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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using static System.Math;
using static AtCoderTemplate.MyExtensions;
using static AtCoderTemplate.MyInputOutputs;
using static AtCoderTemplate.MyNumericFunctions;
using static AtCoderTemplate.MyAlgorithm;

namespace AtCoderTemplate {
    public class Program {
        public enum color {
            none,
            black,
            white,
        }

        public static void Main (string[] args) {
            var N = ReadInt ();
            var uvw = ReadLongColumns (N - 1);
            var u = uvw[0].Select (i => (int) i - 1).ToList ();
            var v = uvw[1].Select (i => (int) i - 1).ToList ();
            var w = uvw[2];

            var dict = new Dictionary<int, color> ();
            foreach (var i in Enumerable.Range (0, N)) {
                dict.Add (i, color.none);
            }

            if (IsEven (w[0])) {
                dict[u[0]] = color.black;
                dict[v[0]] = color.black;
            } else {
                dict[u[0]] = color.white;
                dict[v[0]] = color.white;
            }

            var queue = new Queue<int> (Enumerable.Range (1, N - 2));

            while (!queue.IsEmpty ()) {
                var i = queue.Dequeue ();
                if (dict[u[i]] != color.none) {
                    if (IsEven (w[i])) {
                        dict[v[i]] = dict[u[i]];
                    } else {
                        dict[v[i]] = Reverse (dict[u[i]]);
                    }
                } else if (dict[v[i]] != color.none) {
                    if (IsEven (w[i])) {
                        dict[u[i]] = dict[v[i]];
                    } else {
                        dict[u[i]] = Reverse (dict[v[i]]);
                    }
                } else {
                    queue.Enqueue (i);
                }
            }

            foreach (var d in dict) {
                if (d.Value == color.white) {
                    Print ("0");
                } else if (d.Value == color.black) {
                    Print ("1");
                } else {
                    Print ("none");
                }
            }
        }

        public static color Reverse (color x) {
            if (x == color.white) {
                return color.black;
            } else {
                return color.white;
            }
        }

    }

    public static class MyInputOutputs {
        /* Input & Output*/
        public static int ReadInt () {
            return int.Parse (Console.ReadLine ());
        }
        public static long ReadLong () {
            return long.Parse (Console.ReadLine ());
        }
        public static List<int> ReadInts () {
            return Console.ReadLine ().Split (' ').Select (c => int.Parse (c)).ToList ();
        }
        public static List<long> ReadLongs () {
            return Console.ReadLine ().Split (' ').Select (c => long.Parse (c)).ToList ();
        }
        public static List<List<int>> ReadIntColumns (int n) {
            /*
            入力例
            A1 B1
            A2 B2
            ...
            An Bn

            出力例
            [[A1,A2,...,An], [B1,B2,...,Bn]]
            */
            var rows = Enumerable.Range (0, n).Select (i => ReadInts ()).ToList ();
            var m = rows.FirstOrDefault ()?.Count () ?? 0;
            return Enumerable.Range (0, m).Select (i => rows.Select (items => items[i]).ToList ()).ToList ();
        }
        public static List<List<long>> ReadLongColumns (int n) {
            /*
            入力例
            A1 B1
            A2 B2
            ...
            An Bn

            出力例
            [[A1,A2,...,An], [B1,B2,...,Bn]]
            */
            var rows = Enumerable.Range (0, n).Select (i => ReadLongs ()).ToList ();
            var m = rows.FirstOrDefault ()?.Count () ?? 0;
            return Enumerable.Range (0, m).Select (i => rows.Select (items => items[i]).ToList ()).ToList ();
        }

        public static void Print<T> (T item) {
            Console.WriteLine (item);
        }
        public static void PrintIf<T1, T2> (bool condition, T1 trueResult, T2 falseResult) {
            if (condition) {
                Console.WriteLine (trueResult);
            } else {
                Console.WriteLine (falseResult);
            }
        }

