Manhattan Minimum Spanning Tree

You are given n points on the plane: \((x_1,y_1), (x_2,y_2), \ldots, (x_n,y_n)\).

Consider a complete graph with n nodes where for every pair of nodes \(u\) and \(v\) (with \(1 \le u, v \le n, u \ne v\)), there is an edge connecting them with weight \[ |x_u - x_v| + |y_u - y_v| \] which is the Manhattan distance between the two points.

Your task is to find the total weight of the Minimum Spanning Tree (MST) of this graph.

Note: When \(n = 1\), the MST weight is 0.

inputFormat

The first line contains a single integer n, the number of points.

Each of the following n lines contains two integers \(x_i\) and \(y_i\), representing the coordinates of the \(i\)th point.

Constraints: It is guaranteed that the input is valid and fits in the available memory.

outputFormat

Output a single integer, which is the total weight of the minimum spanning tree of the complete graph defined above.

sample

4
0 0
0 1
1 0
1 1

3