<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:
        n = len(nums) // 2
        num2mask = {i:(1<<i) for i in range(len(nums))}
        def gcd(a,b):
            a,b = max(a,b), min(a,b)
            while a % b > 0:
                a,b = b,a%b
            return b
        if len(nums) == 2:
            return gcd(nums[0], nums[1])
        pairs = []
        for i in range(len(nums)):
            imask = num2mask[i]
            for j in range(i+1, len(nums)):
                jmask = num2mask[j]
                pairs.append([gcd(nums[i], nums[j]), imask|jmask])
        pairs.sort(reverse=True, key=lambda x:x[0])
        max_score = 0
        for p1 in pairs:
            state, scores = p1[1], [p1[0]]
            for p2 in pairs:
                if not p2[1] & state:
                    state |= p2[1]
                    scores.append(p2[0])
                if len(scores) == n:
                    break
            if len(scores) < n:
                continue
            scores = sorted(scores)
            max_score = max(max_score, sum([(i+1)*scores[i] for i in range(n)]))
        return max_score
64