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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'pry'

N = gets.chomp.to_i
arr = gets.chomp.split(' ').map(&:to_i)

# 一つ以上偶数があれば操作可能
# 最大回数操作する為には、偶数はなるべくキープしたい
# 最初に見つけた偶数に対してのみ2で割る操作をして、あとは3倍
# ちなみに、最初に見つけた偶数の添え字が分かっているのであれば、そこより前はチェックしなくて良いはず

operable = true
count = 0

while operable
  even_found = false
  arr = arr.map do |num|
    if even_found
      num * 3
    else
      if num.even?
        even_found = true
        num / 2
      else
        num * 3
      end
    end
  end
  count += 1
  operable = false unless even_found
end

puts count