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 OCaml (4.02.3) (judge verdict: Accepted)

let n = read_int ();;
let g = Array.init 200000 (fun _ -> []);;
let visited = Array.make 200000 false;;

for i = 0 to n - 1 do
  let x, y = Scanf.scanf " %d %d" (fun x y -> x - 1, y - 1 + 100000) in
  g.(x) <- y :: g.(x);
  g.(y) <- x :: g.(y);
done

let rec dfs u cl cr = 
  if not visited.(u) then (
    if u < 100000 then
      cl := !cl + 1
    else
      cr := !cr + 1;
    visited.(u) <- true;
    List.iter (fun v -> dfs v cl cr) g.(u);
  );;


let ans = ref (-n);;
for i = 0 to 199999 do
  let cl = ref 0 and cr = ref 0 in
  dfs i cl cr;
  ans := !ans + !cl * !cr;
done;;

Printf.printf "%d\n" !ans;;