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-----
6
1 2
1 3
1 4
1 5
5 6

-----Sample Output-----
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.

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