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.Scanner;
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int count1 = 0;
    int count4 = 0;
    for(int i = 0; i<n; i++) {
      int a = sc.nextInt();
      if(a % 2 == 1) {
        count1++;
      }else if(a % 4 == 0) {
        count4++;
      }
    }
    if((n%2 == 1) && (count1 == n/2+1) && (count4 == n/2)) System.out.println("Yes");
    else if(count1 <= count4) System.out.println("Yes");
    else System.out.println("No");
  }
}