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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
  $n = trim(fgets(STDIN));
  $a = explode(" ", trim(fgets(STDIN)));
  $count = 0; $two=0;
  for($i=0; $i<$n; $i++){
      if($a[$i]%4 == 0){
          $count++;
          continue;
      }else if($a[$i]%2 == 0){
          $two++;
      }
  }
  if($two > 0) $two--;
  if($n-$two == 1){
      echo "Yes";
      exit;
  }
  echo $count >= (int)(($n-$two)/2) ? "Yes" : "No";