200953: [AtCoder]ARC095 F - Permutation Tree

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