long> vec(length);
    std::vector<int> judge(length);

    long long count=0;
    long long sum=0;
    long long flag=0;

    for(int i=0;i<length;i++) {
        std::cin>>vec[i];
        if(vec[i]%2==0) judge[i]=0;
        else{
            judge[i]=1;
            flag++;
        }
    }

    if(flag==0){
        std::cout<<0<<std::endl;
        return 0;
    }

    for(int i=0;i<length;i++){
        if(judge[i]==0){
            count=0;
            while(vec[i]%2!=1){
                vec[i]/=2;
                count++;
            }
            sum+=count;
        }
    }
    long long ans=sum;
    std::cout<<ans<<std::endl;
    return 0;
}