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.Strict ((!))
import qualified Data.IntMap.Strict as M
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B
 
readInt = fst . fromJust . B.readInt
untilFix f x = if f x == x then x else untilFix f (f x)
 
kruskal n edge = makepath M.empty 0 edge
 where
  makepath _ acc [] = acc
  makepath forest acc (((a,b),d):abd)
   | not p1 && not p2 = makepath forest1 (d+acc) abd
   | not p1 = makepath forest2 (d+acc) abd
   | not p2 = makepath forest3 (d+acc) abd
   | rep1 /= rep2 = makepath forest4 (d+acc) abd
   | otherwise = makepath forest acc abd
   where
    v1 = min a b
    v2 = max a b
    p1 = M.member v1 forest
    p2 = M.member v2 forest
    rep1 = untilFix (forest!) v1
    rep2 = untilFix (forest!) v2
    forest1 = M.insert v2 v1 (M.insert v1 v1 forest)
    forest2 = M.insert v1 rep2 forest
    forest3 = M.insert v2 rep1 forest
    forest4 = M.insert v2 rep1 (M.insert rep2 rep1 forest)
    
main = do
 getLine
 xys <- map ((\[x,y]->(x,y)) . map readInt . B.words) . B.lines <$> B.getContents
 let xyis = zip xys [1..]
 let _n = length xyis
 let xysx = sortOn fst xyis
 let xysy = sortOn (snd.fst) xyis
 print (built _n xysx xysy)
 
built n xysx xysy = kruskal n edge
 where
  edge = sortOn snd (edgex ++ edgey)
  edgex = zipWith mkedge xysx (tail xysx)
  edgey = zipWith mkedge xysy (tail xysy)
 
mkedge ((xi,yi),i) ((xj,yj),j) = ((i,j), min (abs (xj-xi)) (abs (yj-yi)))