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.*;
// warm-up
public class Main {

	static void solve() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(), k = n/2, t = 2;
		boolean ok = false;
		while (n-->0) {
			int a = sc.nextInt();
			if (a%4==0) k--;
			else if ((a&1)==0) t--;
			if (t==0) { t=2; k--; }
			if (k==0) { ok = true; break; }
		}
		System.out.println(ok ? "Yes" : "No");
		sc.close();		
	}

	public static void main(String args[]) {
		solve();
	}

}