You are given $n$ cuboids where each cuboid is represented as a list of three dimensions cuboids[i] = [width_i, length_i, height_i].

Your task is to select a subset of these cuboids and stack them to achieve the maximum total height.

You can place cuboid $i$ on top of cuboid $j$ if and only if:

• width_i $\leq$ width_j

• length_i $\leq$ length_j

• height_i $\leq$ height_j

You may rotate any cuboid so that any of its three dimensions can serve as width, length, or height.

Return the maximum possible total height of the stacked cuboids.

Constraints:

• n $==$ cuboids.length

• $1 \leq$ n $\leq 100$

• $1 \leq$ width_i, length_i, height_i $\leq 100$

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.