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 Data.Maybe
import Data.IntMap ((!))
import qualified Data.IntMap as M
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B
 
_nub = S.toList . S.fromList
readInt = fst . fromJust . B.readInt
untilFix f x = if f x == x then x else untilFix f (f x)

kruskal n edge = makepath uft 0 edge
 where
  uft = M.fromDistinctAscList (zip [1..n] [1..])
  makepath _ acc [] = acc
  makepath forest acc (((a,b),d):abd)
   | rep1 /= rep2 = makepath _forest (d+acc) abd
   | otherwise = makepath forest acc abd
   where
    rep1 = untilFix (forest!) a
    rep2 = untilFix (forest!) b
    _forest = M.insert b rep1 (M.insert rep2 rep1 forest)
    
main = do
 getLine
 xys <- map (map readInt . B.words) . B.lines <$> B.getContents
 let xyis = zip (_nub xys) [1..]
 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 = kruskal n edge
 where
  edge = sortOn snd (edgex ++ edgey)
  edgex = zipWith mkedgex xysx (tail xysx)
  edgey = zipWith mkedgey xysy (tail xysy)
  mkedgex ([xi,_],i) ([xj,_],j) = ((min i j, max i j), xj-xi)
  mkedgey ([_,yi],i) ([_,yj],j) = ((min i j, max i j), yj-yi)