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: Accepted)

if !ENV['RUBY_THREAD_VM_STACK_SIZE']
  require 'rubygems';RUBY=Gem.ruby
  exec({'RUBY_THREAD_VM_STACK_SIZE'=>'100000000'},RUBY,$0) #100MB
end

V = 100_005 # 頂点の最大数+a

n = gets.to_i
to = Array.new(V*2){ [] }
seen = Array.new(V*2, false)
cnt = Array.new(2,0)

n.times do
  x,y = gets.split.map(&:to_i)
  y += V
  to[x] << y
  to[y] << x
end

dfs = -> v do
  return if seen[v]
  seen[v] = true
  cnt[v/V] += 1
  to[v].each do |nv|
    dfs[nv]
  end
end

ans = 0
(V*2).times do |i|
  cnt.fill(0)
  dfs[i]
  ans += cnt[0] * cnt[1]
end
ans -= n
puts ans