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.ArrayList;
import java.util.List;
import java.util.Scanner;

class Main{
    static List<Integer> edges[];
    static List<Integer> edge = new ArrayList<>();
    static boolean[] isLeaf;

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        // 小さい順に挿入
        int n = scan.nextInt();
        edges = new ArrayList[n];
        for(int i=0;i<n;++i)edges[i]=new ArrayList<>();
        for(int i=0;i<n-1;++i){
            int v = scan.nextInt()-1;
            int u = scan.nextInt()-1;
            edges[v].add(u);edges[u].add(v);
        }
        isLeaf = new boolean[n];
        for(int i=0;i<n;++i)if(edges[i].size()==1)isLeaf[i]=true;
        for(int i=0;i<n;++i){
            if(isLeaf[i])continue;
            int cnt = 0;
            for(int u : edges[i])if(!isLeaf[u])++cnt;
            if(cnt<=1)edge.add(i);
            if(cnt>2){
                System.out.println(-1);
                return;
            }
        }
        List<Integer> ans = new ArrayList<>();
        if(edge.size()==2){
            for(int v : edge){
                List<Integer> list = new ArrayList<>();
                list.add(0);
                int bef=-1;
                int u = v;
                boolean flag=true;
                while(flag){
                    list.add(edges[u].size()-2);
                    flag=false;
                    for(int w :edges[u])if(!isLeaf[w]&&w!=bef){
                        flag=true;bef=u;u=w;break;
                    }
                }
                list.add(0);
                if(ans.size()==0)ans=list;
                else{
                    for(int i=0;i<ans.size();++i){
                        if(ans.get(i)==list.get(i))continue;
                        else if(ans.get(i)> list.get(i))ans=list;
                        break;
                    }
                }
            }
        }else{
            ans = new ArrayList<>();
            ans.add(0);
            if(edge.size()>0)ans.add(edges[edge.get(0)].size()-2);
            ans.add(0);
        }



        List<Integer> res = new ArrayList<>();
        int num = 1;
        for(int k : ans){
            for(int i=0;i<k;++i)res.add(1+num++);
            res.add(num++ -k);
        }
        for(int k : res)System.out.print(k+" ");
        System.out.println();

    }
}