        public static void PrintRow<T> (IEnumerable<T> list) {
            /* 横ベクトルで表示
            A B C D ...
            */
            if (!list.IsEmpty ()) {
                Console.Write (list.First ());
                foreach (var item in list.Skip (1)) {
                    Console.Write ($" {item}");
                }
            }
            Console.Write ("\n");
        }
        public static void PrintColomn<T> (IEnumerable<T> list) {
            /* 縦ベクトルで表示
            A
            B
            C
            D
            ...
            */
            foreach (var item in list) {
                Console.WriteLine (item);
            }
        }
        public static void Print2DArray<T> (IEnumerable<IEnumerable<T>> sources) {
            foreach (var row in sources) {
                PrintRow (row);
            }
        }
    }

    public static class MyNumericFunctions {
        public static bool IsEven (int a) {
            return a % 2 == 0;
        }
        public static bool IsEven (long a) {
            return a % 2 == 0;
        }
        public static bool IsOdd (int a) {
            return !IsEven (a);
        }
        public static bool IsOdd (long a) {
            return !IsEven (a);
        }

        /// <summary>
        /// 順列の総数を得る
        /// O(N-K)
        /// </summary>
        /// <param name="n">全体の数</param>
        /// <param name="k">並べる数</param>
        /// <param name="divisor">返り値がlongを超えないようにdivisorで割った余りを得る</param>
        /// <returns>nPk (をdivisorで割った余り)</returns>
        public static long nPk (int n, int k, long divisor) {
            if (k > n) {
                return 0L;
            } else {
                return Enumerable.Range (n - k + 1, k).Aggregate (1L, ((i, m) => (i * m) % divisor));
            }
        }

        public static long nPk (int n, int k) {
            if (k > n) {
                return 0L;
            } else {
                return Enumerable.Range (n - k + 1, k).Aggregate (1L, ((i, m) => (i * m)));
            }
        }

        /// <summary>
        /// 階乗を得る
        /// O(N)
        /// </summary>
        /// <param name="n"></param>
        /// <param name="divisor">返り値がlongを超えないようにdivisorで割った余りを得る</param>
        /// <returns>n! (をdivisorで割った余り)</returns>
        public static long Fact (int n, long divisor) {
            return nPk (n, n, divisor);
        }

        public static long Fact (int n) {
            return nPk (n, n);
        }

        /// <summary>
        /// 組み合わせの総数を得る
        /// </summary>
        /// <param name="n"></param>
        /// <param name="k"></param>
        /// <returns>nCk</returns>
        public static long nCk (int n, int k) {
            if (k > n) {
                return 0L;
            } else {
                return nPk (n, k) / Fact (k);
            }
        }

        /// <summary>
        /// 最大公約数を得る 
        /// O(log N)
        /// </summary>
        /// <param name="m">自然数</param>
        /// <param name="n">自然数</param>
        /// <returns></returns>
        public static long GCD (long m, long n) {
            // GCD(m,n) = GCD(n, m%n)を利用
            // m%n = 0のとき、mはnで割り切れるので、nが最大公約数
            if (m <= 0L || n <= 0L) throw new ArgumentOutOfRangeException ();

            if (m < n) return GCD (n, m);
            while (m % n != 0L) {
                var n2 = m % n;
                m = n;
                n = n2;
            }
            return n;
        }

        /// <summary>
        /// 最小公倍数を得る
        /// O(log N)
        /// </summary>
        /// <param name="m"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static long LCM (long m, long n) {
            var ans = checked ((long) (BigInteger.Multiply (m, n) / GCD (m, n)));
            return ans;
        }

        /// <summary>
        /// 約数列挙(非順序)
        /// O(√N)
        /// </summary>
        /// <param name="m">m > 0</param>
        /// <returns></returns>
        public static IEnumerable<long> Divisor (long m) {
            if (m == 0) throw new ArgumentOutOfRangeException ();
            var front = Enumerable.Range (1, (int) Sqrt (m))
                .Select (i => (long) i)
                .Where (d => m % d == 0);
            return front.Concat (front.Where (x => x * x != m).Select (x => m / x));
        }

