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.util.Scanner;

public class Main {
    static int n;
    static int[] g;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();

        int multiple2 = 0;
        int multiple4 = 0;
        int other= 0;
        for (int i = 0; i < n; i++) {
            int num = sc.nextInt();
            if (num % 4 == 0) {
                multiple4++;
            } else if (multiple2 % 2 == 0) {
                multiple2++;
            } else {
                other++;
            }
        }
        if (multiple4 * 2 < other || (multiple2 < 2 && (multiple4 * 2 - other) < 1)) {
            System.out.println("No");
        } else {
            System.out.println("Yes");
        }
    }
}