Permutation Tree

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

inputFormat

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}

outputFormat

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

样例

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

-1