F - Permutation Tree

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• p_i = 1 である場合、何もしない。
• p_i \neq 1 である場合、p_j < p_i であるような j のうち最大のものを j' とする。 頂点 i と 頂点 j' の間に辺を貼る。

### 制約

• 2 \leq n \leq 10^5
• 1 \leq v_i, w_i \leq n
• 与えられるグラフは木である

### 入力

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


### 入力例 1

6
1 2
1 3
1 4
1 5
5 6


### 出力例 1

1 2 4 5 3 6


(1, 2, 4, 5, 3, 6) という順列を使って木を作ると、次の図のようになります。

これは入力のグラフと同型です。

### 入力例 2

6
1 2
2 3
3 4
1 5
5 6


### 出力例 2

1 2 3 4 5 6


### 入力例 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


### 出力例 3

-1


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