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();

        ArrayList<Integer>[] o=new ArrayList[N];
        ArrayList<Integer>[] w=new ArrayList[N];
        for(int i=0;i<N;i++){
            o[i]=new ArrayList<>();
            w[i]=new ArrayList<>();
        }

        for(int i=0;i<N-1;i++){
            int u=sc.nextInt();
            int v=sc.nextInt();
            int a=sc.nextInt();
            o[u-1].add(v-1);
            w[u-1].add(a);
            o[v-1].add(u-1);
            w[v-1].add(a);
        }
        char[] result=new char[2*N];
        boolean isEven=true;

        Stack<Integer> q=new Stack<>();
        q.add(0);
        Stack<Integer> s=new Stack<Integer>();
        s.add(0);
        Stack<Boolean> bool=new Stack<Boolean>();
        bool.add(true);
        int pos=0;
        int index=0;
        result[0]='0';
        while(q.size()!=0){
            if(result[o[pos].get(index)*2]==0){
                q.add(pos);
                s.add(index);
                bool.add(isEven);
                if((w[pos].get(index)%2==1)){
                    isEven=!isEven;
                }
                pos=o[pos].get(index);
                index=0;
                if(isEven){
                    result[pos*2]='0';
                }else{
                    result[pos*2]='1';
                }
                continue;
            }

            index++;
            if(index==o[pos].size()){
                index=s.pop();
                pos=q.pop();
                isEven=bool.pop();
            }

        }


        for(int i=0;i<N;i++){
            result[2*i+1]='\n';
        }
        System.out.print(new String(result));

    }
    static boolean isMonth(int a){
        return a>0&&a<13;
    }

}