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: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE LambdaCase            #-}
{-# LANGUAGE MagicHash             #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE MultiWayIf            #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}
{-# LANGUAGE ViewPatterns          #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString             as B
import qualified Data.ByteString.Char8       as C
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import qualified Data.Foldable               as F
import           Data.Function
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import qualified Data.List                   as L
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           GHC.Exts
import           Unsafe.Coerce

main :: IO ()
main = do
    n <- readLn :: IO Int
    es <- U.unfoldrN n parseInt3 <$> C.getContents
    putStr.unlines.map show $ solve n es

solve :: Int -> U.Vector (Int, Int, Int) -> [Int]
solve n es = runST $ do
    uf <- newUnionFind (2 * n)
    U.forM_ es $ \(u, v, w) -> do
        let !u' = u - 1
        let !v' = v - 1
        if even w
        then do
            uniteM uf (2 * u') (2 * v')
            uniteM uf (2 * u' + 1) (2 * v' + 1)
        else do
            uniteM uf (2 * u') (2 * v' + 1)
            uniteM uf (2 * u' + 1) (2 * v')
    U.toList <$> U.mapM (\i -> fromEnum <$> equivM uf 0 (2*i)) (U.generate n id)

-------------------------------------------------------------------------------


newtype UnionFind m = UF { parent :: UM.MVector m Int }

newUnionFind :: PrimMonad m => Int -> m (UnionFind (PrimState m))
newUnionFind n = UF <$> UM.replicate n (-1)
{-# INLINE newUnionFind #-}

findM :: PrimMonad m => UnionFind (PrimState m) -> Int -> m Int
findM uf x = go x return
  where
    go !x k = do
        px <- UM.unsafeRead (parent uf) x
        if px < 0
        then k x
        else go px $ \ppx -> do
            UM.unsafeWrite (parent uf) x ppx
            k ppx
{-# INLINE findM #-}

sizeM :: PrimMonad m => UnionFind (PrimState m) -> Int -> m Int
sizeM uf = fix $ \loop x -> do
    px <- UM.unsafeRead (parent uf) x
    if px < 0
    then return $! negate px
    else loop px
{-# INLINE sizeM #-}

uniteM :: PrimMonad m => UnionFind (PrimState m) -> Int -> Int -> m Bool
uniteM uf x y = do
    px <- findM uf x
    py <- findM uf y
    if px == py
    then return False
    else do
        rx <- UM.unsafeRead (parent uf) px
        ry <- UM.unsafeRead (parent uf) py
        if rx < ry
        then do
            UM.unsafeModify (parent uf) (+ry) px
            UM.unsafeWrite (parent uf) py px
        else do
            UM.unsafeModify (parent uf) (+rx) py
            UM.unsafeWrite (parent uf) px py
        return True
{-# INLINE uniteM #-}

equivM :: PrimMonad m => UnionFind (PrimState m) -> Int -> Int -> m Bool
equivM uf x y = (==) `liftM` findM uf x `ap` findM uf y
{-# INLINE equivM #-}

-- | O(n)
countGroupM :: PrimMonad m => UnionFind (PrimState m) -> m Int
countGroupM uf = U.length . U.filter (<0) <$> U.unsafeFreeze (parent uf)
{-# INLINE countGroupM #-}

type Parser a = C.ByteString -> Maybe (a, C.ByteString)

parseInt :: Parser Int
parseInt = C.readInt . C.dropWhile isSpace

parseInt2 :: Parser (Int, Int)
parseInt2 = runStateT $
    (,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)

parseInt3 :: Parser (Int, Int, Int)
parseInt3 = runStateT $
    (,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)

parseInt4 :: Parser (Int, Int, Int, Int)
parseInt4 = runStateT $
    (,,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)