C - *3 or /2

Time Limit: 2 sec / Memory Limit: 1000 MB

配点: 300

問題文

AtCoder Beginner Contest 100 の開催にともなって, AtCoder 社では長さ N の数列 a = {a_1, a_2, a_3, ..., a_N} が飾られることになった.
社員のすぬけ君は, この数列で遊んでみようと思った.

具体的には, 以下の操作をできるだけ多くの回数繰り返そうと思った.

1 \leq i \leq N を満たす全ての i に対して, それぞれ「a_i の値を 2 で割る」「a_i の値を 3 倍する」のどちらかを行う.  
ただし, 全ての i に対して 3 倍することはできず, 操作後の a_i の値は整数でなければならない.  

最大で何回の操作が可能か, 求めなさい.

制約

  • N1 以上 10 \ 000 以下の整数
  • a_i1 以上 1 \ 000 \ 000 \ 000 以下の整数

入力

入力は以下の形式で標準入力から与えられる.

N
a_1 a_2 a_3 ... a_N

出力

すぬけ君が行える最大の操作回数を出力しなさい.


入力例 1

3
5 2 4

出力例 1

3

最初, 数列は {5, 2, 4} であるが, 以下のように操作すれば 3 回の操作を行うことができる.

  • 最初に, a_13 倍し, a_23 倍し, a_32 で割る. すると数列は {15, 6, 2} となる.
  • 次に, a_13 倍し, a_22 で割り, a_33 倍する. すると数列は {45, 3, 6} となる.
  • 最後に, a_13 倍し, a_23 倍し, a_32 で割る. すると数列は {135, 9, 3} となる.

入力例 2

4
631 577 243 199

出力例 2

0

全ての要素が奇数なので, 操作はできない. よって答えは 0 である.


入力例 3

10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776

出力例 3

39

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