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)

module M = Map.Make (struct type t = int let compare = compare end)
module S = Set.Make (struct type t = int let compare = compare end)

let () =
    let main () =
        let n = Scanf.sscanf (read_line ()) "%d" (fun n -> n) in
        let xy = Array.init n (fun _ -> Scanf.sscanf (read_line ()) "%d %d" (fun x y -> x, y)) in
        let xmap = Array.fold_left (fun map (x, y) ->
            M.add x (S.add y (try M.find x map with _ -> S.empty)) map) M.empty xy in
        let ymap = Array.fold_left (fun map (x, y) ->
            M.add y (S.add x (try M.find y map with _ -> S.empty)) map) M.empty xy in
        let cx = Array.make 100002 true in
        let cy = Array.make 100002 true in
        let rec dfs_x px set ax ay =
            cx.(px) <- false;
            S.fold (fun py ((ax, ay) as acc) ->
                if cy.(py) then dfs_y py (M.find py ymap) ax ay else acc) set (ax + 1, ay)
        and dfs_y py set ax ay =
            cy.(py) <- false;
            S.fold (fun px ((ax, ay) as acc) ->
                if cx.(px) then dfs_x px (M.find px xmap) ax ay else acc) set (ax, ay + 1)
        in
        let acc = M.fold (fun x set acc ->
            if cx.(x) && S.cardinal set > 0 then let sx, sy = dfs_x x set 0 0 in acc + sx * sy else acc) xmap 0 in
        let acc = M.fold (fun y set acc ->
            if cy.(y) && S.cardinal set > 0 then let sx, sy = dfs_y y set 0 0 in acc + sx * sy else acc) ymap acc in
        Printf.printf "%d\n" (acc - n)
    in
    main ()