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
error_reporting(0);
$stdin = file_get_contents('php://stdin');
$line = explode("\n",$stdin);
$fi = 0;
$cnt = 0;
$list = array();
$key = new stdclass();
foreach($line as $l) {
  if (strlen($l)==0) continue;
  if ($fi == 0) {
    $a = explode(" ",$l);
    $key->A = $a;
    $fi++;
    continue;
  }
  if ($fi > 0) {
    $a = explode(" ",$l);
    $key->X[] = $a;
  }
}
$N = $key->A[0];
$c1=0;
$c2=0;
$c4=0;
foreach($key->X[0] as $v) {
  $c = $v % 4;
  switch($c) {
  case 1:
  case 3:
    $c1++;
    break;
  case 0:
    $c4++;
    break;
  case 2:
   $c2++;
   break;
  }
}
$flg = false;
if ($c2 == 0) {
  if ($c1 <= $c4+1) {
    $flg = true;
  }
  else {
    $flg = false;
  }
}
else {
  if ($c1 <= $c4) {
    $flg = true;
  }
  else {
    $flg = false;
  }
}
printf("%s\n",$flg?"Yes":"No");