Problem: 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.

Examples

Input

3
1 2 2
2 3 1


Output

0
0
1


Input

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


Output

1
0
1
0
1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.function.*;

class WeightedEdge {
	int from;
	int to;
	int weight;

	WeightedEdge(int from, int to, int weight){
		this.from = from;
		this.to = to;
		this.weight = weight;
	}
}

final class Solver {
	static final Solver INSTANCE = new Solver();

	void solve(Supplier<String> sc) {
		int N = Integer.parseInt(sc.get());
		List<PriorityQueue<WeightedEdge>> edges = new ArrayList<>();
		for (int i = 0; i < N; i++) {
			edges.add(new PriorityQueue<>(Comparator.comparingInt(w -> w.from)));
		}
		for (int i = 0; i < N - 1; i++) {
			int u = Integer.parseInt(sc.get()) - 1;
			int v = Integer.parseInt(sc.get()) - 1;
			int w = Integer.parseInt(sc.get());
			edges.get(u).add(new WeightedEdge(u, v, w));
			edges.get(v).add(new WeightedEdge(v, u, w));
		}

		BitSet black = new BitSet();
		dfs(new BitSet(), black, 0, edges);
		StringJoiner joiner = new StringJoiner("\n");
		for (int i = 0; i < N; i++) {
			joiner.add(black.get(i) ? "1" : "0");
		}
		System.out.println(joiner.toString());
	}

	void dfs(BitSet visited, BitSet black, int start, List<PriorityQueue<WeightedEdge>> ki) {
		if (visited.get(start)) return;
		visited.set(start);
		PriorityQueue<WeightedEdge> edges = ki.get(start);
		while (!edges.isEmpty()) {
			WeightedEdge w = edges.remove();
			if (w == null || w.weight <= 0) {
				continue;
			}
			if (w.weight % 2 == 0) {
				black.set(w.to, black.get(start));
			} else {
				black.set(w.to, !black.get(start));
			}
			dfs(visited,black, w.to, ki);
		}
	}
}

class Main {
	public static void main(String... args) {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		Solver.INSTANCE.solve(new Supplier<String>() {
			StringTokenizer line;

			public String get() {
				try {
					return (line = line != null && line.hasMoreTokens() ? line : new StringTokenizer(reader.readLine())).nextToken();
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
		});
	}
}