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.*;
class Main{
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] a = new int[n];
        int even = 0;
        int four = 0;
        int odd = 0;
        for(int i = 0; i < n; i++){
            a[i] = scanner.nextInt();
            if(a[i] % 4 == 0){
                four++;
            }else if(a[i] % 2 == 0){
                even++;
            }else if(a[i] % 2 == 1){
                odd++;
            }
        }
        //System.out.println(" even : " + even + " four : " + four + " odd : " + odd);
        if((four >= odd-1 && even == 0) || (four >= odd && even % 2 == 1) || (four == odd && even%2 == 0)){
            System.out.println("Yes");
            return;
        }else{
            System.out.println("No");
            return;
        }
    }
}