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.io.*;
import java.util.*;
public class Main{
    public static void main(String[] args) throws IOException{
        Reader r = new Reader();
        int N = r.i();
        int[] u = new int[N-1],
              v = new int[N-1],
              w = new int[N-1];
        ArrayList<int[]>[] T = new ArrayList[N];
        int[] color = new int[N];
        Arrays.fill(color, -1);
        for(int i = 0; i < N; i++)
            T[i] = new ArrayList<>();
        for(int i = 0; i < N-1; i++){
            int[] a = r.ii();
            u[i] = a[0];
            v[i] = a[1];
            w[i] = a[2];
            T[u[i]-1].add(new int[]{v[i], w[i]});
            T[v[i]-1].add(new int[]{u[i], w[i]});
        }
        ArrayList<Integer> A = new ArrayList<>();
        A.add(1);
        color[0] = 0;
        while(A.size() > 0){
            int s = A.remove(0);
            ArrayList<int[]> set = T[s-1];
            for(int[] t : set){
                if(color[t[0]-1] < 0){
                    if(t[1]%2 == 0)
                        color[t[0]-1] = color[s-1];
                    else
                        color[t[0]-1] = 1- color[s-1];
                    A.add(t[0]);
                }
            }
        }
        for(int c : color)
            print(c);
    }
    static void print(Object o){
        System.out.println(o.toString());
    }
    static class Reader extends BufferedReader{
        Reader(){
            super(new InputStreamReader(System.in));
        }
        String s() throws IOException{
            return readLine();
        }
        String[] ss() throws IOException{
            return s().split(" ");
        }
        int Int(String s){
            return Integer.parseInt(s);
        }
        int i() throws IOException{
            return Int(s());
        }
        int[] ii() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            int[] ii = new int[size];
            for(int j = 0; j < size; j++) ii[j] = Int(ss[j]);
            return ii;
        }
    }
}