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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.io.{BufferedReader, InputStream, InputStreamReader}
import java.util.StringTokenizer

import scala.collection.mutable
import scala.util.Sorting
import math.{abs, max, min}

object Main {
  val MOD = 1000000007
  def solve(): Unit = {
    val sc = new InputReader(System.in)
    val N = sc.nextInt()

    val x = Array.ofDim[(Int, Int)](N)
    val y = Array.ofDim[(Int, Int)](N)
    (0 until N) foreach { i =>
      x(i) = (sc.nextInt(), i)
      y(i) = (sc.nextInt(), i)
    }
    Sorting.quickSort(x)(Ordering.by(_._1))
    Sorting.quickSort(y)(Ordering.by(_._1))

    type Edge = (Int, (Int, Int))
    def e(a: Array[(Int, Int)], i: Int, j: Int): Edge = {
      val c = abs(a(i)._1 - a(j)._1)
      val u = a(i)._2
      val v = a(j)._2
      (c, u -> v)
    }

    val q = mutable.PriorityQueue[Edge]()(Ordering.by[Edge, Int](_._1).reverse)
    (0 until N) foreach { i =>
      if (i - 1 >= 0) {
        q.enqueue(e(x, i, i - 1))
        q.enqueue(e(y, i, i - 1))
      }
      if (i + 1 < N) {
        q.enqueue(e(x, i, i + 1))
        q.enqueue(e(y, i, i + 1))
      }
    }

    var ans: Long = 0
    var n: Int = 0
    val uf = new UnionFind(N)
    while(n < N -1) {
      val (c, (u, v)) = q.dequeue()
      if (uf.find(u) != uf.find(v)) {
        uf.unite(u, v)
        ans += c
        n += 1
      }
    }

    println(ans)
  }


  def main(args: Array[String]): Unit = {
    solve()
  }


  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = null

    def next: String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next.toInt
    def nextLong(): Long = next.toLong
    def nextChar(): Char = next.charAt(0)
  }

  class UnionFind(n: Int) {
    private val par = Array.iterate(0, n)(_ + 1)
    private val rank = Array.ofDim[Int](n)

    def find(x: Int): Int = {
      if (par(x) == x) x
      else {
        par(x) = find(par(x))
        par(x)
      }
    }

    def unite(x: Int, y: Int): Unit = {
      val x1 = find(x)
      val y1 = find(y)
      if (x1 != y1) {
        if (rank(x1) < rank(y)) {
          par(x1) = y1
        } else {
          par(y1) = x1
          if (rank(x1) == rank(y1)) rank(x1) += 1
        }
      }
    }
  }
}