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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mmi, mab = math.min, math.abs

local function uf_initialize(n)
  local parent = {}
  for i = 1, n do parent[i] = i end
  return parent
end

local function uf_findroot(idx, parent)
  while parent[idx] ~= idx do
    idx = parent[idx]
  end
  return idx
end

local function kruskal(n, line)
  -- line.c, line.i1, line.i2
  table.sort(line, function(a, b) return a.c < b.c end)
  local parent = uf_initialize(n)
  local totalcost = 0
  local used = 0
  local linenum = #line
  for i = 1, linenum do
    local c, i1, i2 = line[i].c, line[i].i1, line[i].i2
    local r1, r2 = uf_findroot(i1, parent), uf_findroot(i2, parent)
    parent[i1], parent[i2] = r1, r2
    if r1 ~= r2 then
      parent[r2] = r1
      parent[i2] = r1
      totalcost = totalcost + c
      used = used + 1
      if used == n - 1 then break end
    end
  end
  return totalcost
end

local n = io.read("*n")
local t = {}
for i = 1, n do
  local tbl = {}
  tbl.i, tbl.x , tbl.y = i, io.read("*n", "*n")
  t[i] = tbl
end

local line = {}

table.sort(t, function(a, b) return a.x > b.x end)
for i = 1, n - 1 do
  local tmp = {}
  tmp.c = t[i].x - t[i + 1].x
  tmp.i1, tmp.i2 = t[i].i, t[i + 1].i
  table.insert(line, tmp)
end

table.sort(t, function(a, b) return a.y > b.y end)
for i = 1, n - 1 do
  if t[i].y - t[i + 1].y < mab(t[i].x - t[i + 1].x) then
    local tmp = {}
    tmp.c = t[i].y - t[i + 1].y
    tmp.i1, tmp.i2 = t[i].i, t[i + 1].i
    table.insert(line, tmp)
  end
end

print(kruskal(n, line))