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.Scanner;

class Main{




	public static void main(String[] args) {


		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.nextInt();
		int[] a = new int[n];


		for(int i =0;i < n;i++){
			a[i] = sc.nextInt();
		}
		
		
		int f = 0;


		for(int i =0;i < n;i++){
			if(a[i] % 4 == 0){
				f++;		
			}
		}

		int t = 0;
		for(int i = 0;i < n;i++){
			if(a[i] % 4 != 0 && a[i] % 2 == 0){
				t ++;
			}
		}

		if(f >= (n-t)/2 ){
			System.out.println("Yes");
		}else{
			System.out.println("No");

		}
	}
}


