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) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] a = new long[n];
        int count4 = 0;
        int count2 = 0;
        int count22 = 0;
        for (int i = 0; i < a.length; i++) {
            a[i] = sc.nextLong();
            if(a[i] % 4 == 0) {
                count4++;
            } else if(a[i] == 2) {
                count2++;
            }
            if(a[i] % 4 == 0) {

            } else if(a[i] % 2 == 0) {
                count22++;
            }
        }

        double b = Math.ceil((n -1) / 2.0);
        double c = b - count4;
        if(b <= count4) {
            System.out.println("Yes");
        }
        else if(n == count2){
            System.out.println("Yes");
        }
        else if (count2 > c){
            System.out.println("Yes");
        }
//        else if(n == count22){
//            System.out.println("Yes");
//        }
        else if (count22 > c){
            System.out.println("Yes");
        }
        else {
            System.out.println("No");
        }
    }
}