You are given two $2 ext{D}$ integer arrays bottomLeft and topRight, each of length n, representing n axis aligned rectangles on a $2 ext{D}$ Cartesian plane.

The $i^{ ext{th}}$ rectangle is defined by its bottom left coordinate bottomLeft[i] and its top right coordinate topRight[i].

Return the maximum possible area of a square that can fit completely inside the intersecting region of at least $2$ rectangles. If no two rectangles intersect, return $0$.

Constraints:

• n $==$ bottomLeft.length $==$ topRight.length

• $2 \leq$ n $\leq 10^3$

• bottomLeft[i].length $==$ topRight[i].length $== 2$

• $1 \leq$ bottomLeft[i][0], bottomLeft[i][1] $\leq 10^7$

• $1 \leq$ topRight[i][0], topRight[i][1] $\leq 10^7$

• bottomLeft[i][0] $<$ topRight[i][0]

• bottomLeft[i][1] $<$ topRight[i][1]

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.