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 static java.lang.Integer.*;
import static java.lang.Long.*;
import static java.lang.Math.*;
import static java.lang.System.*;

import java.io.PrintWriter;

public class Main {
	public static void main(String[] args) {
		int i=0,j=0,k=0;
		Scanner sc = new Scanner(in);
		int n = parseInt(sc.next());
		int[] a = new int[n];
		int x2=0;
		int x4=0;
		for(i=0;i<n;i++) {
			a[i] = parseInt(sc.next());
			if(a[i]%4==0) {
				x4++;
				continue;
			}
			if(a[i]%2==0) {
				x2++;
				continue;
			}
		}
		sc.close();
		out.println(x2/2+x4>=n/2?"Yes":"No");
	}
}
