Minimum Network Cost

You are given a collection of station locations on a two-dimensional grid, where each station is represented by its coordinates points[i] = [xᵢ, yᵢ].

Your goal is to construct a network that connects all stations together using the minimum total wiring cost. The cost of laying a wire between any two stations at coordinates [xᵢ, yᵢ] and [xⱼ, yⱼ] is computed as the taxicab distance between them: |xᵢ - xⱼ| + |yᵢ - yⱼ|, where |val| represents the absolute value of val.

Return the minimum total cost required to wire all stations together such that every station is reachable from every other station through the network. A valid network ensures that there exists exactly one simple path between any pair of stations (i.e., the network forms a tree structure with no cycles).

Note: The taxicab distance (also known as Manhattan distance or L1 distance) measures the distance between two points along axes at right angles, similar to how a taxi would navigate a city grid where it can only travel along streets.