You are given a $2 D$ binary array grid. You need to find $3$ non overlapping rectangles with horizontal and vertical sides such that every $1$ in grid is covered by at least one rectangle.

Return the minimum possible sum of the areas of these $3$ rectangles.

Note: The rectangles cannot overlap with each other, but they may share boundaries.

Constraints:

• $1 \leq$ grid.length, grid[i].length $\leq 30$

• grid[i][j] is either $0$ or $1$.

• The input is generated such that there are at least $3$ occurrences of $1$ in grid.

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.