<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 dfs(vector<int> &nums,int mask,vector<vector<int>> &dp,int op){

        if(op > nums.size()){
             return 0; 
        }
         
    
        if(dp[mask][op] != -1){
             return dp[mask][op]; 
        }

        int maxi = 0; 

        for(int i = 0;i<nums.size();i++){
             for(int j = i+1;j<nums.size();j++){ 
              

                 if(((int)1 << i)&mask){
                     continue;
                 }
                 if(((int)1 << j)&mask){
                     continue;
                 }

                 int temp = mask; 

                 mask |= ((int)1 << i); 
                 mask |= ((int)1 << j); 

                 maxi = max(op*__gcd(nums[i],nums[j])+dfs(nums,mask,dp,op+1),maxi); 

                 mask = temp; 

             }
        }

        return dp[mask][op] = maxi; 
         
    }
    int maxScore(vector<int>& nums) {
        vector<vector<int>> dp(16387,vector<int>(nums.size()+1,-1)); 
        int mask = 0; 
        return dfs(nums,mask,dp,1); 
    }
};
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