<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 {
public:
using ll = long long;
map<vector<ll>, ll> dp;
    int getidx(int mask) {
        int idx = 0;

        while(mask != 1) {
            mask = (mask >> 1);
            idx++;
        }

        return idx;
    }

    ll solve(int mask, ll level, vector<int>& nums) {
        if (dp.find({mask, level}) != dp.end()) return dp[{mask, level}];

        int a = (1 << 13);
        ll ans = 0;

        for (; a != 1; a = (a >> 1)) {
            if ((mask & a) == 0) continue;

            for (int b = (a >> 1); b != 0; b = (b >> 1)) {
                if ((mask & b) == 0) continue;

                int n1 = nums[getidx(a)];
                int n2 = nums[getidx(b)];

                ll tmp = level*__gcd(n1, n2);
                tmp += solve(mask ^ a ^ b, level + 1, nums);
                ans = max(ans, tmp);
            }
        }

        dp[{mask, level}] = ans;
        return ans;
    }

    int maxScore(vector<int>& nums) {
        int n = nums.size();
        ll mask = (1 << n);
        mask--;

        return solve(mask, 1, nums);
    }
};
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