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)

{-# LANGUAGE BangPatterns #-}
import Control.Monad
import Data.Maybe
import Debug.Trace
import Data.List
import qualified Data.Map.Strict as Map
import qualified Data.IntMap.Strict as IntMap
import qualified Data.Set as Set
import qualified Data.IntSet as IntSet
import Data.Functor
import Data.Array
-- import Data.Array.Unboxed
import Control.Monad.ST
import Data.Array.ST

main :: IO ()
main = do
  n <- readLn :: IO Int
  uvws <- replicateM (n-1) $ map read . words <$> getLine :: IO [[Int]]
  putStr . unlines . map show $ solve' n uvws

solve' :: Int -> [[Int]] -> [Int]
solve' n uvws = map color [1..n]
  where
    (evens, odds) = partition (\(_:_:w:_) -> even w) uvws
    initial = ufFromList [0..n]
    evenUf = foldl' (\tree (u:v:w:_) -> ufUnite u v tree) initial $ evens
    zero = if null evens 
           then 1
           else (\(u:_:_:_) -> u) $ head evens
    zeroRoot = ufFind zero evenUf
    
    uf = go evenUf odds
    go tree [] = tree
    go tree ((u:v:_:_):uvws) 
      | ufFind u tree == zeroRoot = go (ufUnite v 0 tree) uvws
      | ufFind v tree == zeroRoot = go (ufUnite u 0 tree) uvws
      | otherwise = go tree $ uvws ++ [[u, v, 0]]
    color i = if ufFind i uf == zeroRoot
      then 0
      else 1

type UnionFind = (IntMap.IntMap Int, IntMap.IntMap Int)

ufFromList :: [Int] -> UnionFind
ufFromList as = (IntMap.fromList $ zip as as, IntMap.fromList $ zip as (repeat 1))

ufIsRoot :: Int -> UnionFind -> Bool
ufIsRoot k uf = k == ((fst uf) IntMap.! k)

ufFind :: Int -> UnionFind -> Int 
ufFind k uf | ufIsRoot k uf = k
            | otherwise = ufFind ((fst uf) IntMap.! k) uf

ufSize :: Int -> UnionFind -> Int
ufSize k uf = let p = ufFind k uf in (snd uf) IntMap.! p

ufUnite :: Int -> Int -> UnionFind -> UnionFind
ufUnite k l uf 
  | (ufFind k uf) == (ufFind l uf) = uf
  | otherwise = if nk < nl 
                then (IntMap.adjust (\_->pl) pk $ fst uf, IntMap.adjust (\_->nk+nl) pl $ snd uf)
                else (IntMap.adjust (\_->pk) pl $ fst uf, IntMap.adjust (\_->nk+nl) pk $ snd uf)
    where
      pk = ufFind k uf
      nk = ufSize k uf
      pl = ufFind l uf
      nl = ufSize l uf