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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) {
        try {
            // 標準入力
            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            int n = Integer.parseInt(br.readLine());
            int count2 = 0;
            int count4 = 0;
            String strArr[] = br.readLine().split(" ");
            for (int i = 0; i < n; i++) {
                long temp = Long.parseLong(strArr[i]);
                if (temp % 4 == 0) {
                    count4++;
                } else if (temp % 2 == 0) {
                    count2++;
                }
            }
            if (count2 > 1) {
                n = n - (count2 - 1);
            }
            n = n / 2;
            n -= count4;
            if (n > 0) {
                System.out.println("No");
            } else {
                System.out.println("Yes");
            }
        } catch (IOException e) {
            e.printStackTrace();
           }
    }
}
