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: Wrong Answer)

n = gets.to_i
MX = 100001
x = Array.new(MX){[]}
y = Array.new(MX){[]}
n.times do
	xi,yi = gets.split.map(&:to_i)
	x[xi] << yi
	y[yi] << xi
end

sum = 0
visitedx = []
x.each_with_index do |ax,index|
	next if ax.empty?
	next if visitedx.include? index
	edgenum = 0
	visitedx << index
	xnum = 1
	visitedy = []
	until ax.empty?
		tax = ax.shift
		next if visitedy.include? tax
		edgenum += 1
		visitedy << tax
		y[tax].each do |tay|
			next if visitedx.include? tay
			edgenum += 1
			visitedx << tay
			xnum += 1
			ax += x[tay]
		end
	end
	(sum += xnum * visitedy.size - edgenum)if (xnum >= 2) && (visitedy.size >= 2)
end

puts sum