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.*;

public class Main {
    static Scanner sc;
    static List<Node> nodes = new ArrayList<>();

    public static void main(String[] args) {
        sc = new Scanner(System.in);
        int n = sc.nextInt();

        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            nodes.add(new Node(i));
        }
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt()-1;
            int v= sc.nextInt()-1;
            int w = sc.nextInt();
            nodes.get(u).next.put(nodes.get(v), w);
            nodes.get(v).next.put(nodes.get(u), w);
        }
        boolean[] done = new boolean[n];
        Deque<Node> deque = new ArrayDeque<>();
        deque.add(nodes.get(0));
        while(!deque.isEmpty()) {
            Node a = deque.poll();
            done[a.num] = true;
            ans[a.num] = a.c;
            for(Node next : a.next.keySet()) {
                if(done[next.num]) {
                    continue;
                }
                next.c = (a.c + a.next.get(next)) % 2;
                deque.add(next);
            }
        }
        for (int i = 0; i < n; i++) {
            System.out.println(ans[i]);
        }
    }


    static class Node {
        int num;
        Map<Node, Integer> next;
        int c = 0;

        public Node(int num) {
            this.num = num;
            next = new HashMap<>();
        }
    }
}