Problem:
Score : 600 points

Problem Statement

There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).

We will repeat the following operation as long as possible:

Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.

We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.

Constraints

1 \leq N \leq 10^5

1 \leq x_i, y_i \leq 10^5

If i \neq j, x_i \neq x_j or y_i \neq y_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the maximum number of times we can do the operation.

Sample Input 1

3
1 1
5 1
5 5

Sample Output 1

1

By choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1, 5). We cannot do the operation any more, so the maximum number of operations is 1.

Sample Input 2

2
10 10
20 20

Sample Output 2

0

There are only two dots, so we cannot do the operation at all.

Sample Input 3

9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5

Sample Output 3

16

We can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 \leq i,j \leq 5), and no more. Thus, the maximum number of operations is 16.

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require 'set'

class Group
  attr_accessor :x_list, :y_list
  def initialize
    @x_list = Set.new
    @y_list = Set.new
  end
end

class Pos
  attr_accessor :x, :y
  def initialize(array)
    @x = array[0]
    @y = array[1]
  end
end

def x_push(pos_list)
  pos_list.each do |pos|
    x_pos_list = @pos_hash_by_x[pos.x]
    next if x_pos_list.nil?
    @group.x_list << pos.x
    @pos_hash_by_x.delete(pos.x)
    y_push(x_pos_list)
  end
end

def y_push(pos_list)
  pos_list.each do |pos|
    y_pos_list = @pos_hash_by_y[pos.y]
    next if y_pos_list.nil?
    @group.y_list << pos.y
    @pos_hash_by_y.delete(pos.y)
    x_push(y_pos_list)
  end
end

N = gets.chop.to_i

@pos_list = []
N.times { @pos_list << Pos.new(gets.chop.split.map(&:to_i)) }
@pos_hash_by_x = @pos_list.group_by(&:x)
@pos_hash_by_y = @pos_list.group_by(&:y)

@groups = []
until @pos_hash_by_x.empty?
  key = @pos_hash_by_x.keys[0]
  x_pos_list = @pos_hash_by_x[key]
  @pos_hash_by_x.delete(key)
  @group = Group.new
  @group.x_list = [x_pos_list[0].x]
  y_push(x_pos_list)
  @groups << @group
end

puts @groups.map { |g| g.x_list.size * g.y_list.size }.inject(0, &:+) - N