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.*;
import java.io.*;

public class Main {
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		Dijkstra dk = new Dijkstra(n);
		for(int i = 1; i < n; i ++) {
			int from = sc.nextInt() - 1;
			int to = sc.nextInt() - 1;
			long cost = sc.nextLong();
            dk.addEdge(from, to, cost);  
            dk.addEdge(to, from, cost);
		}
		dk.dijkstra(0);
		
		int[] color = new int[n];
		for(int i = 1; i < n; i++) {
			long dist = dk.dist[i];
			if (dist % 2 == 1)
				color[i] = 1;
		}
		for(int i = 0; i < n; i++) {
			out.println(color[i]);
		}
		
		out.close();
	}
	public static class Dijkstra {
        int n; long[] dist;
        ArrayList<Pair>[] list;
        final long inf = Long.MAX_VALUE/10;
        public Dijkstra(int n) {
            this.n = n;
            this.dist = new long[n];
            list = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                list[i] = new ArrayList<>();
                dist[i] = inf;
            }
        }
        public void addEdge(int from, int to, long cost) {
            list[from].add(new Pair(to, cost));
        }
	//始点sから各頂点への最短距離を求めてdistに格納
        public void dijkstra(int s) {
            PriorityQueue<Pair> Q = new PriorityQueue<>();
            Q.add(new Pair(s, 0));
            boolean[] used = new boolean[n];
            while (!Q.isEmpty()) {
                Pair p = Q.poll();
                if (used[p.to]) continue;
                used[p.to] = true;
                dist[p.to] = p.cost;
                for (Pair edge : list[p.to]) {
                    Q.add(new Pair(edge.to, p.cost + edge.cost));
                }
            }
        }
        class Pair implements Comparable<Pair> {
            int to; long cost;
            Pair(int to, long cost) {
                this.to = to;
                this.cost = cost;
            }
            public int compareTo(Pair p) {
                return Long.compare(cost, p.cost);
            }
        }
}

//無向グラフ用のエッジ
public static class Pair implements Comparable<Pair> {
    int from; int to; long cost;
    Pair(int from,int to, long cost) {
    	this.from = from;
        this.to = to;
        this.cost = cost;
    }
    public int compareTo(Pair p) {
        return Long.compare(cost, p.cost);
    }
}

static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}
}