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();
    long[] a = new long[N];
    int con4 =0, con2 =0;
    for (int i =0; i<N; i++) {
      a[i] = sc.nextLong();
      if (a[i] % 4 ==0) {
        con4++;
      } else if (a[i] % 2 ==0) {
        con2++;
      }
    }
    if (N % 2 == 0) {
      if (con4 * 2 + con2 >= N) {
        System.out.print("Yes");
      } else {
        System.out.print("No");
      }
    }
    if (N % 2 == 1) {
      if (con4 * 3 + con2 >= N) {
        System.out.print("Yes");
      } else {
        System.out.print("No");
      }
    }
  }
}