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) {
		new Main().solve();
	}
	
	void solve(){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] a=new int[n];
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
		}
		int[]b=new int[n];
		for(int i=0;i<n;i++){
			b[i]=check(a[i]);
		}
		int count2=0;
		int count1=0;
		int count0=0;
		for(int i=0;i<n;i++){
			if(b[i]==2)count2++;
			else if(b[i]==1)count1++;
			else if(b[i]==0)count0++;
		}
		if(count1==0){
			if(count2>=count0-1){
				System.out.println("Yes");
			}else{
				System.out.println("No");
			}
		}
		else{
			if(count2>=count0){
				System.out.println("Yes");
			}else{
				System.out.println("No");
			}
		}
	}
	int check(int n){
		int ret=0;
		while(true){
			if(ret>=2){
				return ret;
			}
			if(n%2==0){
				n/=2;
				ret++;
			}else{
				break;
			}
		}
		return ret;
	}
}