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.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;

public class Main {
    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int[] u = new int[N];
            int[] v = new int[N];
            int[] w = new int[N];
            for (int i = 0; i < N - 1; i++) {
                u[i] = in.nextInt() - 1;
                v[i] = in.nextInt() - 1;
                w[i] = in.nextInt();
            }

            ArrayList<Pair<Integer, Integer>>[] vAndDists = new ArrayList[N];
            for (int i = 0; i < vAndDists.length; i++) {
                vAndDists[i] = new ArrayList<>();
            }
            for (int i = 0; i < N; i++) {
                vAndDists[u[i]].add(new Pair<Integer, Integer>(v[i], w[i]));
                vAndDists[v[i]].add(new Pair<Integer, Integer>(u[i], w[i]));
            }

            LinkedList<Pair<Integer, Integer>> queue = new LinkedList<>();
            int[] dist = new int[N];
            Arrays.fill(dist, -1);
            {
                queue.add(new Pair<Integer, Integer>(0, 0));
                dist[0] = 0;
            }
            for (; !queue.isEmpty();) {
                Pair<Integer, Integer> current = queue.poll();
                int currentV = current.first.intValue();
                int currentDist = current.second.intValue();
                for (Pair<Integer, Integer> vAndDist : vAndDists[currentV]) {
                    int nextV = vAndDist.first.intValue();
                    if (dist[nextV] != -1) {
                        continue;
                    }
                    int nextDist = currentDist + vAndDist.second.intValue();
                    queue.add(new Pair<Integer, Integer>(nextV, nextDist));
                    dist[nextV] = nextDist;
                }
            }

            for (int i = 0; i < N; i++) {
                System.out.println(dist[i] & 1);
            }
        }
    }
}

class Pair<T extends Comparable<T>, S> implements Comparable<Pair<T, S>> {
    public T first;
    public S second;

    public Pair(T t, S s) {
        this.first = t;
        this.second = s;
    }

    private int hash = 0;

    @Override
    public int hashCode() {
        if (hash == 0) {
            final int prime = 31;
            int result = 1;
            result = prime * result + ((first == null) ? 0 : first.hashCode());
            result = prime * result + ((second == null) ? 0 : second.hashCode());
            hash = result;
        }
        return hash;
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Pair<T, S> other = (Pair<T, S>) obj;
        if (first == null) {
            if (other.first != null)
                return false;
        } else if (!first.equals(other.first))
            return false;
        if (second == null) {
            if (other.second != null)
                return false;
        } else if (!second.equals(other.second))
            return false;
        return true;
    }

    @Override
    public int compareTo(Pair<T, S> o) {
        return first.compareTo(o.first);
    }
}