You are given an integer n representing the dimensions of an n $ imes$ n grid, and a $2$D integer array rectangles where rectangles[i] = [start_x, start_y, end_x, end_y] denotes a rectangle on the grid.

A cut is a horizontal or vertical line spanning entirely across the grid. A cut is valid if it does not intersect the interior of any rectangle, though it may touch a rectangle along its edges.

Return true if it is possible to make either $2$ horizontal cuts or $2$ vertical cuts such that the grid is divided into at least $3$ non empty sections, where each section contains at least $1$ rectangle. Otherwise, return false.

Constraints:

• $3 \leq$ n $\leq 10^9$

• $3 \leq$ rectangles.length $\leq 10^5$

• $0 \leq$ rectangles[i][0] $<$ rectangles[i][2] $\leq$ n

• $0 \leq$ rectangles[i][1] $<$ rectangles[i][3] $\leq$ n

• No two rectangles overlap.

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.