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 PHP (5.6.30) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d", $n);
$l2 = explode(' ', trim(fgets(STDIN)));

$cnt_multiples_of_4 = 0;
$cnt_2 = 0;
$cnt_other = 0;

for ($i = 0; $i < $n; $i++) {
  if ($l2[$i] % 4 == 0) {
    $cnt_multiples_of_4++;
    continue;
  }
  if ($l2[$i] % 2 == 0) {
    $cnt_2++;
    if ($cnt_2 > 1) {
      continue;
    }
  }
  $cnt_other++;
}

if ($cnt_other - 2 < $cnt_multiples_of_4) {
  $res = 'Yes';
} else {
  $res = 'No';
}
echo $res;