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.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static class Pair {
        int u;
        int v;

        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return u == pair.u &&
                    v == pair.v;
        }

        @Override
        public int hashCode() {
            return Objects.hash(u, v);
        }
    }

    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        Map<Integer, Set<Integer>> nodes = new HashMap<>();
        Map<Pair, Long> weights = new HashMap<>();

        for (int i = 0; i < n - 1; ++i) {
            int u = scanner.nextInt();
            int v = scanner.nextInt();
            long w = scanner.nextLong();

                Set<Integer> uEnds = nodes.getOrDefault(u, new HashSet<>());
                uEnds.add(v);
                nodes.put(u, uEnds);
                Set<Integer> vEnds = nodes.getOrDefault(v, new HashSet<>());
                vEnds.add(u);
                nodes.put(v, vEnds);
                weights.put(new Pair(u, v), w);
                weights.put(new Pair(v, u), w);
        }

        int [] colors = new int[n + 1];
        for (int i = 1; i <= n; ++i) {
            colors[i] = -1;
        }
        PriorityQueue<Integer> uncolors = new PriorityQueue<>();
        uncolors.add(1);
        colors[1] = 0;
        while (!uncolors.isEmpty()) {
            int current = uncolors.poll();
            int currentColor = colors[current];
            for (Integer end : nodes.getOrDefault(current, new HashSet<>())) {
                if (colors[end] == -1) {
                    long weight = weights.get(new Pair(current, end));
                    if (weight % 2 == 0) {
                        colors[end] = currentColor;
                    } else {
                        colors[end] = 1 - currentColor;
                    }
                    uncolors.add(end);
                }
            }
        }
        for (int i = 1; i <= n; ++i) {
            System.out.println(colors[i]);
        }



    }

}