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:

public class Main {

    private static void solve() {
        int n = ni();
        int[] from = new int[n - 1];
        int[] to = new int[n - 1];
        int[] w = new int[n - 1];
        for (int i = 0; i < n - 1; i++) {
            from[i] = ni() - 1;
            to[i] = ni() - 1;
            w[i] = ni();
        }
        int[][][] g = packWU(n, from, to, w);
        int[] ret = new int[n];
        dfs(0, -1, g, ret, 0);

        for (int v : ret) {
            out.println(v);
        }
    }

    private static void dfs(int now, int pre, int[][][] g, int[] ret, int eo) {
        ret[now] = eo;
        for (int[] v : g[now]) {
            int nex = v[0];
            int w = v[1];
            if (nex == pre)
                continue;

            dfs(nex, now, g, ret, eo ^ (w % 2 == 0 ? 0 : 1));
        }
    }

    public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
        return packWU(n, from, to, w, from.length);
    }

    public static int[][][] packWU(int n, int[] from, int[] to, int[] w, int sup) {
        int[][][] g = new int[n][][];
        int[] p = new int[n];
        for (int i = 0; i < sup; i++)
            p[from[i]]++;
        for (int i = 0; i < sup; i++)
            p[to[i]]++;
        for (int i = 0; i < n; i++)
            g[i] = new int[p[i]][2];
        for (int i = 0; i < sup; i++) {
            --p[from[i]];
            g[from[i]][p[from[i]]][0] = to[i];
            g[from[i]][p[from[i]]][1] = w[i];
            --p[to[i]];
            g[to[i]][p[to[i]]][0] = from[i];
            g[to[i]][p[to[i]]][1] = w[i];
        }
        return g;
    }

    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            @Override
            public void run() {
                long start = System.currentTimeMillis();
                String debug = args.length > 0 ? args[0] : null;
                if (debug != null) {
                    try {
                        is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
                    } catch (Exception e) {
                        throw new RuntimeException(e);
                    }
                }
                reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
                solve();
                out.flush();
                tr((System.currentTimeMillis() - start) + "ms");
            }
        }, "", 64000000).start();
    }

    private static java.io.InputStream is = System.in;
    private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
    private static java.util.StringTokenizer tokenizer = null;
    private static java.io.BufferedReader reader;

    public static String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new java.util.StringTokenizer(reader.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    private static double nd() {
        return Double.parseDouble(next());
    }

    private static long nl() {
        return Long.parseLong(next());
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = ni();
        return a;
    }

    private static char[] ns() {
        return next().toCharArray();
    }

    private static long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nl();
        return a;
    }

    private static int[][] ntable(int n, int m) {
        int[][] table = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                table[i][j] = ni();
            }
        }
        return table;
    }

    private static int[][] nlist(int n, int m) {
        int[][] table = new int[m][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                table[j][i] = ni();
            }
        }
        return table;
    }

    private static int ni() {
        return Integer.parseInt(next());
    }

    private static void tr(Object... o) {
        if (is != System.in)
            System.out.println(java.util.Arrays.deepToString(o));
    }
}