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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main(void)
{
	int f_num = 0;
    int odd_num = 0;
    int num;
    int diff_4num;
  
    scanf("%d", &num);
	for(int i = 0; i < num; i++)
	{
        int val;
        scanf("%d", &val);
        if(val % 4 == 0)
          f_num++;
        else if(val % 2 == 0)
          odd_num++;
	}
    num -= (odd_num / 2) * 2;
    diff_4num = abs(f_num - num);
  
    if(diff_4num == f_num + 1 || diff_4num % 2 == 0)
      puts("Yes");
    else 
      puts("No");
  
    return 0;
}