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: Runtime Error)

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

void main(int argc, char const *argv[])
{
  int n;
  scanf("%d", &n);
  int *m = (int *)malloc(sizeof(int) * n);
  int mod2 = 0, mod4 = 0, zero = 0;
  int i = 0;
  int tmp;
  while (n-- > 0)
  {
    scanf("%d", &tmp);
    if (tmp % 4 == 0)
    {
      mod4++;
    }
    else if (tmp % 2 == 0)
    {
      mod2++;
    }
    else
    {
      zero++;
    }
  }
  if (mod4 + 1 >= zero && mod2 > 1)
  {
    printf("Yes");
  }
  else
  {
    printf("No");
  }

  return;
}