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{
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
        
        Dijkstra g = new Dijkstra(n);
        
        for(int i=0; i<n-1; i++){
            int u = Integer.parseInt(sc.next())-1;
            int v = Integer.parseInt(sc.next())-1;
            int w = Integer.parseInt(sc.next());
            g.addEdge(u,v,w);
        }
        
        long[] color = g.build(0);
        
        for(int i=0; i<n; i++){
            System.out.println(color[i]%2);
        }
    }
}



class Dijkstra{
    
    public final long INF = (long)1e18;
    private int n;
    private List<Edge>[] edge;
    
    public Dijkstra(int n){
        this.n = n;
        edge = new List[n];
        for(int i=0; i<n; i++){
            edge[i] = new ArrayList<>();
        }
    }
    
    public void addEdge(int from, int to, int cost){
        edge[from].add(new Edge(from, to, cost));
        edge[to].add(new Edge(to, from, cost));
    }
    
    public long[] build(int from){
        long[] dist = new long[n];
        Arrays.fill(dist, INF);
        dist[from] = 0;
        
        PriorityQueue<Vertex> q = new PriorityQueue<>();
        q.add(new Vertex(from, 0));
        while(q.size() != 0){
            int u = q.poll().ver;
            
            for(Edge ne : edge[u]){
                int v = ne.to;
                long weight = ne.cost;
                if(dist[v] > dist[u]+weight){
                    dist[v] = dist[u]+weight;
                    q.add(new Vertex(v, dist[v]));
                }
            }
        }
        
        return dist;
    }
}

class Edge implements Comparable<Edge>{
    public int from = 0;
    public int to = 0;
    public int cost = 0;
    
    public Edge(int from, int to, int cost) {
        this.from = from;
        this.to = to;
        this.cost = cost;
    }
    
    @Override
    public int compareTo(Edge o) {
        return this.cost - o.cost;
    }
}

class Vertex implements Comparable<Vertex>{
    public int ver = 0;
    public long cost = 0;
    
    public Vertex(int ver, long cost) {
        this.ver = ver;
        this.cost = cost;
    }
    
    @Override
    public int compareTo(Vertex o) {
        long tmp = this.cost - o.cost;
        if(tmp == 0) return 0;
        return (int)(tmp/Math.abs(tmp));
    }
}