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 split str delim =
  let open String in
  let rec doit s acc =
    match
      try Some (rindex s delim) with _ -> None
    with
    | None -> s :: acc
    | Some i -> doit (sub s 0 i) (sub s (i + 1) (length s - i - 1) :: acc) in
  doit str []

let find_set s x =
  let rec doit x =
    if x <> fst s.(x) then s.(x) <- (doit (fst s.(x)), snd s.(x));
    fst s.(x) in
  doit x

let unite s x y =
  let (a, b) = (find_set s x, find_set s y) in
  if snd s.(a) > snd s.(b) then s.(b) <- (a, snd s.(b))
  else begin
    s.(a) <- (b, snd s.(a));
    if snd s.(a) = snd s.(b) then s.(b) <- (fst s.(b), snd s.(b) + 1)
  end

let same_p s x y = find_set s x = find_set s y

let solve n q =
  let s = Array.init n (fun i -> (i, 0)) in
  let rec doit i =
    if i < q then begin
      begin match List.map int_of_string (split (read_line ()) ' ') with
      | 0 :: x :: y :: _ -> unite s x y
      | 1 :: x :: y :: _ -> print_endline (if same_p s x y then "1" else "0")
      | _ -> ()
      end;
      doit (i + 1)
    end in
  doit 0

let () =
  match List.map int_of_string (split (read_line ()) ' ') with
  | [n; q] -> solve n q
  | _ -> ()