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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import Data.List
import Data.Bits
import Debug.Trace
import Data.Maybe
import qualified Data.ByteString.Char8 as C

main :: IO ()
main = do
  [n] <- readInts
  input <- readInts
  print $ solve input

solve :: [Int] -> Int
solve = foldr (\x a-> (get2p x 0) + a) 0
  where
    get2p n p = if n `rem` 2 == 0
      then get2p (n `div` 2) (p + 1)
      else p

-- 以下ライブラリ

readInts :: IO [Int]
readInts = map (fst . fromJust . C.readInt) . C.words <$> C.getLine

readNInts :: Int -> IO [[Int]]
readNInts = flip replicateM readInts

readIntegers :: IO [Integer]
readIntegers = map (fst . fromJust . C.readInteger) . C.words <$> C.getLine

readNIntegers :: Int -> IO [[Integer]]
readNIntegers = flip replicateM readIntegers

getNLns :: Int -> IO [String]
getNLns = flip replicateM getLine

toTup2 :: [[a]] -> [(a, a)]
toTup2 = map (\ys -> case ys of y : z : zs -> (y, z))

encIdx2 :: Int -> (Int, Int) -> Int
encIdx2 mx (y, x) = y * mx + x

decIdx2 :: Int -> Int -> (Int, Int)
decIdx2 mx idx = (idx `div` mx, idx `mod` mx)

encIdx3 :: (Int, Int) -> (Int, Int, Int) -> Int
encIdx3 (my, mx) (z, y, x) = z * my * mx + y * mx + x

decIdx3 :: (Int, Int) -> Int -> (Int, Int, Int)
decIdx3 (my, mx) idx = (z, y, x)
  where
    basez = my * mx
    z = idx `div` basez
    y = (idx `mod` basez) `div` mx
    x = idx `mod` mx

while :: Monad m => m Bool -> m () -> m ()
while cond body = do
  b <- cond
  when b $ do
    body
    while cond body