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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//#include <conio.h>
#include <algorithm>
#include <vector>
#include <string>
#include <iostream>

using namespace std;

int main()
{
	int count4 = 0,count2 = 0;
	int n;
	cin >> n;
	string str = "No";
	int *arr = new int[n];
	for (int i = 0; i < n; i++)
		cin >> arr[i];
	if (n == 2)
	{

		if (arr[0] % 4 == 0 || arr[1] % 4 == 0 || ( arr[0] % 2 == 0 && arr[1] % 2 == 0))
			cout << "Yes";
		else cout << "No";
		return 0;
	}
	for (int i = 0; i < n; i++)
	{
		if (arr[i] % 4 == 0)
			count4++;
		if (arr[i] % 2 == 0 && arr[i] % 4 != 0)
			count2++;
	}
	if (n % 2 == 0){
		if (count4 >= n / 2 - count2 + 1)
			str = "Yes";
	}
	else{
		if (count4 >= n / 2 - 1 - count2 + 1)
			str = "Yes";
	}
	cout << str;
	//_getch();
	return 0;
}