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 Adjacent {
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    int n = scan.nextInt();
    if (2 <= n && n <= 1.0e5) {
      int[] sunukenoaho = new int[n];
      for (int i = 0; i < n ; i++) {
        sunukenoaho[i] = scan.nextInt();
        sunukenoaho[i] = sunukenoaho[i] % 4;
      }
      int sum = 0;
      for (int i = 1; i < n; i++) {
        if (sunukenoaho[i] * sunukenoaho[i - 1] % 4 == 0) {
          sum++;
        }
      }

      if (sum == n - 1) {
        System.out.println("Yes");
      } else {
        System.out.println("No");
      }
    }


  }
}
