2172\. Maximum AND Sum of Array

Hard

You are given an integer array `nums` of length `n` and an integer `numSlots` such that `2 * numSlots >= n`. There are `numSlots` slots numbered from `1` to `numSlots`.

You have to place all `n` integers into the slots such that each slot contains at **most** two numbers. The **AND sum** of a given placement is the sum of the **bitwise** `AND` of every number with its respective slot number.

*   For example, the **AND sum** of placing the numbers `[1, 3]` into slot `1` and `[4, 6]` into slot `2` is equal to `(1 AND 1) + (3 AND 1) + (4 AND 2) + (6 AND 2) = 1 + 1 + 0 + 2 = 4`.

Return _the maximum possible **AND sum** of_ `nums` _given_ `numSlots` _slots._

**Example 1:**

**Input:** nums = [1,2,3,4,5,6], numSlots = 3

**Output:** 9

**Explanation:** One possible placement is [1, 4] into slot 1, [2, 6] into slot 2, and [3, 5] into slot 3.

This gives the maximum AND sum of (1 AND 1) + (4 AND 1) + (2 AND 2) + (6 AND 2) + (3 AND 3) + (5 AND 3) = 1 + 0 + 2 + 2 + 3 + 1 = 9.

**Example 2:**

**Input:** nums = [1,3,10,4,7,1], numSlots = 9

**Output:** 24

**Explanation:** One possible placement is [1, 1] into slot 1, [3] into slot 3, [4] into slot 4, [7] into slot 7, and [10] into slot 9.

This gives the maximum AND sum of (1 AND 1) + (1 AND 1) + (3 AND 3) + (4 AND 4) + (7 AND 7) + (10 AND 9) = 1 + 1 + 3 + 4 + 7 + 8 = 24.

Note that slots 2, 5, 6, and 8 are empty which is permitted.

**Constraints:**

*   `n == nums.length`
*   `1 <= numSlots <= 9`
*   `1 <= n <= 2 * numSlots`
*   `1 <= nums[i] <= 15`