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.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void debug(String str) {
        boolean debug = false;
        if (debug == false) {
            return;
        }
        System.out.println(str);
    }

    public static class Edge {
        int u;
        int v;
        int w;

        public Edge(int u, int v, int w) {
            this.u = u;
            this.v = v;
            this.w = w;

        }
    }

    public static void main(String[] args) {

        int N;
        HashMap<Integer,List<Edge>> set;

        try (Scanner sc = new Scanner(System.in)) {
            N = sc.nextInt();
            set = new HashMap<>();
            for (int i = 0; i < N - 1; i++) {
                int u = sc.nextInt();
                int v = sc.nextInt();
                int w = sc.nextInt();
                Edge e = new Edge(u, v, w);
                setSet(set,e,u);
                setSet(set,e,v);
            }
        }
        int[] distans = new int[N];
        HashSet<Edge> visited = new HashSet<>();
        Deque<Integer> queue = new ArrayDeque<>();
        queue.push(1);
        distans[0] = 0;
        Integer target;
        while((target = queue.pollFirst()) != null){
            List<Edge> list = set.get(target);
            for(Edge e : list){
                if(visited.contains(e)){
                    continue;
                }else{
                    int d = (distans[target-1] + e.w) %2;
                    int i;
                    if(e.u != target ){
                        i = e.u;
                    }else{
                        i = e.v;
                    }
                    queue.addLast(i);
                    distans[i  -1] = d;
                    debug(i+":"+distans[i  -1]);
                    visited.add(e);
                }
            }
        }
        for(int i : distans){
            System.out.println(i%2);
        }
    }

    private static void setSet(HashMap<Integer,List<Edge>> set,Edge e, int i){
        List<Edge> list = set.get(i);
        if(list == null){
            list = new ArrayList<>();
        }
        list.add(e);
        set.put(i, list);
    }

}