100692: [AtCoder]ABC069 C - 4-adjacent

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Score : $400$ points

Problem Statement

We have a sequence of length $N$, $a = (a_1, a_2, ..., a_N)$. Each $a_i$ is a positive integer.

Snuke's objective is to permute the element in $a$ so that the following condition is satisfied:

  • For each $1 ≤ i ≤ N - 1$, the product of $a_i$ and $a_{i + 1}$ is a multiple of $4$.

Determine whether Snuke can achieve his objective.

Constraints

  • $2 ≤ N ≤ 10^5$
  • $a_i$ is an integer.
  • $1 ≤ a_i ≤ 10^9$

Input

Input is given from Standard Input in the following format:

$N$
$a_1$ $a_2$ $...$ $a_N$

Output

If Snuke can achieve his objective, print Yes; otherwise, print No.


Sample Input 1

3
1 10 100

Sample Output 1

Yes

One solution is $(1, 100, 10)$.


Sample Input 2

4
1 2 3 4

Sample Output 2

No

It is impossible to permute $a$ so that the condition is satisfied.


Sample Input 3

3
1 4 1

Sample Output 3

Yes

The condition is already satisfied initially.


Sample Input 4

2
1 1

Sample Output 4

No

Sample Input 5

6
2 7 1 8 2 8

Sample Output 5

Yes

Input

题意翻译

## 题目描述 一个数列长为n。你的任务是将数列进行排列,使得当1 ≤ i ≤ N − 1 时,a[i]与a[i+1]的积是4的倍数。 请判断你是否能完成这个任务。 ## 输入格式 第一行包含一个正整数n,为数列的长度。 第二行包含n个正整数,为数列内的数。 ## 输出格式 如果你能完成这个任务,输出Yes,否则输出No。

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