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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

long a[100000] = {};

int main()
{
	long n;
	long x = 0, y = 0, z = 0;
	scanf("%ld", &n);
	for (long i = 0; i < n; i++)
	{
		scanf("%ld", &a[i]);
	}
	for (long i = 0; i < n; i++)
	{
		if (a[i] % 4 == 0)
		{
			x++;
		}
		else if (a[i] % 2 == 0)
		{
			y = 1;
		}
		else
		{
			z++;
		}
	}
	if ((x + 1) >= (z + y))
	{
		printf("Yes");
	}
	else
	{
		printf("No");
	}
	return 0;
}