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.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner((System.in));
		int N = sc.nextInt();
		int[] n = new int[N + 1];
		String ans = "No";
		int c4 = 0, c2 = 0;

		for (int i = 0; i < N; i++) {
			n[i] = sc.nextInt();
			if (n[i] % 4 == 0) {
				c4++;
			} else if (n[i] % 2 == 0) {
				c2++;
			}
		}

		if (c2 == N) {
			ans = "Yes";
		} else {
			if (c2 >= 2) {
				N -= c2;
				if ((N % 2) == 0 && (N / 2) == c4) {
					ans = "Yes";
				} else if ((N % 2) != 0 && (c4 * 2) >= (N + 1)) {
					ans = "Yes";
				}
			} else {
				if ((N % 2) == 0 && (N / 2) == c4) {
					ans = "Yes";
				} else if ((N % 2) != 0 && (c4 * 2) >= (N - 1)) {
					ans = "Yes";
				}
			}
		}

		System.out.println(ans);

		sc.close();
	}
}