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 (1.0.0) (judge verdict: Accepted)

data class Edge(val f: Int, val t: Int, val d: Long)
fun main(args: Array<String>) {
    val N = nextInt()
    val XY = Array(N) { listOfLong(-1) }
    val Sx = (0 until N).sortedBy { XY[it][0] }
    val Sy = (0 until N).sortedBy { XY[it][1] }
    val Edges = mutableListOf<Edge>()
    for (n in 1 until N) {
        val fx = Sx[n]
        val tx = Sx[n - 1]
        val dx = XY[fx][0] - XY[tx][0]
        Edges.add(Edge(fx, tx, dx))
        val fy = Sy[n]
        val ty = Sy[n - 1]
        val dy = XY[fy][1] - XY[ty][1]
        Edges.add(Edge(fy, ty, dy))
    }
    Edges.sortBy { it.d }
    var ans = 0L
    val uf = UnionFind(N)
    for ((t, f, d) in Edges) {
        if (uf.unite(t, f)) ans += d
    }
    println(ans)
}


fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfInt(vararg deltas: Int) = listOfString().map { Integer.parseInt(it) }.mapIndexed { index, int -> int + deltas[index % deltas.size] }
fun listOfLong(offset: Long = 0L) = listOfString().map { it.toLong() + offset}

class UnionFind(n: Int) {
    var rank: IntArray
    var par:  IntArray
    var size: IntArray
    init {
        this.rank = IntArray(n) { 0 }
        this.par  = IntArray(n) { it }
        this.size = IntArray(n) { 1 }
    }
    fun union(x: Int, y: Int): Boolean {
        var rx = this.root(x)
        var ry = this.root(y)
        if (rx == ry) return false
        if (this.rank[rx] < this.rank[ry]) {
            val w = rx
            rx = ry
            ry = w
        } else if (this.rank[rx] == this.rank[ry]) {
            this.rank[rx] += 1
        }
        this.par[ry] = rx
        this.size[rx] += this.size[ry]
        return true
    }
    fun find(x: Int): Int {
        if (this.par[x] == x) return x
        else {
            this.par[x] = this.find(this.par[x])
            return this.par[x]
        }
    }
    fun isSame(x: Int, y: Int) = this.root(x) == this.root(y)
    fun size(x: Int): Int = this.size[this.find(x)]
    fun root(x: Int): Int = this.find(x)
    fun unite(x: Int, y: Int) = this.union(x, y)
}