Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3
1 10 100

Sample Output 1

Yes

One solution is (1, 100, 10).

Sample Input 2

4
1 2 3 4

Sample Output 2

No

It is impossible to permute a so that the condition is satisfied.

Sample Input 3

3
1 4 1

Sample Output 3

Yes

The condition is already satisfied initially.

Sample Input 4

2
1 1

Sample Output 4

No

Sample Input 5

6
2 7 1 8 2 8

Sample Output 5

Yes

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int[] a = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = scan.nextInt();
        }
        int odd = 0;
        int four = 0;
        for (int i = 0; i < N; i++) {
            if (a[i] % 2 == 1) {
                odd += 1;
            }
            if (a[i] % 4 == 0) {
                four += 1;
            }
        }
        if (N == 2) {
            if (four == 1) {
                System.out.println("Yes");
            } else if (odd == 1) {
                System.out.println("No");
            } else {
                System.out.println("Yes");
            }
            return;
        }
        if (N == 3) {
            if (2 < odd) {
                System.out.println("No");
            } else if (odd == 2 && 1 <= four) {
                System.out.println("Yes");
            } else if (odd == 1 && 1 <= four) {
                System.out.println("Yes");
            } else {
                System.out.println("Yes");
            }
            return;
        }
        if (2 < odd) {
            System.out.println("No");
        } else if (odd == 2 && 2 <= four) {
            System.out.println("Yes");
        } else if (odd == 1 && 1 <= four) {
            System.out.println("Yes");
        } else {
            System.out.println("Yes");
        }
    }
}