<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:
    
    def maxScore(self, nums: List[int]) -> int:
        # def getPrimeFactors(num):
        #     factors = {}
        #     while num % 2 == 0:
        #         if 2 not in factors:
        #             factors[2] = 0
        #         factors[2] += 1
        #         num /= 2
        #     for x in range(3, int(num) + 1, 2):
        #         while num % x == 0:
        #             if x not in factors:
        #                 factors[x] = 0
        #             factors[x] += 1
        #             num /= x
        #     return factors
        # prime_factorization = []
        
        # for num in nums:
        #     prime_factorization.append(getPrimeFactors(num))
        gcd = {}
        for idx, num in enumerate(nums):
            for idx2, num2 in enumerate(nums):
                if idx2 > idx:
                    # primeFactorsNum1 = prime_factorization[idx]
                    # primeFactorsNum2 = prime_factorization[idx2]
                    # gcd_val = 1
                    # for factor in primeFactorsNum1:
                    #     if factor in primeFactorsNum2:
                    #         gcd_val *= factor * min(primeFactorsNum1[factor], primeFactorsNum2[factor])
                    gcd[(num, num2)] = math.gcd(num, num2)
        allPossibilities = [[]]
        for num in nums:
            newList = []
            for item in allPossibilities:
                newList.append(item + [num])
            for item in newList:
                allPossibilities.append(item)
        for idx in range(len(allPossibilities)):
            allPossibilities[idx] = tuple(allPossibilities[idx])
        dp = {}
        def rec(tup):
            if tup == ():
                return 0
            if tup in dp:
                return dp[tup]
            dp[tup] = 0
            multiplier = int(len(tup) / 2)
            for idx in range(len(tup)):
                for idx2 in range(idx + 1, len(tup)):
                    dp[tup] = max(dp[tup], rec(tuple([item for idx3, item in enumerate(tup) if idx3 != idx and idx3 != idx2])) + multiplier * gcd[(tup[idx], tup[idx2])])
            return dp[tup]
        
        for item in allPossibilities:
            if len(item) % 2 == 0:
                rec(item)
        # print(dp)
        return dp[tuple(nums)]
2294