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.*;
import java.math.*;


public class Main {

public static void main(String[] args) {

   Scanner in = new Scanner(System.in);

   int N = in.nextInt();
   int A = 0;// 4で割り切れる数
   int B = 0;// 2で割り切れる数
   int C = 0;// 1
   int D = 0;// 上記以外

   for(int cnt = 0; cnt < N; cnt++){
       int num = in.nextInt();
       if(num % 4 == 0){
           A++;
       }
       else if(num % 2 == 0){
           B++;
           if(B % 2 == 0){
               B = B - 2;
               A++;
           }
       }
       else{
           C++;
       }
   }
   //2nが偶数個
   if(A >= N / 2){
       System.out.println("Yes");
   }
   else{
       System.out.println("No");
   }
   in.close();
}}