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.util.Scanner;

public class Main {

    public static void main(String[] args) {
	Main m = new Main();
	m.answer();
    }

    private Scanner scan = new Scanner(System.in);
    private int N;
    private int[] count;

    public Main() {
	N = Integer.parseInt(scan.next());
	count = new int[3];
	for (int i = 0; i < N; i++) {
	    int a = Integer.parseInt(scan.next());

	    if(a%4 == 0) count[0]++;
	    else if(a%2 == 0) count[1]++;
	    else count[2]++;
	}
	scan.close();
    }

    public final void answer() {
	int hoge = count[2] - count[0];
	String ans = "Yes";

	if(hoge == 1 && count[1] > 0) ans = "No";
	else if(hoge >= 2) ans = "No";

	System.out.println(ans);
    }
}