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.HashMap;
import java.util.Scanner;

public class Main {
    
    private static HashMap<Integer, HashMap<Integer,Integer>> map1;
    private static boolean[] visited;
    private static boolean[] white;

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int u,v,w;
        map1 = new HashMap<>();
        for(int i = 0; i < n-1; i++){
            u = Integer.parseInt(sc.next());
            v = Integer.parseInt(sc.next());
            w = Integer.parseInt(sc.next());
            if(map1.containsKey(u)){
                map1.get(u).put(v, w);
            }else{
                HashMap<Integer,Integer> map2 = new HashMap<>();
                map2.put(v, w);
                map1.put(u, map2);
            }
            if(map1.containsKey(v)){
                map1.get(v).put(u, w);
            }else{
                HashMap<Integer,Integer> map2 = new HashMap<>();
                map2.put(u, w);
                map1.put(v, map2);
            }
        }
        
        visited = new boolean[n+1];
        white = new boolean[n+1];
        if(!map1.isEmpty()){
            dfs(1);
        }
        
        StringBuilder sb = new StringBuilder();
        for(int i = 1; i <= n; i++){
            if(white[i]){
                sb.append("0").append(System.lineSeparator());
            }else{
                sb.append("1").append(System.lineSeparator());
            }
        }
        System.out.print(sb);
    }
    
    private static void dfs(int v){
        
        visited[v] = true;
        
        for(Integer i : map1.get(v).keySet()){
            if(!visited[i]){
                if(map1.get(v).get(i) % 2 == 0){
                    white[i] = white[v];
                }else{
                    white[i] = !white[v];
                }
                dfs(i);
            }
        }
    }
}