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 scan_int () = Scanf.scanf " %d" (fun x -> x)
let print_int n = Printf.printf "%d\n" n

module Union_find :
  sig
    type t
    val init  : int -> t
    val get   : t -> int -> int
    val find  : t -> int -> int
    val size  : t -> int -> int
    val unite : t -> int -> int -> unit
    val same  : t -> int -> int -> bool
  end =
  struct
    type t = int array
    let init n = Array.make (n+1) (-1)
    let get data x = data.(x)
    let rec find data x =
      if data.(x) < 0 then x
      else let _ = data.(x) <- find data data.(x) in data.(x)
    let size data x = - data.(find data x)
    let unite data x y =
      let x = find data x and y = find data y in
      if x <> y then
        if data.(x) < data.(y) then
          let _ = data.(x) <- data.(x) + data.(y) in
          data.(y) <- x
        else
          let _ = data.(y) <- data.(x) + data.(y) in
          data.(x) <- y
    let same data x y =
      let x = find data x and y = find data y in (x == y)
  end

let () =
  let n = scan_int() in
  let max_n = 100000 in
  let v = Array.make (max_n+1) [] in
  let uf = Union_find.init max_n in
  let _ =
    for i = 1 to n do
      let a = scan_int() and b = scan_int() in
      v.(a) <- b :: v.(a)
    done in
  let _ =
    for i = 1 to max_n do
      if List.length v.(i) > 1 then
        let f x = Union_find.unite uf (List.hd v.(i)) x in
        List.iter f v.(i)
    done in
  let rec calc arr i ret =
    let ret =
      if List.length v.(i) > 0 then ret + Union_find.size uf (List.hd v.(i))
      else ret in
    if i == max_n then ret
    else calc arr (i+1) ret in
  print_int (calc v 0 (-n))