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
public class Main {
    private static java.util.Scanner scanner = new java.util.Scanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt();
        int c = 0, c2 = 0, c4 = 0;
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            if ((a[i] = scanner.nextInt()) % 4 == 0) c4++;
            else if (a[i] % 2 == 0) c2++;
            else c++;
        }

        System.out.println(c - (c2 == 0 ? 1 : 0) <= c4 ? "Yes" : "No");
    }
}