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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>){
    val N = readLine()!!.toInt()
    var a: Array<Int> = readLine()!!.split(' ').map { it -> it.toInt() }.toTypedArray()

    val e = a.filter { it -> it!! % 2 == 0 }
    var size = e.size
    var ea: Array<Int?> = arrayOfNulls(size)
    for (j in 0 until size){
        ea[j] = e.get(j)
    }

    size = ea.size

    ea.sort()
    var p2c = 0
    for (k in size downTo  1) {
        while (ea[k - 1]!! % 2 == 0) {
            p2c++
            ea[k - 1] = ea[k - 1]!! / 2
        }
        for (l in 0 until p2c){
            if (k != 1){
                ea[k - 2] = ea[k - 2]!! * 3
            }else{
                break
            }
        }
    }

    println(p2c)
}