You are given two integers, n and m, representing a grid that contains $n + 2$ horizontal bars and $m + 2$ vertical bars. The horizontal bars are numbered from $1$ to $n + 2$, and the vertical bars are numbered from $1$ to $m + 2$.

You are also given two integer arrays, hBars and vBars.
The array hBars contains the indices of horizontal bars that can be removed.
The array vBars contains the indices of vertical bars that can be removed.

A hole is a contiguous empty region formed by removing some bars. Return the maximum area of a square hole that can be created by removing any combination of the available bars.

Constraints:

• $1 \leq$ n $\leq 10^9$

• $1 \leq$ m $\leq 10^9$

• $1 \leq$ hBars.length $\leq 100$

• $2 \leq$ hBars[i] $\leq$ n $+ 1$

• $1 \leq$ vBars.length $\leq 100$

• $2 \leq$ vBars[i] $\leq$ m $+ 1$

• All values in hBars are distinct.

• All values in vBars are distinct.

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.