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.PrintWriter;
import java.util.Vector;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Stack;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ribhav
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ETestsForProblemD solver = new ETestsForProblemD();
        solver.solve(1, in, out);
        out.close();
    }

    static class ETestsForProblemD {
        public void solve(int testNumber, FastReader s, PrintWriter out) {
            int n = s.nextInt();
            HashMap<Integer, ArrayList<Integer>> map = new HashMap<>();
            for (int i = 0; i < n - 1; i++) {
                int src = s.nextInt();
                int dest = s.nextInt();

                ArrayList<Integer> list = map.getOrDefault(src, new ArrayList<>());
                list.add(dest);
                map.put(src, list);

                list = map.getOrDefault(dest, new ArrayList<>());
                list.add(src);
                map.put(dest, list);
            }

            Stack<Integer> stack = new Stack<>();
            stack.add(1);
            int[] ans = new int[2 * n];
            boolean[] visited = new boolean[2 * n + 1];
            visited[1] = true;
            int currPos = 1;
            ans[0] = 1;
            while (!stack.isEmpty()) {
                int curr = stack.pop();
                ArrayList<Integer> list = map.getOrDefault(curr, new ArrayList<>());
                for (Integer next : list) {
                    if (!visited[next]) {
                        stack.add(next);
                        ans[currPos++] = next;
                        visited[next] = true;
                    }
                }
                ans[currPos++] = -curr;
            }
//        out.println(arrays.printArr(ans));
            ETestsForProblemD.pair[] arr = new ETestsForProblemD.pair[n + 1];
            for (int i = 1; i <= n; i++) {
                arr[i] = new ETestsForProblemD.pair();
            }
            for (int i = 0; i < 2 * n; i++) {
                if (ans[i] > 0) {
                    arr[ans[i]].from = i + 1;
                } else {
                    arr[-ans[i]].to = i + 1;
                }
            }

            for (int i = 1; i <= n; i++) {
                out.println(arr[i].from + " " + arr[i].to);
            }

        }

        private static class pair {
            int from;
            int to;

            public pair() {

            }

            public pair(int from) {
                this.from = from;
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}