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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;

/**
 * ACB069
 * C - 4-adjacent
 */
public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line;
		String[] words;


		int N = parseInt(br.readLine());
		int[] c = new int[3];

		StringTokenizer st = new StringTokenizer(br.readLine());

		for (int i = 0; i < N; i++) {
			int a = parseInt(st.nextToken());
			if (a % 4 == 0) {
				c[2]++;
			} else if (a % 2 == 0) {
				c[1]++;
			} else {
				c[0]++;
			}
		}

		boolean ans = false;

		if (c[1] > 0) {
			if (c[2] >= c[0]) ans = true;
		} else {
			if (c[2] >= c[0] - 1) ans = true;
		}

		System.out.println(ans ? "Yes" : "No");
	}
}