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.*;
import java.io.*;

public class Main {
    static boolean[] v = new boolean[1000000];
    static boolean[] color = new boolean[1000000];

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        // long[][] w = new long[n][n];
        Map<Integer, List<Edge>> w = new HashMap<>();
        // List<Edge> w = new ArrayList<>();
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            long weight = sc.nextLong();
            // w[u][v] = weight;
            // w[v][u] = weight;
            if (!w.containsKey(u)) {
                w.put(u, new ArrayList<>());
            }
            if (!w.containsKey(v)) {
                w.put(v, new ArrayList<>());
            }
            w.get(u).add(new Edge(v, weight));
            w.get(v).add(new Edge(u, weight));
        }
        // System.out.println(Arrays.deepToString(w));
        dfs(0, w);
        for (int i = 0; i < n; i++) {
            if (color[i]) {
                System.out.println("1");
            } else {
                System.out.println("0");
            }
        }
    }

    public static void dfs(int now, Map<Integer, List<Edge>> w) {
        v[now] = true;
        for (Edge e : w.get(now)) {
            if (v[e.to]) {
                continue;
            }
            if (e.cost % 2 == 0) {
                color[e.to] = color[now];
            } else {
                color[e.to] = !color[now];
            }
            dfs(e.to, w);
        }
    }
}

class Edge {
    int to;
    long cost;

    public Edge(int to, long cost) {
        this.to = to;
        this.cost = cost;
    }
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}