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

ini_set('error_reporting', E_ALL & ~E_NOTICE & ~E_WARNING);
ini_set('display_errors', 'Off');

// define('DEBUG', true);
define('DEBUG', false);

fscanf(STDIN, "%d", $N);
$a = explode(" ", trim(fgets(STDIN)));

$odd = $even = $half = 0;

for ($i = 0; $i < $N; $i++) {
    switch ($a[$i] % 4) {
        case 1:
            $odd++;
            break;
        case 0:
            $even++;
            break;
        case 3:
            $odd++;
            break;
        case 2:
            $half++;
            break;
    }
}

if ($half == 0) {
    if ($odd <= $even + 1) {
        echo "Yes\n";
    } else {
        echo "No\n";
    }
} else {
    if ($odd <= $even) {
        echo "Yes\n";
    } else {
        echo "No\n";
    }
}