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: Accepted)

import Data.IntMap ((!))
import qualified Data.IntMap.Strict as M
import Data.List
import Data.Maybe
import Control.Applicative

untilFix f x = if f x == x then x else untilFix f (f x)

main = do
 [n,q] <- map read . words <$> getLine
 cxys <- map ((\[c,x,y]->(c,(x,y))) . map read . words) . lines <$> getContents
 mapM_ print (uft n q cxys)

uft :: Int -> Int -> [(Int,(Int,Int))] -> [Int]
uft n q = reverse . fst . foldl' process ([],(M.fromDistinctAscList (zip [0..n-1] [0..])))

process (lg,m) (c,(x,y))
 | c==0 = (lg, M.insert (max x y) v1 (M.insert v2 v1 m))
 | c==1 = ((if v1==v2 then 1 else 0) : lg, m)
 where
  v1 = untilFix (m!) (min x y)
  v2 = untilFix (m!) (max x y)