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 cnt = 0;
      int a = 0;
      for(int i = 0;i < n;i++){
        int x = sc.nextInt();
        while(x%2==0&&a <=1){
          cnt++;
          a++;
          x =x/2;
        }
        a=0;
      }
      if(n%2==0){
      	if(cnt >= n)System.out.println("Yes");
      	else System.out.println("No");
      }else{
      	if(cnt >= n-1)System.out.println("Yes");
        else System.out.println("No");
      }
    }
}
