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: Accepted)

using System.Collections.Generic;
using System;

public class PriorityQueue<T> where T : IComparable
{
	private IComparer<T> _comparer = null;
	private int _type = 0;
	private T[] _heap;
	private int _sz = 0;
	private int _count = 0;
	public PriorityQueue(int maxSize, IComparer<T> comparer)
	{
		_heap = new T[maxSize];
		_comparer = comparer;
	}
	public PriorityQueue(int maxSize, int type = 0)
	{
		_heap = new T[maxSize];
		_type = type;
	}
	private int Compare(T x, T y)
	{
		if (_comparer != null) return _comparer.Compare(x, y);
		return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
	}
	public void Push(T x)
	{
		_count++;
		var i = _sz++;
		while (i > 0)
		{
			var p = (i - 1) / 2;

			if (Compare(_heap[p], x) <= 0) break;

			_heap[i] = _heap[p];
			i = p;
		}
		_heap[i] = x;
	}
	public T Pop()
	{
		_count--;
		T ret = _heap[0];
		T x = _heap[--_sz];

		int i = 0;
		while (i * 2 + 1 < _sz)
		{
			//children
			int a = i * 2 + 1;
			int b = i * 2 + 2;

			if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

			if (Compare(_heap[a], x) >= 0) break;

			_heap[i] = _heap[a];
			i = a;
		}
		_heap[i] = x;
		return ret;
	}
	public int Count()
	{
		return _count;
	}
	public T Peek()
	{
		return _heap[0];
	}
	public bool Contains(T x)
	{
		for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
		return false;
	}
	public void Clear()
	{
		while (this.Count() > 0) this.Pop();
	}
	public IEnumerator<T> GetEnumerator()
	{
		var ret = new List<T>();
		while (this.Count() > 0)
		{
			ret.Add(this.Pop());
		}
		foreach (var r in ret)
		{
			this.Push(r);
			yield return r;
		}
	}
	public T[] ToArray()
	{
		T[] array = new T[_sz];
		int i = 0;
		foreach (var r in this)
		{
			array[i++] = r;
		}
		return array;
	}
}
public class Edge
{
	public int to { get; set; }
	public int d { get; set; }
}
public class Node : IComparable
{
	public int id { get; set; }
	public int d { get; set; }
	public int CompareTo(object obj)
	{
		var x = (Node)obj;
		if (this.d > x.d) return 1;
		else if (this.d == x.d) return 0;
		else return -1;
	}
}

public class Hello
{
	public static void Main()
	{
		var n = int.Parse(Console.ReadLine().Trim());
		var aa = new List<Edge>[n];
		for (int i = 0; i < n; i++) aa[i] = new List<Edge>();
		for (int i = 0; i < n-1; i++)
		{
			string[] line = Console.ReadLine().Trim().Split(' ');
			var a = int.Parse(line[0]) - 1;
			var b = int.Parse(line[1]) - 1;
			var d = int.Parse(line[2]) % 2;
			aa[a].Add(new Edge { to = b, d = d });
			aa[b].Add(new Edge { to = a, d = d });
		}
		var mind = new int[n];
		for (int i = 0; i < n; i++) mind[i] = int.MaxValue;
		goDijk(aa, 0, mind);
		for (int i = 0; i < n; i++) mind[i] = mind[i] % 2;
		Console.WriteLine(string.Join("\n",mind));
	}
	public static void goDijk(List<Edge>[] aa, int r, int[] mind)
	{
		var pq = new PriorityQueue<Node>(100000, 0);
		pq.Push(new Node { id = r, d = 0 });
		while (pq.Count() > 0)
		{
			var targ = pq.Pop();
			var nowd = targ.d;
			var nowid = targ.id;
			if (mind[nowid] < nowd) continue;
			mind[nowid] = nowd;
			foreach (var x in aa[nowid])
				if (nowd + x.d < mind[x.to])
				{
					mind[x.to] = nowd + x.d;
					pq.Push(new Node { id = x.to, d = nowd + x.d });
				}

		}
	}
}