You are given nums, an array of positive integers of size 2 * n. You must perform n operations on this array.
In the ith operation (1-indexed), you will:
- Choose two elements,
xandy. - Receive a score of
i * gcd(x, y). - Remove
xandyfromnums.
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: (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 <= 7nums.length == 2 * n1 <= nums[i] <= 106