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 Haskell (judge verdict: Time Limit Exceeded)

import Data.List
import qualified Data.Set as S

type Element = Int
type SetElement =S.Set Element
type Family = S.Set SetElement
type Command = [Int]


main = do
    contents <- getContents
    let ([n, q] : queries) = map parse (lines contents)
    let family = S.fromList $ (map S.singleton $ take n [0::Int ..])
    let families = init $ scanl (\f [c,x,y] -> if c == 1 then f else unite x y f) family queries
    let output = filter (>=0) (map (\(f, [c,x,y]) -> if c == 0 then -1 else if same x y f then 1 else 0) $ zip families queries)
    mapM_ print output


parse :: String -> Command
parse = map read . words


pivot :: Element -> Family -> (SetElement, Family)
pivot x family = (S.elemAt 0 sxs, rxs)
    where
    (sxs, rxs) = S.partition (S.member x) family


same :: Element -> Element -> Family -> Bool
same x y family = sx == sy
    where
    (sx, rxs) = pivot x family
    (sy, rys) = pivot y family


unite :: Element -> Element -> Family -> Family
unite x y family = if same x y family then family else S.insert sxy rxys
    where
    (sx, rxs) = pivot x family
    (sy, rys) = pivot y family
    sxy = S.union sx sy
    rxys = S.intersection rxs rys