You are given an array points representing integer coordinates of some points on a $2 {D}$ plane, where points[i] $= [x_i, y_i]$.

The cost of connecting two points $[x_i, y_i]$ and $[x_j, y_j]$ is the Manhattan distance between them: $|x_i - x_j| + |y_i - y_j|$.

Return the minimum total cost to connect all points such that there is exactly one simple path between any pair of points.

Constraints:

• $1 \leq$ points.length $\leq 1000$

• $-10^6 \leq x_i, y_i \leq 10^6$

• All pairs $(x_i, y_i)$ 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.