Problem H
Grid MST
This is a very simple problem. You are given $N$ points. Some points may be repeated. The weight (distance) between two points is given by the Manhattan distance between the two points. Find the weight of a Minimum Spanning Tree that spans these $N$ points.
Input
The input consists of:

One line with one integer $N$ ($1 \leq N \leq 100\, 000$), the number of points,

$N$ lines each with two integers $x$ and $y$ ($0 \leq x,y < 1\, 000$), the coordinates of each point.
Output
Output one line with a single integer: The weight of a Minimum Spanning Tree that spans these $N$ points.
Sample Input 1  Sample Output 1 

4 0 0 0 1 1 0 1 1 
3 
Sample Input 2  Sample Output 2 

5 0 0 10 0 10 0 11 1 12 2 
14 