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:
//package com.company;

import java.io.*;
import java.util.*;

public class Main {
    public static class Task {
        class DJS {
            int[] a;
            public DJS(int n) {
                a = new int[n];
                Arrays.fill(a, -1);
            }
            int find (int x) {
                if (a[x] < 0) return x;
                return a[x] = find(a[x]);
            }
            boolean union(int x, int y) {
                int rx = find(x), ry = find(y);
                if (rx== ry) return false;
                a[rx] = ry;
                return true;
            }
        }
        int glob = 0;
        List<Integer>[] edges;
        int[] start;
        int[] end;
        void dfs(int u, int p) {
            for (int v: edges[u]) if (v != p) {
                end[v] = glob--;
            }
            start[u] = glob--;
            for (int i = 0; i < edges[u].size(); i++) {
                int v = edges[u].get(edges[u].size() - 1- i);
                if (v == p) continue;
                dfs(v, u);
            }
        }

        public void solve(Scanner sc, PrintWriter pw) throws IOException {
            int n = sc.nextInt();
            edges = new List[n];
            for (int i = 0; i < n; i++) {
                edges[i] = new ArrayList<>();
            }
            for (int i = 0; i < n - 1; i++) {
                int a = sc.nextInt() - 1;
                int b = sc.nextInt() - 1;
                edges[a].add(b);
                edges[b].add(a);
            }
            glob = 2 * n;
            start = new int[n];
            end = new int[n];
            end[0] = glob--;

            dfs(0, -1);
            for (int i = 0; i < n;i ++) {
                pw.println(start[i] + " " + end[i]);
            }
        }

    }

    static long TIME_START, TIME_END;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = new Scanner(new FileInputStream("input_line"));
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("input_line"));

        Runtime runtime = Runtime.getRuntime();
        long usedMemoryBefore = runtime.totalMemory() - runtime.freeMemory();
        TIME_START = System.currentTimeMillis();
        Task t = new Task();
        t.solve(sc, pw);
        TIME_END = System.currentTimeMillis();
        long usedMemoryAfter = runtime.totalMemory() - runtime.freeMemory();
        pw.close();
        System.err.println("Memory increased: " + (usedMemoryAfter - usedMemoryBefore) / 1000000);
        System.err.println("Time used: " + (TIME_END - TIME_START) + ".");
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}