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;

public class Main {

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();

			int num4 = 0;
			int num2 = 0;
			for(int i = 0; i < n; i++) {
				int tmp = sc.nextInt();
				if (tmp % 4 == 0) {
					num4++;
				} else if (tmp % 2 == 0) {
					num2++;
				}
			}

			int result = n - num4 * 2;
			result -= num2;
			if (n % 2 == 1) {
				result--;
			}

			if (0 < result) {
				System.out.println("No");
			} else {
				System.out.println("Yes");
			}
		}
	}
}