<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 dp[1<<14];
    int gcd(int num1,int num2)
    {
        if(num2==0) return num1;
        return gcd(num2,num1%num2);
    }
    int dfs(vector<int>& nums,int state,int current)
    {
        if(current==0) return 0;
        if(dp[state]) return dp[state];
        int result=0,n=nums.size();
        
        vector<int> total;
		
		//remaining element
        for(int i=0;i<n;i++)
            if(state&(1<<i))
                total.push_back(i);
				
        
        for(int i=0;i<total.size();i++)
            for(int j=i+1;j<total.size();j++)
                result=max(result,gcd(nums[total[i]],nums[total[j]])*current+dfs(nums,(state&(~((1<<total[i])|(1<<total[j])))),current-1));
        
        dp[state]=result;
        return result;
    }
    int maxScore(vector<int>& nums) 
    {
        memset(dp,0,sizeof(dp));
        return dfs(nums,(1<<14)-1,nums.size()/2);
    }
};
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