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 {
    static Scanner scanner = new Scanner(System.in);
 
    public static void main(String[]$) {
        int n = scanner.nextInt();
        int[] d = new int[n];
        Arrays.fill(d, 1, n, Integer.MAX_VALUE);
        Map<Integer, Map<Integer, Integer>> dist = new HashMap<>();
        for (int i = 0; i < n; i++) {
            dist.put(i, new HashMap<>());
        }
 
        for (int i = 0; i < n - 1; i++) {
            int u = scanner.nextInt() - 1;
            int v = scanner.nextInt() - 1;
            int w = scanner.nextInt() & 1;
            dist.get(u).put(v, w);
            dist.get(v).put(u, w);
        }
 
        Deque<Integer> deque = new ArrayDeque<>();
        deque.add(0);
        while (!deque.isEmpty()) {
            int i = deque.poll();
            for (Map.Entry<Integer, Integer> entry : dist.get(i).entrySet()) {
                if (d[entry.getKey()] > d[i] + entry.getValue()) {
                    d[entry.getKey()] = d[i] + entry.getValue();
                    deque.add(entry.getKey());
                }
            }
        }
 
        for (int i : d) {
            System.out.println(i & 1);
        }
    }
}