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 Julia (0.5.0) (judge verdict: Wrong Answer)

function main()
	lines=readlines()
	N=parse(Int,shift!(lines))
	T=10^5
	A=Array{Tuple{Int,Int}}(0)
	parent=collect(1:T)
	S=ones(Int,T)
	function find(u)
		if u==parent[u]
			u
		else
			parent[u]=find(parent[u])
		end
	end
	for i=1:N
		x,y=map(x->parse(Int,x),split(shift!(lines)))
		push!(A,(x,y))
	end
	sort!(A)
	px,py=-1,-1
	for (x,y)=A
		if px==x
			s=find(py)
			t=find(y)
			if S[s]>S[t]
				parent[t]=s
				S[s]+=S[t]
			else
				parent[s]=t
				S[t]+=S[s]
			end
		end
		px,py=x,y
	end
	ans=-N
	px,py=-1,-1
	for (x,y)=A
		if px!=x
			ans+=S[find(y)]
		end
		px,py=x,y
	end
	println(ans)
end
main()