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)

N = gets.chomp.to_i
points = N.times.map { gets.chomp.split(' ').map(&:to_i) }

if points.size < 3
  puts 0
  exit
end

xy = points.each_with_object(Hash.new { |o, k | o[k] = [] }) { |(x, y), h|
  h[x].push(y)
}

yx = points.each_with_object(Hash.new { |o, k | o[k] = [] }) { |(x, y), h|
  h[y].push(x)
}

add = -> (x, y) do
  xy[x].push(y)
  yx[y].push(x)
end

count = 0

execute = -> do
  current_count = count
  yx.each do |y, xs|
    xs.each_cons(2) do |x1, x2|
      y1 = xy[x1].find { |n| n > y }
      y2 = xy[x2].find { |n| n > y }
      case
      when y1.nil? && y2.nil?
        next
      when y1.nil? && y2
        add[x1, y2]
        count += 1
      when y1 && y2.nil?
        add[x2, y1]
        count += 1
      when y1 < y2
        add[x2, y1]
        count += 1
      when y2 < y1
        add[x1, y2]
        count += 1
      end
    end
  end
  xy.each do |x, ys|
    ys.each_cons(2) do |y1, y2|
      x1 = yx[y1].find { |n| n > x }
      x2 = yx[y2].find { |n| n > x }
      case
      when x1.nil? && x2.nil?
        next
      when x1.nil? && x2
        add[x2, y1]
        count += 1
      when x1 && x2.nil?
        add[x1, y2]
        count += 1
      when x1 < x2
        add[x1, y2]
        count += 1
      when x2 < x1
        add[x2, y1]
        count += 1
      end
    end
  end

  execute[] if current_count != count
end

execute[]
puts count