<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:
    int sol(vector<int> &nums,int n,int round,int vis[],int &mask,vector<vector<int>> &dp)
    {
        if(round>n)
        {
            return 0;
        }
        if(dp[round][mask]!=-1)
        {
            return dp[round][mask];
        }
        int ans=0;
        for(int i=0;i<n;i++)
        {
            for(int j=i+1;j<n;j++)
            {
                if(!(mask>>i&1) && !(mask>>j&1))
                {
                    mask+=1<<i;
                    mask+=1<<j;
                    ans=max(ans,round*(__gcd(nums[i],nums[j]))+sol(nums,n,round+1,vis,mask,dp));
                    mask-=1<<i;
                    mask-=1<<j;
                }
            }
        }
        return dp[round][mask]=ans;
    }
    int maxScore(vector<int>& nums) {
        int n=nums.size();
        int vis[n+1];
        int mask=0;
        vector<vector<int>> dp(n+1,vector<int> ((1<<(n+2))+1,-1));
        for(int  i=0;i<n;i++) vis[i]=0;   
        return sol(nums,n,1,vis,mask,dp);
    }
};
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