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)

N = gets.to_i
Xs, Ys = readlines.map{|l| l.split.map(&:to_i)}.transpose

require 'set'

@p = Array.new(2*N + 1, -1)

def root(x)
  @p[x] < 0 ? x : @p[x] = root(@p[x])
end

def unite(x, y)
  x, y = root(x), root(y)
  if x != y
    x, y = y, x if @p[y] < @p[x]
    @p[x] += @p[y]
    @p[y] = x
  end
end

hx, hy = {}, {}
Xs.zip(Ys, [*0 ... N]) do |x, y, i|
  unite(i, hx[x]) if hx[x]
  hx[x] = i
  unite(i, hx[y]) if hy[y]
  hy[y] = i
end
sx, sy = Array.new(N){Set.new}, Array.new(N){Set.new}
N.times do |i|
  sx[root(i)] << Xs[i]
  sy[root(i)] << Ys[i]
end
puts  N.times.inject(0){|s, i| s + sx[i].size * sy[i].size} - N