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.Scanner;

public class Main{

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
	    int N = sc.nextInt();
	   
	    
	    long m = 1;
	   
	    int count_4 =0;
	    int count_2=0;
	    int count_odd=0;
	    for (int i = 0; i<N; i++){
	    	m=sc.nextLong();
	    	if (m%4==0){
	    		count_4++;
	    	}
	    	else if (m%2==0){
	    		count_2++;
	    	}
	    	else 
	    		count_odd++;
	    }
	    sc.close();
	    
	    
	    if (count_odd==0)
	    	System.out.println("Yes");
	    
	    else if (count_2==0){
	    	if (count_4+1>=count_odd)
	    		System.out.println("Yes");
	    	else
	    		System.out.println("No");
	    }
	    else if (count_2!=0){
	    	if (count_4>=count_odd)
	    		System.out.println("Yes");
	    	else
	    		System.out.println("No");
	    }

	    else
	    	System.out.println("No");
	}

}