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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Deque;
import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    public static void main(String[] args) throws NumberFormatException, IOException {
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(stdin.readLine());
        
        Map<Integer, Map<Integer, Integer>> weights 
            = IntStream.range(0, n)
                       .boxed()
                       .collect(Collectors.toMap(Function.identity(), unused -> new HashMap<>()));
        for (int i = 0; i < n - 1; i++) {
            String[] line = stdin.readLine().split(" ");
            int u = Integer.parseInt(line[0]) - 1;
            int v = Integer.parseInt(line[1]) - 1;
            int w = Integer.parseInt(line[2]);
            weights.get(u).put(v, w);
            weights.get(v).put(u, w);
        }
        
        
        int[] colors = new int[n];
        Arrays.fill(colors, -1);
        colors[0] = 0;
        
        Deque<Integer> stack = new ArrayDeque<>();
        stack.push(0);
        
        while (!stack.isEmpty()) {
            int current = stack.pop();
            for (Entry<Integer, Integer> e : weights.get(current).entrySet()) {
                int next = e.getKey();
                if (colors[next] != -1) {
                    continue;
                }
                
                if (e.getValue() % 2 == 0) {
                    colors[next] = colors[current];
                } else {
                    colors[next] = 1 - colors[current];
                }
                stack.push(next);
            }
        }
        
        Arrays.stream(colors).forEach(System.out::println);
    }
}