        /// <summary>
        /// 公約数列挙(非順序)
        /// O(√N)
        /// </summary>
        /// <param name="m">m > 0</param>
        /// <param name="n">n > 0</param>
        /// <returns></returns>
        public static IEnumerable<long> CommonDivisor (long m, long n) {
            if (m < n) return CommonDivisor (n, m);
            return Divisor (m).Where (md => n % md == 0);
        }
    }

    public static class MyAlgorithm {
        /// <summary>
        /// 二分探索法
        /// O(log N)
        /// </summary>
        /// <param name="list">探索するリスト</param>
        /// <param name="predicate">条件の述語関数</param>
        /// <param name="ng">条件を満たさない既知のindex</param>
        /// <param name="ok">条件を満たす既知のindex</param>
        /// <typeparam name="T">順序関係を持つ型(IComparableを実装する)</typeparam>
        /// <returns>条件を満たすindexの内、境界に最も近いものを返す</returns>
        public static int BinarySearch<T> (IList<T> list, Func<T, bool> predicate, int ng, int ok)
        where T : IComparable<T> {
            while (Abs (ok - ng) > 1) {
                int mid = (ok + ng) / 2;
                if (predicate (list[mid])) {
                    ok = mid;
                } else {
                    ng = mid;
                }
            }
            return ok;
        }

        /// <summary>
        /// 辺の集まりを操作するオブジェクト
        /// </summary>
        public class Edge {
            long[, ] edge;
            public int NodeNum { get; }
            public Edge (int nodeNum, long overDistance) {
                var edge = new long[nodeNum, nodeNum];
                foreach (var i in Enumerable.Range (0, nodeNum)) {
                    foreach (var j in Enumerable.Range (0, nodeNum)) {
                        if (i != j) {
                            edge[i, j] = overDistance;
                        } else {
                            edge[i, j] = 0;
                        }
                    }
                }

                this.edge = edge;
                this.NodeNum = nodeNum;
            }
            public Edge (Edge edge) {
                this.edge = new long[edge.NodeNum, edge.NodeNum];
                foreach (var i in Enumerable.Range (0, edge.NodeNum)) {
                    foreach (var j in Enumerable.Range (0, edge.NodeNum)) {
                        this.edge[i, j] = edge.GetLength (i, j);
                    }
                }
                this.NodeNum = edge.NodeNum;
            }

            public List<List<long>> ToList () {
                return Enumerable.Range (0, NodeNum).Select (i =>
                    Enumerable.Range (0, NodeNum).Select (j =>
                        edge[i, j]
                    ).ToList ()
                ).ToList ();
            }

            public void Add (int node1, int node2, long distance) {
                edge[node1, node2] = distance;
            }

            public long GetLength (int node1, int node2) {
                return edge[node1, node2];
            }
        }

        /// <summary>
        /// ワーシャルフロイド法
        /// O(N^3)
        /// </summary>
        /// <param name="edge">Edgeオブジェクト</param>
        /// <param name="nodeNum">ノードの数</param>
        /// <returns>各ノード間の最短距離を辺として持つEdgeオブジェクト</returns>
        public static Edge WarshallFloyd (Edge edge) {
            var res = new Edge (edge);
            foreach (var b in Enumerable.Range (0, edge.NodeNum)) {
                foreach (var a in Enumerable.Range (0, edge.NodeNum)) {
                    foreach (var c in Enumerable.Range (0, edge.NodeNum)) {
                        res.Add (a, c, Min (res.GetLength (a, c), res.GetLength (a, b) + res.GetLength (b, c)));
                    }
                }
            }
            return res;
        }
    }

    public static class MyExtensions {
        // AppendとPrependが、.NET Standard 1.6からの追加で、Mono 4.6.2 はそれに対応して仕様はあるが、実装がない
        public static IEnumerable<T> Append<T> (this IEnumerable<T> source, T element) {
            return source.Concat (Enumerable.Repeat (element, 1));
        }

        public static IEnumerable<T> Prepend<T> (this IEnumerable<T> source, T element) {
            return Enumerable.Repeat (element, 1).Concat (source);
        }

        // TakeLastとSkipLastが、.Net Standard 2.1からの追加で、Mono 4.6.2 はそれに対応していない
        public static IEnumerable<T> TakeLast<T> (this IEnumerable<T> source, int count) {
            return source.Skip (source.Count () - count);
        }

        public static IEnumerable<T> SkipLast<T> (this IEnumerable<T> source, int count) {
            return source.Take (source.Count () - count);
        }

        public static bool IsEmpty<T> (this IEnumerable<T> source) {
            return !source.Any ();
        }

