Problem:
Disjoint Set

Write a program which manipulates a disjoint set S = {S1, S2, . . . , Sk}.

First of all, the program should read an integer n, then make a disjoint set where each element consists of 0, 1, ... n−1 respectively.

Next, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:

unite(x, y): unites sets that contain x and y, say Sx and Sy, into a new set.

same(x, y): determine whether x and y are in the same set.

Input

n q
com1 x1 y1
com2 x2 y2
...
comq xq yq

In the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.

Output

For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.

Constraints

1 ≤ n ≤ 10000

1 ≤ q ≤ 100000

x ≠ y

Sample Input

5 12
0 1 4
0 2 3
1 1 2
1 3 4
1 1 4
1 3 2
0 1 3
1 2 4
1 3 0
0 0 4
1 0 2
1 3 0

Sample Output

0
0
1
1
1
0
1
1

Solution in OCaml (judge verdict: Accepted)

let read_lines () =
  let rec iter xs =
    try read_line() :: xs |> iter
    with End_of_file -> xs
  in iter [] |> List.rev

let split_nums str =
  Str.split (Str.regexp " ") str
  |> List.map int_of_string

let read_ints () =
  read_line () |> split_nums |> Array.of_list


let init n = Array.init n (fun x -> x)

let rec find i a =
  if a.(i) = i then i
  else compress a.(i) a
and compress i a =
  a.(i) <- find i a;
  a.(i)

let same x y a =
  find x a = find y a

let void _ = ()

let unite x y a =
  let i = find x a
  and j = find y a in
  if i = j then ()
  else a.(i) <- j

let () =
  let first_line = read_ints () in
  let tree = init first_line.(0) in
  let answer com x y =
    match com with
    | 0 -> unite x y tree;
    | 1 ->
       Printf.printf "%d\n" (if same x y tree then 1 else 0);
    | _ -> raise Not_found in

  for i = 1 to first_line.(1) do
    let xs = read_ints () in
    answer xs.(0) xs.(1) xs.(2)
  done