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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
<?php
    fscanf(STDIN, "%d", $total);
    $input = trim(fgets(STDIN));
    $numbers = explode(" ", $input);
    $two = 0;
    $four = 0;
    for ($i = 0; $i < $total; $i++) {
        if (($numbers[$i] % 4) == 0) {
            $four++;
        } else {
            if (($numbers[$i] % 2) == 0) {
                $two++;
            }
        }
    }
    $output = "No\n";
    if (($two + ($four * 2)) >= ($total-1)) {$output = "Yes\n";}
	echo $output;
?>
