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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.BufferedWriter

fun main() = Case().exec(::solve)
fun solve(c: Case) {
    val n = c.long().toInt()
    val towns = (0 until n).map { ind -> c.intList().let { Town(ind, it[0], it[1]) }}
    val edges = towns.sortedBy { it.x }.zipWithNext().map {
        Kruskal.Edge(it.first.id, it.second.id, it.second.x - it.first.x)
    } + towns.sortedBy { it.y }.zipWithNext().map {
        Kruskal.Edge(it.first.id, it.second.id, it.second.y - it.first.y)
    }
    c.println(Kruskal.solve(n, edges))
}

data class Town(val id: Int, val y: Int, val x: Int)

object Kruskal {
    fun solve(nodeSize: Int, edges: List<Edge>): Long {
        val unionFind = UnionFind(nodeSize)
        var cost = 0L
        edges.sortedBy { it.cost }.forEach { edge ->
            if (unionFind.same(edge.from, edge.to)) return@forEach
            unionFind.unite(edge.from, edge.to)
            cost += edge.cost
        }
        return cost
    }

    data class Edge(val from: Int, val to: Int, val cost: Int)

    private class UnionFind(n: Int) {
        val par = (0 until n).toMutableList()
        fun root(x: Int): Int = if (par[x] == x) x else root(par[x]).also { par[x] = it }
        fun same(x: Int, y: Int): Boolean = root(x) == root(y)
        fun unite(x: Int, y: Int) {
            if (root(x) != root(y)) par[root(x)] = root(y)
        }
    }
}

class Case(
    private val input: BufferedReader = System.`in`.bufferedReader(),
    private val out: BufferedWriter = System.out.bufferedWriter()
) {
    fun exec(fn: (Case) -> Unit) = input.use { out.use { execInThread(fn) } }
    private fun execInThread(fn: (Case) -> Unit) =
        Thread(null, { fn(this) }, "solve", 64 * 1024 * 1024)
            .apply { setUncaughtExceptionHandler { _, e -> e.printStackTrace(); kotlin.system.exitProcess(1) } }
            .apply { start() }.join()

    fun println(c: CharSequence?) = out.appendln(c)
    fun println(c: Number) = println(c.toString())
    fun string(): String = input.readLine().trimEnd()
    fun int(): Int = string().toInt()
    fun long(): Long = string().toLong()
    fun intList(): List<Int> = string().split(" ").map { it.toInt() }
    fun longList(): List<Long> = string().split(" ").map { it.toLong() }
}