Connect Cartesian Coordinates

You are given a two-dimensional list of integers points where each element contains [x, y] representing a cartesian coordinate. We can make an undirected edge between two points (x0, y0) and (x1, y1), which costs abs(x0 - x1) + abs(y0 - y1).

Given that we can connect any number of points, return the minimum cost necessary such that every point is connected by a path.

Constraints

• 0 ≤ n ≤ 1,000 where n is the length of points

https://binarysearch.com/problems/Connect-Cartesian-Coordinates

Examples

Example 1

Input

• points =

[[ 0, 0],
 [ 0, 1],
 [ 0,-1],
 [ 1, 0],
 [-1, 0]]

Output

• answer = 4

Explanation

We can create an edge from (0, 0) to every other point.

Solution