Problem:
Score : 900 points

Problem Statement

Takahashi has an ability to generate a tree using a permutation (p_1,p_2,...,p_n) of (1,2,...,n), in the following process:

First, prepare Vertex 1, Vertex 2, ..., Vertex N.
For each i=1,2,...,n, perform the following operation:

If p_i = 1, do nothing.

If p_i \neq 1, let j' be the largest j such that p_j < p_i. Span an edge between Vertex i and Vertex j'.

Takahashi is trying to make his favorite tree with this ability.
His favorite tree has n vertices from Vertex 1 through Vertex n, and its i-th edge connects Vertex v_i and w_i.
Determine if he can make a tree isomorphic to his favorite tree by using a proper permutation.
If he can do so, find the lexicographically smallest such permutation.

Notes

For the definition of isomorphism of trees, see wikipedia. Intuitively, two trees are isomorphic when they are the "same" if we disregard the indices of their vertices.

Constraints

2 \leq n \leq 10^5

1 \leq v_i, w_i \leq n

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

n
v_1 w_1
v_2 w_2
:
v_{n-1} w_{n-1}

Output

If there is no permutation that can generate a tree isomorphic to Takahashi's favorite tree, print -1.
If it exists, print the lexicographically smallest such permutation, with spaces in between.

Sample Input 1

6
1 2
1 3
1 4
1 5
5 6

Sample Output 1

1 2 4 5 3 6

If the permutation (1, 2, 4, 5, 3, 6) is used to generate a tree, it looks as follows:

This is isomorphic to the given graph.

Sample Input 2

6
1 2
2 3
3 4
1 5
5 6

Sample Output 2

1 2 3 4 5 6

Sample Input 3

15
1 2
1 3
2 4
2 5
3 6
3 7
4 8
4 9
5 10
5 11
6 12
6 13
7 14
7 15

Sample Output 3

-1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using System.Numerics;
using static System.Math;
namespace Program {
	public class Solver {
		Random rnd = new Random();
		public void Solve() {
			var n = ri;
			var G = Enumerate(n, x => new List<int>());
			for (int i = 0; i < n - 1; i++) {
				var u = ri - 1;
				var v = ri - 1;
				G[u].Add(v);
				G[v].Add(u);
			}
			Func<int, int> calc = r => {
				Action<int, int, int> dfs = null;
				var max = -1;
				var id = -1;
				dfs = (p, c, d) => {
					if (max < d) {
						max = d; id = c;
					}
					foreach (var t in G[c])
						if (t != p) dfs(c, t, d + 1);
				};
				dfs(-1, r, 0);
				return id;
			};
			int P = calc(0);
			int Q = calc(P);
			Debug.WriteLine($"{P} {Q}");
			Action<int, int, List<int>> f = null;
			f = (p, c, a) => {
				Debug.WriteLine($"{p} {c}: {a.AsJoinedString()}");
				var l = 0;
				int ll = p == -1 ? 0 : 1;
				foreach (var t in G[c])
					if (t != p && G[t].Count == 1) l++;
				if (l + ll == G[c].Count) {
					for (int i = 0; i < l - 1; i++) {
						a.Add(a.Count + 1);
						var u = a[a.Count - 1]; var v = a[a.Count - 2];
						a[a.Count - 1] = v; a[a.Count - 2] = u;
					}
					a.Add(a.Count + 1);
				}
				else {
					for (int i = 0; i < l; i++) {
						a.Add(a.Count + 1);
						var u = a[a.Count - 1]; var v = a[a.Count - 2];
						a[a.Count - 1] = v; a[a.Count - 2] = u;
					}
					foreach (var t in G[c])
						if (t != p && G[t].Count != 1) { a.Add(a.Count + 1); f(c, t, a); break; }
				}
			};
			var A = new List<int>() { 1 };
			f(-1, P, A);
			var B = new List<int>() { 1 };
			f(-1, Q, B);
			if (A.Count != n) {
				Console.WriteLine(-1);
				return;
			}
			var ans = A;
			Debug.WriteLine(A.AsJoinedString());
			Debug.WriteLine(B.AsJoinedString());
			for (int i = 0; i < n; i++)
				if (ans[i] > B[i]) { ans = B; break; }
				else if (ans[i] < B[i]) break;
			Console.WriteLine(ans.AsJoinedString());

		}

		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		int ri { get { return sc.Integer(); } }
		long rl { get { return sc.Long(); } }
		double rd { get { return sc.Double(); } }
		string rs { get { return sc.Scan(); } }
		public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n];
			for (int i = 0; i < a.Length; ++i) a[i] = f(i);
			return a;
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}
	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = true });
		var solver = new Program.Solver();
		/* 
		var t = new System.Threading.Thread(solver.Solve, 50000000);
		t.Start();
		t.Join();
		*/
		solver.Solve();
		Console.Out.Flush();
	}
}
#endregion
#region Ex
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}

	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}
}

#endregion