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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
import java.util.*;
public class Main {
	public static void main(String[] args)  {
		Scanner scan = new Scanner(System.in);
		int n = Integer.parseInt(scan.next());scan.nextLine();
		int a;
		int count_2 = 0;
		int count_4 = 0;
		int tmp;
		for (int i = 0;i < n; ++i){
			tmp =0;
			a = Integer.parseInt(scan.next());
			for (int k = 0;k < 2; ++k){
				if (a%2==0)++tmp;
				else break;
				a=a>>1;
			}
			if (tmp==2)++count_4;
			else if (tmp==1)++count_2;
		}
		if (count_4>=(n-(count_2/2)*2)/2 && count_2>=n-count_4*3){
			System.out.print("Yes");
		}else{
			System.out.print("No");
		}


	}
}
//end
