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.IOException;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int a;
		int nCnt = 0;
		int n2Cnt = 0;
		int n4Cnt = 0;
		boolean judge = false;

		for (int i=0; i<N; i++){
			a = sc.nextInt();
			if (a % 4 == 0){
				n4Cnt++;
			} else if (a % 2 == 0){
				n2Cnt++;
			} else {
				nCnt++;
			}
		}

		if (nCnt == 0) {
			judge = true;
		} else {
			if (nCnt <= n4Cnt){
				judge = true;
			} else if (nCnt +1 == n4Cnt){
				if (n2Cnt == 0){
					judge = true;
				}
			}
		}

		if (judge){
			System.out.println("Yes");
		} else {
			System.out.println("Yes");
		}

	}

}