Score: $300$ points

问题描述

当 AtCoder 初级比赛第100场正在进行时，AtCoder, Inc. 的办公室被一个长度为 $N$ 的序列 $a = ${$a_1, a_2, a_3, ..., a_N$} 装饰着。
Snuke，一名员工，想要玩弄这个序列。

具体来说，他想尽可能多地重复以下操作：

对于满足 $1 \leq i \leq N$ 的每一个 $i$，执行以下之一：“将 $a_i$ 除以 $2$”和“将 $a_i$ 乘以 $3$”。  
这里，不允许对每一个 $i$ 都选择“将 $a_i$ 乘以 $3$”，且操作后 $a_i$ 的值必须是整数。

最多可以进行多少次操作？

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 17:18:39