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 in = new Scanner(System.in);
    int num = in.nextInt();
    int[] count = new int[3];
    while(in.hasNextInt()) {
      int tmp = in.nextInt() & 3;
      if ((tmp & 1) == 1) {
        count[0]++;
      } else if ((~tmp & 3) == 1) {
        count[1]++;
      } else {
        count[2]++;
      }
    }
    String ans = "Yes";
    int t = count[1] > 0 ? 1 : 0;
    if (count[2] + 1 < count[0] + t) ans = "No"; 
    System.out.println(ans);
  }
}