        /// <summary>
        /// インデックスiの位置の要素からk個取り除く
        /// O(N)
        /// </summary>
        public static IEnumerable<T> TakeAwayRange<T> (this IEnumerable<T> source, int i, int count) {
            return source.Take (i).Concat (source.Skip (i + count));
        }

        /// <summary>
        /// インデックスiの位置の要素を取り除く
        /// O(N)
        /// </summary>
        public static IEnumerable<T> TakeAwayAt<T> (this IEnumerable<T> source, int i) {
            return source.TakeAwayRange (i, 1);
        }

        /// <summary>
        /// インデックスiの位置にシーケンスを挿入する
        /// O(N + K)
        /// </summary>
        public static IEnumerable<T> InsertEnumAt<T> (this IEnumerable<T> source, int i, IEnumerable<T> inserted) {
            return source.Take (i).Concat (inserted).Concat (source.Skip (i));
        }

        /// <summary>
        /// 順列を得る
        /// O(N!)
        /// </summary>
        public static IEnumerable<IEnumerable<T>> Perm<T> (this IEnumerable<T> source, int n) {
            if (n == 0 || source.IsEmpty () || source.Count () < n) {
                return Enumerable.Empty<IEnumerable<T>> ();
            } else if (n == 1) {
                return source.Select (i => new List<T> { i });
            } else {
                var nexts = source.Select ((x, i) =>
                    new { next = source.Take (i).Concat (source.Skip (i + 1)), selected = source.Take (i + 1).Last () });
                return nexts.SelectMany (next => Perm (next.next, n - 1).Select (item => item.Prepend (next.selected)));
            }
        }

        /// <summary>
        /// シーケンスの隣り合う要素を2引数の関数に適用したシーケンスを得る
        /// </summary>
        /// <para>O(N)</para>
        /// <param name="source">元のシーケンス</param>
        /// <param name="func">2引数関数</param>
        /// <example>[1,2,3,4].MapAdjacent(f) => [f(1,2), f(2,3), f(3,4)]</example>
        public static IEnumerable<TR> MapAdjacent<T1, TR> (this IEnumerable<T1> source, Func<T1, T1, TR> func) {
            var list = source.ToList ();
            return Enumerable.Range (1, list.Count - 1)
                .Select (i => func (list[i], list[i - 1]));
        }

        /// <summary>
        /// 累積項を要素にもつシーケンスを得る(初項は、first)
        /// <para>O(N)</para>
        /// </summary>
        /// <param name="source">元のシーケンス</param>
        /// <param name="func">2引数関数f</param>
        /// <param name="first">func(first, source[0])のための初項</param>
        /// <example> [1,2,3].Scanl1(f,0) => [0, f(0,1), f(f(0,1),2), f(f(f(0,1),2),3)]</example>
        public static IEnumerable<TR> Scanl<T, TR> (this IEnumerable<T> source, TR first, Func<TR, T, TR> func) {
            var list = source.ToList ();
            var result = new List<TR> { first };
            foreach (var i in Enumerable.Range (0, source.Count ())) {
                result.Add (func (result[i], list[i]));
            }
            return result;
        }
        /// <summary>
        /// 累積項を要素にもつシーケンスを得る（初項は、source.First()）
        /// <para>O(N)</para>
        /// </summary>
        /// <param name="source">元のシーケンス</param>
        /// <param name="func">2引数関数f</param>
        /// <example> [1,2,3].Scanl1(f) => [1, f(1,2), f(f(1,2),3)]</example>
        public static IEnumerable<T> Scanl1<T> (this IEnumerable<T> source, Func<T, T, T> func) {
            var list = source.ToList ();
            var result = new List<T> { list[0] };
            foreach (var i in Enumerable.Range (1, source.Count () - 1)) {
                result.Add (func (result[i - 1], list[i]));
            }
            return result;
        }

        /// <summary>
        /// 昇順にソートしたインデックスを得る
        /// </summary>
        /// <para>O(N * log N)</para>
        public static IEnumerable<int> SortIndex<T> (this IEnumerable<T> source) {
            return source
                .Select ((item, i) => new { Item = item, Index = i })
                .OrderBy (x => x.Item)
                .Select (x => x.Index);
        }
    }
}