Problem: We had a really tough time generating tests for problem D. In order to prepare strong tests, we had to solve the following problem.

Given an undirected labeled tree consisting of n vertices, find a set of segments such that:

  1. both endpoints of each segment are integers from 1 to 2n, and each integer from 1 to 2n should appear as an endpoint of exactly one segment; 
  2. all segments are non-degenerate; 
  3. for each pair (i, j) such that i ≠ j, i ∈ [1, n] and j ∈ [1, n], the vertices i and j are connected with an edge if and only if the segments i and j intersect, but neither segment i is fully contained in segment j, nor segment j is fully contained in segment i. 



Can you solve this problem too?

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the number of vertices in the tree.

Then n - 1 lines follow, each containing two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i) denoting the endpoints of the i-th edge.

It is guaranteed that the given graph is a tree.

Output

Print n pairs of integers, the i-th pair should contain two integers l_i and r_i (1 ≤ l_i < r_i ≤ 2n) — the endpoints of the i-th segment. All 2n integers you print should be unique.

It is guaranteed that the answer always exists.

Examples

Input


6
1 2
1 3
3 4
3 5
2 6


Output


9 12
7 10
3 11
1 5
2 4
6 8


Input


1


Output


1 2

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            ETestsForProblemD solver = new ETestsForProblemD();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class ETestsForProblemD {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            Node[] nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
            }
            for (int i = 1; i < n; i++) {
                Node a = nodes[in.readInt() - 1];
                Node b = nodes[in.readInt() - 1];
                a.next.add(b);
                b.next.add(a);
            }

            dfs(nodes[0], null);
            for (int i = 0; i < n; i++) {
                Splay.splay(nodes[i].left);
                out.append(nodes[i].left.size - nodes[i].left.right.size).append(' ');
                Splay.splay(nodes[i].right);
                out.println(nodes[i].right.size - nodes[i].right.right.size);
            }
        }

        public Splay dfs(Node root, Node p) {
            root.next.remove(p);
            Splay splay = Splay.NIL;
            for (int i = 0; i < root.next.size(); i++) {
                Node node = root.next.get(i);
                Splay child = dfs(node, root);
                if (splay == Splay.NIL) {
                    splay = child;
                    continue;
                }
                splay = Splay.selectKthAsRoot(splay, i);
                Splay right = Splay.splitRight(splay);
                splay = Splay.merge(splay, child);
                splay = Splay.merge(splay, right);
            }

            splay = Splay.merge(root.left, splay);
            splay = Splay.selectKthAsRoot(splay, root.next.size() + 1);
            Splay right = Splay.splitRight(splay);
            splay = Splay.merge(splay, root.right);
            splay = Splay.merge(splay, right);

            return splay;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Node {
        List<Node> next = new ArrayList<>();
        Splay left = new Splay();
        Splay right = new Splay();

    }

    static class Splay implements Cloneable {
        public static final Splay NIL = new Splay();
        Splay left = NIL;
        Splay right = NIL;
        Splay father = NIL;
        int size = 1;
        int key;

        static {
            NIL.left = NIL;
            NIL.right = NIL;
            NIL.father = NIL;
            NIL.size = 0;
        }

        public static void splay(Splay x) {
            if (x == NIL) {
                return;
            }
            Splay y, z;
            while ((y = x.father) != NIL) {
                if ((z = y.father) == NIL) {
                    y.pushDown();
                    x.pushDown();
                    if (x == y.left) {
                        zig(x);
                    } else {
                        zag(x);
                    }
                } else {
                    z.pushDown();
                    y.pushDown();
                    x.pushDown();
                    if (x == y.left) {
                        if (y == z.left) {
                            zig(y);
                            zig(x);
                        } else {
                            zig(x);
                            zag(x);
                        }
                    } else {
                        if (y == z.left) {
                            zag(x);
                            zig(x);
                        } else {
                            zag(y);
                            zag(x);
                        }
                    }
                }
            }

            x.pushDown();
            x.pushUp();
        }

        public static void zig(Splay x) {
            Splay y = x.father;
            Splay z = y.father;
            Splay b = x.right;

            y.setLeft(b);
            x.setRight(y);
            z.changeChild(y, x);

            y.pushUp();
        }

        public static void zag(Splay x) {
            Splay y = x.father;
            Splay z = y.father;
            Splay b = x.left;

            y.setRight(b);
            x.setLeft(y);
            z.changeChild(y, x);

            y.pushUp();
        }

        public void setLeft(Splay x) {
            left = x;
            x.father = this;
        }

        public void setRight(Splay x) {
            right = x;
            x.father = this;
        }

        public void changeChild(Splay y, Splay x) {
            if (left == y) {
                setLeft(x);
            } else {
                setRight(x);
            }
        }

        public void pushUp() {
            size = left.size + right.size + 1;
        }

        public void pushDown() {
        }

        public static void toString(Splay root, StringBuilder builder) {
            if (root == NIL) {
                return;
            }
            root.pushDown();
            toString(root.left, builder);
            builder.append(root.key).append(',');
            toString(root.right, builder);
        }

        public Splay clone() {
            try {
                return (Splay) super.clone();
            } catch (CloneNotSupportedException e) {
                throw new RuntimeException(e);
            }
        }

        public static Splay cloneTree(Splay splay) {
            if (splay == NIL) {
                return NIL;
            }
            splay = splay.clone();
            splay.left = cloneTree(splay.left);
            splay.right = cloneTree(splay.right);
            return splay;
        }

        public static Splay selectMaxAsRoot(Splay root) {
            if (root == NIL) {
                return root;
            }
            root.pushDown();
            while (root.right != NIL) {
                root = root.right;
                root.pushDown();
            }
            splay(root);
            return root;
        }

        public static Splay splitRight(Splay root) {
            root.pushDown();
            Splay right = root.right;
            right.father = NIL;
            root.setRight(NIL);
            root.pushUp();
            return right;
        }

        public static Splay merge(Splay a, Splay b) {
            if (a == NIL) {
                return b;
            }
            if (b == NIL) {
                return a;
            }
            a = selectMaxAsRoot(a);
            a.setRight(b);
            a.pushUp();
            return a;
        }

        public static Splay selectKthAsRoot(Splay root, int k) {
            if (root == NIL) {
                return NIL;
            }
            Splay trace = root;
            Splay father = NIL;
            while (trace != NIL) {
                father = trace;
                trace.pushDown();
                if (trace.left.size >= k) {
                    trace = trace.left;
                } else {
                    k -= trace.left.size + 1;
                    if (k == 0) {
                        break;
                    } else {
                        trace = trace.right;
                    }
                }
            }
            splay(father);
            return father;
        }

        public String toString() {
            StringBuilder builder = new StringBuilder().append(key).append(":");
            toString(cloneTree(this), builder);
            return builder.toString();
        }

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}