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: Accepted)

import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.nextLine());
        String[] input = sc.nextLine().split(" ");
        int co4 = 0;
        int co2 = 0;
        int co1 = 0;
        int[] num = new int[N];

        for(int i=0; i<N; i++){
            num[i] = Integer.parseInt(input[i]);
        }
        for(int i=0; i<N; i++){
            if(num[i] % 4 == 0){
                co4++;
            }
            else if(num[i] % 2 == 0){
                co2++;
            }
            else{
                co1++;
            }
        }
        if(co2 == 0){
            if(co4 + 1 >= co1){
                System.out.println("Yes");
            }
            else{
                System.out.println("No");
            }
        }
        else{
            if(co4 >= co1){
                System.out.println("Yes");
            }
            else{
                System.out.println("No");
            }
        }
    }
}