Problem:
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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){
			
			int N = scan.nextInt();
			int[]a = new int[N];
			int kiko = 0;
			int yon = 0;
			for(int i = 0;i<N;i++) {
				a[i] = scan.nextInt();
				if(a[i]%2==1)kiko++;
				if(a[i]%4==0)yon++;
			}
			
			int kisu = N/2+N%2;//kisu個より多い奇数があったらダメ
			
			if(kiko>kisu) {
				System.out.println("No");
			}else{//限界より小さい奇数の数
				if(kisu==0) {
					System.out.println("Yes");
				}else {
					if(N%2==1&&kiko==N/2+1) {
						if(yon+1==kiko)System.out.println("Yes");
						else System.out.println("No");
					}else{
						if(yon>=kiko)System.out.println("Yes");
						else System.out.println("No");
					}
				}
				
			}
			
		}
		
		
	}
		

}