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: Time Limit Exceeded)

require 'set'
def check_and_put(x, y)
  return 0 if XS[x] != nil && XS[x].include?(y)
  XS[x] ||= Set[]
  XS[x] << y
  YS[y] ||= Set[]
  YS[y] << x
  1
end

N = gets.to_i
points = N.times.map{ gets.split.map(&:to_i) }
XS = {}
YS = {}
points.each do |point|
  check_and_put(point[0], point[1])
end

score = 0
loop do
  score_incr = 0
  XS.keys.each do |x|
    XS[x].each do |y|
      # for every point
      x_siblings = YS[y].select{|i| i != x }
      y_siblings = XS[x].select{|i| i != y }
      x_siblings.product(y_siblings).each do |nx, ny|
        score_incr += check_and_put(nx, ny)
      end
    end
  end
  break if score_incr == 0
  score += score_incr
  break
end
puts score