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{
  public static void main(String[] args){
    Scanner scanner = new Scanner(System.in);
    int N = scanner.nextInt();
    int[] a = new int[N];
    int[] count = new int[3];
    for (int i = 0; i < N; i++){
      a[i] = scanner.nextInt();
    }
    for (int i = 0; i < N; i++){
      if (a[i] % 4 == 1 || a[i] % 4 == 3){
        count[0]++;
      } else if (a[i] % 4 == 2){
        count[1]++;
      } else if (a[i] % 4 == 0){
        count[2]++;
      }
    }
    if (N >= 4) {
        if (count[0] == count[2] || count[0] < count[2]){
          System.out.println("Yes");
        } else {
          System.out.println("No");
        }
    }
    if (N == 3){
      if (count[0] == 2 & count[2] == 1){
        System.out.println("Yes");
      } else if (count[0] == 1 & count[1] == 1 & count[2] == 1){
        System.out.println("Yes");
      } else if (count[0] == 1 & count[2] == 2){
        System.out.println("Yes");
      } else if (count[0] == 0){
        System.out.println("Yes");
      } else if (count[1] == 3){
        System.out.println("Yes");
      } else {
        System.out.println("No");
      }
    }
    if (N == 2){
      if (count[0] == 0){
        System.out.println("Yes");
      } else if (count[0] == 1 & count[2] == 1){
        System.out.println("Yes");
      } else if (count[1] == 1 & count[2] == 1){
        System.out.println("Yes");
      } else {
        System.out.println("No");
      }
    }
  }
}