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 Ruby (2.3.3) (judge verdict: Accepted)

N = gets.to_i

uf = Array.new(N,&:itself)
class << uf
  def _root(i)
    self[i] = (self[i] == i ? i : _root(self[i]))
  end
  def same?(i,j)
    _root(i) == _root(j)
  end
  def union(i,j)
    self[_root(j)] = _root(i)
  end
end


XY = Array.new(2){ Hash.new(-1) }

N.times.map do |u|
  gets.split.map(&:to_i).each_with_index do |k, axis|
    if XY[axis][k] >= 0
      uf.union(XY[axis][k], u) 
    else
      XY[axis][k] = u
    end
  end
end

E = 2.times.with_object([]) do |axis, o|
  XY[axis].keys.sort.each_cons(2) do |a,b|
    o << [b - a, XY[axis][a], XY[axis][b]]
  end
end
E.sort_by!(&:first)

ans = E.inject(0) do |total, (cost, u, v)|
  unless uf.same?(u,v)
    uf.union(u, v)
    total + cost
  else
    total
  end
end
puts ans