Given an integer array nums, determine the maximum sum of three distinct elements from nums such that their sum is divisible by $3$. If no such triplet exists, return $0$.

Constraints:

• $3 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

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.