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.

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.

Examples

Input

6
1 2
1 3
1 4
1 5
5 6


Output

1 2 4 5 3 6


Input

6
1 2
2 3
3 4
1 5
5 6


Output

1 2 3 4 5 6


Input

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


Output

-1

import java.util.Arrays;

public class Main {
  private static void solve() {
    int n = ni();
    int[] from = new int[n - 1];
    int[] to = new int[n - 1];
    for (int i = 0; i < n - 1; i ++) {
      from[i] = ni() - 1;
      to[i] = ni() - 1;
    }
    int[][] g = packU(n, from, to);
    int[] d = diameter(g);
    
    int[] a1 = f(g, d[1]);
    int[] a2 = f(g, d[2]);

    if (a1 == null) {
      System.out.println(-1);
      return;
    }
    boolean flg = true;
    for (int i = 0; i < n; i ++) {
      if (a1[i] > a2[i]) {
        break;
      } else if (a1[i] < a2[i]) {
        flg = false;
        break;
      }
    }
    digit(flg ? a2 : a1);
  }

  private static void digit(int[] a) {
    for (int v : a) {
      out.print(v + " ");
    }
    out.println();
  }

  private static int[] f(int[][] g, int s) {
    int n = g.length;
    int[] ret = new int[n];
    int ptr = 0;

    int pre = -1;
    int now = s;
    while (now >= 0 && now < n) {
      int deg = g[now].length - (now == s ? 1 : 2);
      
      int next = -1;
      for (int v : g[now]) {
        if (v == pre) continue;
        if (g[v].length > 1) {
          if (next >= 0) return null;
          next = v;
        }
      }

      int v = ptr;
      for (int i = 0; i < deg; i ++) {
        ret[ptr] = ptr + 2;
        ptr ++;
      }
      ret[ptr ++] = v + 1;
      pre = now;
      now = next;
    }
    ret[n - 1] = n;
    return ret;
  }
  
  public static int[][] packU(int n, int[] from, int[] to){ return packU(n, from, to, from.length); }
  public static int[][] packU(int n, int[] from, int[] to, int sup)
  {
      int[][] g = new int[n][];
      int[] p = new int[n];
      for(int i = 0;i < sup;i++)p[from[i]]++;
      for(int i = 0;i < sup;i++)p[to[i]]++;
      for(int i = 0;i < n;i++)g[i] = new int[p[i]];
      for(int i = 0;i < sup;i++){
          g[from[i]][--p[from[i]]] = to[i];
          g[to[i]][--p[to[i]]] = from[i];
      }
      return g;
  }
  
  public static int[] diameter(int[][] g)
  {
      int n = g.length;
      int f0 = -1, f1 = -1, d01 = -1;
      int[] q = new int[n];
      boolean[] ved = new boolean[n];
      {
          int qp = 0;
          q[qp++] = 0; ved[0] = true;
          for(int i = 0;i < qp;i++){
              int cur = q[i];
              for(int e : g[cur]){
                  if(!ved[e]){
                      ved[e] = true;
                      q[qp++] = e;
                      continue;
                  }
              }
          }
          f0 = q[n-1];
      }
      {
          int[] d = new int[n];
          int qp = 0;
          Arrays.fill(ved, false);
          q[qp++] = f0; ved[f0] = true;
          for(int i = 0;i < qp;i++){
              int cur = q[i];
              for(int e : g[cur]){
                  if(!ved[e]){
                      ved[e] = true;
                      q[qp++] = e;
                      d[e] = d[cur] + 1;
                      continue;
                  }
              }
          }
          f1 = q[n-1];
          d01 = d[f1];
      }
      return new int[]{d01, f0, f1};
  }
  
  
  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

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

  private static long nl() {
    return Long.parseLong(next());
  }

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

  private static char[] ns() {
    return next().toCharArray();
  }

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

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}


