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.*;
class Main{
  public static void main(String[] args){
    Scanner scan=new Scanner(System.in);
    int N=scan.nextInt();
    int[] a=new int[N];
    for(int i=0;i<N;i++){
      a[i]=scan.nextInt();
    }
    int count4=0;
    int count2=0;
    for(int i=0;i<N;i++){
      if(a[i]%4==0){
        count4++;
      }
      else if(a[i]%2==0){
        count2++;
      }
    }

    if(count4>=N/2){
      System.out.println("Yes");
    }
    else if(N-count2-count4==count4){
      System.out.println("Yes");
    }else if(count2==N){
      System.out.println("Yes");
    }
    else{
      System.out.println("No");
    }
  }
}