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<HashMap<Integer, Boolean>> graph = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            graph.add(new HashMap<>());
        }
        for (int i = 0; i < n - 1; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            boolean c = (sc.nextInt() % 2 == 1);
            graph.get(a).put(b, c);
            graph.get(b).put(a, c);
        }
        boolean[] ans = new boolean[n];
        setAns(0, 0, false, graph, ans);
        StringBuilder sb = new StringBuilder();
        for (boolean b : ans) {
            if (b) {
                sb.append(1);
            } else {
                sb.append(0);
            }
            sb.append("\n");
        }
        System.out.print(sb);
    }
    
    static void setAns(int idx, int parent, boolean value, ArrayList<HashMap<Integer, Boolean>> graph, boolean[] ans) {
        ans[idx] = value;
        for (Map.Entry<Integer, Boolean> entry : graph.get(idx).entrySet()) {
            if (entry.getKey() == parent) {
                continue;
            }
            boolean next = value;
            if (entry.getValue()) {
                next ^= true;
            }
            setAns(entry.getKey(), idx, next, graph, ans);
        }
    }
}