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
$n = trim(fgets(STDIN));
$a = explode(" ",trim(fgets(STDIN)));
$i = 0;
$o = 0;
$ee = 0;
while($i < $n){
if($a[$i] % 2 == 1){
++$o;
}elseif($a[$i] % 4 == 0){
++$ee;
}
++$i;
}
 
if($o <= $ee){
echo "Yes";
}elseif($o == $ee + 1){
if($o + $ee == $n){
echo "Yes";
}else{
echo "No";
}
}else{
echo "No";
}