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 sc = new Scanner(System.in);
        int n = sc.nextInt();

        int even4 = 0;
        int even2 = 0;
        int odd = 0;

        for (int i = 0 ; i < n; i++) {
            int num = sc.nextInt();

            if (num % 4 == 0) {
               even4++;
            } else if (num % 2 == 0) {
                even2++;
            } else {
                odd++;
            }
        }

        if (even2 != 0) {
            odd++;
        }

        String ans = (even4 >= odd - 1) ? "Yes" : "No";

        System.out.println(ans);

    }

}
