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) throws Exception {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        
        long[] a = new long[N];

        int x4 = 0;
        int ki = 0;
        for(int i=0; i<N; i++) {
            a[i] = Long.parseLong(sc.next());
            if(a[i] % 4 == 0) {
                x4++;
            }else if(a[i] % 2 == 0) {
                continue;
            }else {
                ki++;
            }
        }
        if(x4 >= ki) System.out.println("Yes");
        else if(x4 == N/2 && ki == N/2+1) System.out.println("Yes");
        else System.out.println("No");
        
        
    }
}
