Problem:
Score : 400 points

Problem Statement

We have a tree with N vertices numbered 1 to N.
The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i.
Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:

For any two vertices painted in the same color, the distance between them is an even number.

Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq u_i < v_i \leq N

1 \leq w_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}

Output

Print a coloring of the vertices that satisfies the condition, in N lines.
The i-th line should contain 0 if Vertex i is painted white and 1 if it is painted black.

If there are multiple colorings that satisfy the condition, any of them will be accepted.

Sample Input 1

3
1 2 2
2 3 1

Sample Output 1

0
0
1

Sample Input 2

5
2 5 2
2 3 10
1 3 8
3 4 2

Sample Output 2

1
0
1
0
1

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

-- import qualified Data.Vector.Unboxed as U
-- import qualified Data.Vector as V
import qualified Data.ByteString.Char8 as C
-- import Data.Array.IO
import Debug.Trace
import Data.List
import Control.Monad
import Data.Ord(comparing)
-- import Data.Char
import qualified Data.Map.Strict as Map
-- import Data.Graph


type Vertex = Int
type Weight = Int

type Graph = Map.Map Vertex [(Vertex, Weight, Visited)]
type Visited = Bool
{-
collapseW :: Int -> Tree -> [(Weight, Vertex)]
collapseW wac (Node (w,v) []) = [(w+wac,v)] 
collapseW wac (Node (w,v) xs) =  (w+wac,v) : concat (map (collapseW (w+wac)) xs)
-}
{--
r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine
-}
r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

readAsc :: IO [(Vertex,[(Vertex,Weight,Visited)])]
readAsc = do
    [u,v,w] <- r'
    case even w of
        True -> return [(u,[(v,0,False)]),(v,[(u,0,False)])]
        _    -> return [(u,[(v,1,False)]),(v,[(u,1,False)])]


main :: IO ()
main = do
    n <- readLn :: IO Int
    uvw <- concat <$> replicateM (n-1) readAsc
    let graph = Map.fromListWith fsNubConcat uvw
    -- print graph
    let res = solve graph 0 1
    print 0
    mapM_ print $ map snd $ (sortBy $ comparing fst) res
    -- print res



solve :: Graph -> Weight -> Vertex -> [(Vertex,Weight)]
solve mp curW root = {-traceShow (mp,curW,root) $-} case Map.lookup root mp of
                    Just xs -> let unvisited = filter (\(v,w,b)->not b) xs 
                                in if unvisited == [] then []
                                    else concat $ map (\(v,w,b) ->
                                            let newW = (w+curW) `mod`2
                                            in (root,w):solve (recVisit root v newW mp) newW v 
                                        ) unvisited
                    Nothing -> error ("No entry with key " ++ show root ++ " found.")



recVisit :: Vertex -> Vertex -> Weight -> Graph -> Graph
recVisit u v w = (Map.insertWith fsNubConcat u [(v,w,True)] . Map.insertWith fsNubConcat v [(u,w,True)])



fsNubConcat a b = nubBy (\(a,b,_)(x,y,_)->a==x && b==y) (a++b)