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.*;
import java.math.BigInteger;
import java.util.*;

// written by luchy0120

public class Main {
    public static void main(String[] args) throws Exception {

        new Main().run();
    }


    int cnt=1;
    int ps[][];

    void dfs(int rt,int fa){
        int sz =g[rt].size();

        for(int i=0;i<sz;++i){
            int v = g[rt].get(i);
            if(v==fa) continue;
            if(ps[v][0]==0) {
                ps[v][0] = cnt++;
            }else{
                ps[v][1] = cnt++;
            }
        }

            ps[rt][1] = cnt++;

        for(int i=sz-1;i>=0;--i){
            int v = g[rt].get(i);
            if(v==fa) continue;
            dfs(v, rt);
        }
    }

    List<Integer> g[];
    void solve(){
        int n = ni();
       ps =new int[n+1][2];
        g = new ArrayList[n+1];

        for(int i=1;i<=n;++i){
            g[i] = new ArrayList<>();
        }

        for(int i=0;i<n-1;++i){
            int u = ni();
            int v = ni();
            g[u].add(v);
            g[v].add(u);
        }
        ps[1][0] = cnt++;
        dfs(1,-1);
        for(int i=1;i<=n;++i){
           println(ps[i][0]+" "+ps[i][1]);
        }








    }



    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }








//    void solve() {
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                int v = ni();
//                a[i][j] = v;
//                if(v>0) {
//                    vis_row[i][v] = true;
//                    vis_col[j][v] = true;
//                    vis_room[get_room(i, j)][v] = true;
//                }else{
//                    space++;
//                }
//            }
//        }
//
//
//        prepare = new int[space][2];
//
//        int p = 0;
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                if(a[i][j]==0){
//                    prepare[p][0] = i;
//                    prepare[p][1]= j;p++;
//                    List<Integer> temp =new ArrayList<>();
//                    for(int k=1;k<=9;++k){
//                        if(!vis_col[j][k]&&!vis_row[i][k]&&!vis_room[get_room(i,j)][k]){
//                            temp.add(k);
//                        }
//                    }
//                    int sz = temp.size();
//                    val[i][j] = new int[sz];
//                    for(int k=0;k<sz;++k){
//                        val[i][j][k] = temp.get(k);
//                    }
//                }
//            }
//        }
//        Arrays.sort(prepare,(x,y)->{
//           return Integer.compare(val[x[0]][x[1]].length,val[y[0]][y[1]].length);
//        });
//        dfs(0);
//
//
//
//
//
//
//
//
//
//
//    }




    InputStream is;
    PrintWriter out;

    void run() throws Exception {
        is = System.in;
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

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

    private char nc() {
        return (char) skip();
    }

    private char ncc() {
        int b = readByte();
        return (char) b;
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private String nline() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[][] nm(int n, int m) {
        char[][] a = new char[n][];
        for (int i = 0; i < n; i++) a[i] = ns(m);
        return a;
    }

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

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

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    void print(Object obj) {
        out.print(obj);
    }

    void println(Object obj) {
        out.println(obj);
    }

    void println() {
        out.println();
    }

    void printArray(int a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }

    void printArray(long a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }
}