You are given an integer array nums whose length is a multiple of $3$.

In each step, you select any $3$ elements from nums, determine the median of these $3$ elements, and remove them from nums. You repeat this process until nums is empty.

Return the maximum possible sum of the medians of all selected triplets.

Note: The median of $3$ numbers is the value located in the middle when the numbers are sorted in nondecreasing order.

Constraints:

• $1 \leq$ nums.length $\leq 5 imes 10^5$

• nums.length $\\% 3 = 0$

• $1 \leq$ nums[i] $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.