<p>You are given <code>nums</code>, an array of positive integers of size <code>2 * n</code>. You must perform <code>n</code> operations on this array.</p>

<p>In the <code>i<sup>th</sup></code> operation <strong>(1-indexed)</strong>, you will:</p>

<ul>
	<li>Choose two elements, <code>x</code> and <code>y</code>.</li>
	<li>Receive a score of <code>i * gcd(x, y)</code>.</li>
	<li>Remove <code>x</code> and <code>y</code> from <code>nums</code>.</li>
</ul>

<p>Return <em>the maximum score you can receive after performing </em><code>n</code><em> operations.</em></p>

<p>The function <code>gcd(x, y)</code> is the greatest common divisor of <code>x</code> and <code>y</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2]
<strong>Output:</strong> 1
<strong>Explanation:</strong>&nbsp;The optimal choice of operations is:
(1 * gcd(1, 2)) = 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,4,6,8]
<strong>Output:</strong> 11
<strong>Explanation:</strong>&nbsp;The optimal choice of operations is:
(1 * gcd(3, 6)) + (2 * gcd(4, 8)) = 3 + 8 = 11
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6]
<strong>Output:</strong> 14
<strong>Explanation:</strong>&nbsp;The optimal choice of operations is:
(1 * gcd(1, 5)) + (2 * gcd(2, 4)) + (3 * gcd(3, 6)) = 1 + 4 + 9 = 14
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 7</code></li>
	<li><code>nums.length == 2 * n</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution:
    def maxScore(self, nums: List[int]) -> int:
        def gcd(a:int, b:int):
            if a==0 or b==0:
                return max(a, b)
            if a>b:
                return gcd(a%b, b)
            return gcd(b%a, a)
        
        n = len(nums)
        gcds = [[gcd(nums[i], nums[j]) for j in range(n)] for i in range(n)]
        dp_len = 1<<n
        dp = [-1 for mask in range(dp_len)]
        def rec(mask:int, multiplier:int):
            print(mask)
            if mask == dp_len:
                return 0
            if dp[mask]!= -1:
                return dp[mask]
            
            take = 0
            for i in range(n):
                if not(1<<i & mask):
                    for j in range(i+1, n):
                        if not(1<<j & mask):
                            mask = mask | 1<<i | 1<<j
                            take = + max(take,  multiplier*gcds[i][j] + rec(mask, multiplier-1))
                            mask = mask ^ 1<<i ^ 1<<j
            
            dp[mask] = take
            return take

        return rec(0, n//2)
20000