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.*;
class Main{
	public static void main(String[] args) {
		Scanner sn=new Scanner(System.in);
		int n=sn.nextInt();
		int a=0;
		int cnt=0;
		int cnt4=0;
		int cnt2=0;
		do{
			a=sn.nextInt();
			if(a%4==0)
				cnt4++;
			else if(a%2==0)
				cnt2++;
			cnt++;
	}while(cnt<n);
	cnt4+=cnt2/2;
		if(cnt4>=n/2)
			System.out.println("Yes");
		else
			System.out.println("No");
	}
}