Problem:
Score : 500 points

Problem Statement

There are N towns on a plane. The i-th town is located at the coordinates (x_i,y_i). There may be more than one town at the same coordinates.

You can build a road between two towns at coordinates (a,b) and (c,d) for a cost of min(|a-c|,|b-d|) yen (the currency of Japan). It is not possible to build other types of roads.

Your objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?

Constraints

2 ≤ N ≤ 10^5

0 ≤ x_i,y_i ≤ 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.

Sample Input 1

3
1 5
3 9
7 8

Sample Output 1

3

Build a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.

Sample Input 2

6
8 3
4 9
12 19
18 1
13 5
7 6

Sample Output 2

8

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B
import Data.Maybe

nub' = S.toList . S.fromList

readInt = fst . fromJust . B.readInt

kruskal n edge = makepath (map return [0..n-1]) [] edge
 where
  makepath _ acc [] = acc
  makepath ts acc (((a,b),d):abd)
   | disjoint a b ts = makepath (link a b ts) ((((a,b),d)):acc) abd
   | otherwise = makepath ts acc abd
   where
    disjoint a b = not . any (\t -> elem a t && elem b t)
    link a b ts = let (ab,ts') = partition (\t -> elem a t || elem b t) ts in concat ab : ts'

main = do
 getLine
 xys <- map (map readInt . B.words) . B.lines <$> B.getContents
 let xyis = zip (nub' xys) [0..]
 let n' = length xyis
 let xysx = sortOn (head.fst) xyis
 let xysy = sortOn (last.fst) xyis
 print (built n' xysx xysy)

built n xysx xysy = sum $ map snd (kruskal n edge)
 where
  edge = sortOn snd (edgex ++ edgey)
  edgex = zipWith make xysx (tail xysx)
  edgey = zipWith make xysy (tail xysy)

make ([xi,yi],i) ([xj,yj],j) = ((i,j), min (abs (xj-xi)) (abs (yj-yi)))