1799 - Maximize Score After N Operations.

Hard

You are given nums, an array of positive integers of size 2 * n. You must perform n operations on this array.

In the <code>i^th</code> operation (1-indexed) , you will:

• Choose two elements, x and y.

• Receive a score of i * gcd(x, y).

• Remove x and y from nums.

Return the maximum score you can receive after performing n operations.

The function gcd(x, y) is the greatest common divisor of x and y.

Example 1:

Input: nums = 1,2

Output: 1

Explanation: The optimal choice of operations is:

v(1 \* gcd(1, 2)) = 1

Example 2:

Input: nums = 3,4,6,8

Output: 11

Explanation: The optimal choice of operations is:

(1 \* gcd(3, 6)) + (2 \* gcd(4, 8)) = 3 + 8 = 11

Example 3:

Input: nums = 1,2,3,4,5,6

Output: 14

Explanation: The optimal choice of operations is:

(1 \* gcd(1, 5)) + (2 \* gcd(2, 4)) + (3 \* gcd(3, 6)) = 1 + 4 + 9 = 14

Constraints:

• 1 <= n <= 7

• nums.length == 2 * n

• <code>1 <= numsi<= 10⁶</code>