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.*;
import java.lang.*;

// class Pair implements Comparable<Pair>{
//   long a;
//   int cnt;
//   public Pair(long i, int j){
//     this.a = i;
//     this.cnt = j;
//   }
//   public int compareTo(Pair p){
//     if(this.cnt>=2 && p.cnt >=2 && this.a<p.a) return -1;
//     if(this.cnt<2 && p.cnt>=2) return -1;
//     return 1;
//   }
// }

class Main{
  public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      int cnt4 = 0;
      int cnt2 = 0;
      int odd = 0;
      int N = Integer.parseInt(sc.next());
      for(int i = 0; i<N; i++){
        long a = Long.parseLong(sc.next());
        if(a%2 == 0){
          a/= 2;
          if(a%2 == 0) cnt4++;
          else cnt2++;
        }
        else odd++;
      }
      if(cnt2==0 && odd <= cnt4+1) System.out.println("Yes");
      else if(cnt2>0 && odd<=cnt4) System.out.println("Yes");
      else System.out.println("No");

  }
}