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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.math.*;
import java.util.*;
public class Main {
 
	public static void main(String[] args) {  
		Scanner input = new Scanner(System.in);
		int N = input.nextInt();
		int T = 0;
		int F = 0; //Two and four
		for (int i = 0; i < N; i++) {
			int x = input.nextInt();
			if (x%4==0) F++;
			else if (x%2==0) T++;
		}
		if (T>1) N-=T; //multiples of two can be joined as one contiguous sub-array since 2^2 = 4
		N-=3;
		F--;
		N-=F*2;
		System.out.println(N<=0?"Yes":"No");
	}
}