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.io.*;
import java.util.*;

class Main{
	public static void main(String[] args){
		solve();
	}
	public static 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[] num = new int[3];
		for(int i=0;i<n;i++){
			if(a[i]%4==0){
				num[0]++;
			}
			else if(a[i]%2==0){
				num[1]++;
			}
			else{
				num[2]++;
			}
		}
		if(num[2]>num[0] && num[1]!=0){
			System.out.println("No");
		}
		else if(num[2]!=0 && num[0]==0){
			System.out.println("No");
		}
		else{
			System.out.println("Yes");
		}
	} 
}