Maximize Score After N Operations
<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>
Bit Manipulation; Array; Math; Dynamic Programming; Backtracking; Bitmask; Number Theory
func maxScore(nums []int) int {
	m := len(nums)
	g := [14][14]int{}
	for i := 0; i < m; i++ {
		for j := i + 1; j < m; j++ {
			g[i][j] = gcd(nums[i], nums[j])
		}
	}
	f := make([]int, 1<<m)
	for k := 0; k < 1<<m; k++ {
		cnt := bits.OnesCount(uint(k))
		if cnt%2 == 0 {
			for i := 0; i < m; i++ {
				if k>>i&1 == 1 {
					for j := i + 1; j < m; j++ {
						if k>>j&1 == 1 {
							f[k] = max(f[k], f[k^(1<<i)^(1<<j)]+cnt/2*g[i][j])
						}
					}
				}
			}
		}
	}
	return f[1<<m-1]
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}