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 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
// warm-up
public class Main {

	static void solve() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(), i = 0, k = n/2, t = 2;
		boolean ok = false;
		while (n-->0) {
			int a = sc.nextInt();
			if (a==2) t--;
			if (a%4==0) k--;
			if (t==0) { t=2; k--; }
			if (k==0) { ok = true; break; }
		}
		System.out.println(ok ? "Yes" : "No");
		sc.close();		
	}

	public static void main(String args[]) {
		solve();
	}

}