Problem: We have a tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and Vertex b_i.

Takahashi loves the number 3. He is seeking a permutation p_1, p_2, \ldots , p_N of integers from 1 to N satisfying the following condition:

* For every pair of vertices (i, j), if the distance between Vertex i and Vertex j is 3, the sum or product of p_i and p_j is a multiple of 3.



Here the distance between Vertex i and Vertex j is the number of edges contained in the shortest path from Vertex i to Vertex j.

Help Takahashi by finding a permutation that satisfies the condition.

Constraints

* 2\leq N\leq 2\times 10^5
* 1\leq a_i, b_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
a_2 b_2
\vdots
a_{N-1} b_{N-1}


Output

If no permutation satisfies the condition, print `-1`.

Otherwise, print a permutation satisfying the condition, with space in between. If there are multiple solutions, you can print any of them.

Example

Input

5
1 2
1 3
3 4
3 5


Output

1 2 5 4 3

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.Queue;
import java.util.stream.IntStream;

public class Main {
    private static final int RED = 0;
    private static final int BLUE = 1;

    private static void dfs(AdjacencyList al,
                            Queue<Integer> red,
                            Queue<Integer> blue,
                            int parentVertexId,
                            int vertexId,
                            int color) {
        switch (color) {
            case RED:
                red.offer(vertexId);
                break;
            case BLUE:
                blue.offer(vertexId);
                break;
            default:
                throw new AssertionError(color);
        }
        for (Edge e : al.edgesFrom(vertexId)) {
            if (e.to == parentVertexId) {
                continue;
            }
            dfs(al, red, blue, vertexId, e.to, color == RED ? BLUE : RED);
        }
    }
    static void solve(MyScanner in, MyWriter out) {
        int n = in.nextInt();
        if (n <= 3) {
            out.joinAndPrintln(IntStream.rangeClosed(1, n).toArray());
            return;
        }
        int[][] ab = in.nextVerticalIntArrays(2, n - 1);
        int[] a = decrement(ab[0]);
        int[] b = decrement(ab[1]);
        AdjacencyList al =
                AdjacencyList.forUndirectedGraph(n, Edge.listOf(a, b));
        Queue<Integer> red = new ArrayDeque<>();
        Queue<Integer> blue = new ArrayDeque<>();
        dfs(al, red, blue, -1, 0, BLUE);
        int[] ans = new int[n];
        int m = n / 3;
        if (red.size() > m && blue.size() > m) {
            for (int i = 1; i <= n; i++) {
                if (i % 3 == 1) {
                    ans[blue.poll()] = i;
                } else if (i % 3 == 2) {
                    ans[red.poll()] = i;
                }
            }
            for (int i = 3; i <= n; i += 3) {
                if (!blue.isEmpty()) {
                    ans[blue.poll()] = i;
                } else {
                    ans[red.poll()] = i;
                }
            }
        } else if (red.size() <= m) {
            for (int i = 1; i <= n; i++) {
                if (i % 3 == 0 && !red.isEmpty()) {
                    ans[red.poll()] = i;
                } else {
                    ans[blue.poll()] = i;
                }
            }
        } else {
            for (int i = 1; i <= n; i++) {
                if (i % 3 == 0 && !blue.isEmpty()) {
                    ans[blue.poll()] = i;
                } else {
                    ans[red.poll()] = i;
                }
            }
        }
        out.joinAndPrintln(ans);
    }
    static final class Edge {
        final int from;
        final int to;
        final long weight;
        final int id;

        Edge(int from, int to) {
            this(from, to, 1);
        }
        Edge(int from, int to, int weight) {
            this(from, to, weight, -1);
        }
        Edge(int from, int to, long weight, int id) {
            if (from < 0 || to < 0) {
                throw new IllegalArgumentException();
            }
            this.from = from;
            this.to = to;
            this.weight = weight;
            this.id = id;
        }
        int from() {
            return from;
        }
        int to() {
            return to;
        }
        long weight() {
            return weight;
        }
        Edge reverse() {
            return new Edge(to, from, weight, id);
        }
        static List<Edge> listOf(int[] from, int[] to) {
            return listOf(from, to, null);
        }
        static List<Edge> listOf(int[] from, int[] to, int[] weight) {
            if (from.length != to.length
                || (weight != null && from.length != weight.length)) {
                throw new IllegalArgumentException();
            }
            List<Edge> result = new ArrayList<>(from.length);
            for (int i = 0; i < from.length; i++) {
                result.add(new Edge(from[i],
                                    to[i],
                                    weight == null ? 1 : weight[i],
                                    i));
            }
            return result;
        }
    }
    static final class AdjacencyList {
        private final List<List<Edge>> list;

        private AdjacencyList(List<List<Edge>> list) {
            this.list = list;
        }
        int vertexCount() {
            return list.size();
        }
        List<Edge> edgesFrom(int vertexId) {
            return list.get(vertexId);
        }
        static AdjacencyList forDirectedGraph(int vertexCount,
                                              List<Edge> edges) {
            List<List<Edge>> list =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            list.replaceAll(e -> new ArrayList<>());
            for (Edge e : edges) {
                list.get(e.from).add(e);
            }
            return new AdjacencyList(list);
        }
        static AdjacencyList forUndirectedGraph(int vertexCount,
                                                List<Edge> edges) {
            List<List<Edge>> list =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            list.replaceAll(e -> new ArrayList<>());
            for (Edge e : edges) {
                list.get(e.from).add(e);
                list.get(e.to).add(e.reverse());
            }
            return new AdjacencyList(list);
        }
    }
    private static int[] decrement(int[] a) {
        for (int i = 0; i < a.length; i++) {
            a[i]--;
        }
        return a;
    }
    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        solve(new MyScanner(System.in), w);
        w.flush();
    }
    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;

        MyScanner(InputStream in) {
            this.in = in;
        }
        private byte readByte() {
            if (point < readLength) {
                byte result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isPrintableCharExceptSpace(byte c) {
            return 33 <= c && c <= 126;
        }
        public char nextChar() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        public String next() {
            return next(16);
        }
        public String next(int n) {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return b.toString();
        }
        public long nextLong() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long result = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                result = result * 10L + (c - '0');
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return minus ? -result : result;
        }
        public int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        public long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        public char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        public char[][] next2dCharArray(int n, int m) {
            char[][] result = new char[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        public int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        public long[][] nextVerticalLongArrays(int arrayCount,
                                               int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        public char[][] nextVerticalCharArrays(int arrayCount,
                                               int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        public void joinAndPrintln(int[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(int[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(long[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(long[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(Iterable<?> iterable) {
            joinAndPrintln(iterable, " ");
        }
        public void joinAndPrintln(Iterable<?> iterable, String delimiter) {
            StringBuilder b = new StringBuilder();
            for (Iterator<?> i = iterable.iterator(); i.hasNext();) {
                b.append(i.next());
                while (i.hasNext()) {
                    b.append(delimiter).append(i.next());
                }
            }
            println(b.toString());
        }
    }
}