There are $3n$ piles of coins of varying size, represented by an integer array piles.

You, Alice, and Bob take turns collecting piles according to the following rules:

• In each round, you choose any $3$ piles of coins.

• Alice picks the pile containing the maximum number of coins.

• You pick the pile containing the next maximum number of coins.

• Bob picks the remaining pile.

• This process repeats until no piles of coins remain.

Return the maximum number of coins that you can collect.

Constraints:

• $3 \leq$ piles.length $\leq 10^5$

• piles.length $\\% 3 = 0$

• $1 \leq$ piles[i] $\leq 10^4$

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.