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.

3
5 2 4

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 ${135, 9, 3}$.

4
631 577 243 199

0

No operation can be performed since all the elements are odd. Thus, the answer is $0$.

10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776

39