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Time Limit: 2 sec / Memory Limit: 976 MB
配点: 300 点
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
- N は 1 以上 10 \ 000 以下の整数
- a_i は 1 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_1 を 3 倍し, a_2 を 3 倍し, a_3 を 2 で割る. すると数列は {15, 6, 2} となる.
- 次に, a_1 を 3 倍し, a_2 を 2 で割り, a_3 を 3 倍する. すると数列は {45, 3, 6} となる.
- 最後に, a_1 を 3 倍し, a_2 を 3 倍し, a_3 を 2 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