Complete Mirror

题意翻译

给定一个$n$个点的无根树，求一个树根$root$,使得对于任意两个节点$v_1,v_2$，若满足$dist(v_1,root)=dist(v_2,root)$,则必有$dgr(v_1)=dgr(v_2)$，无解输出$-1$。 $dist(u,v)$定义为$u,v$之间的边数，$dgr(v)$定义为与$v$点直接相连的点的个数。

题目描述

You have given tree consist of $ n $ vertices. Select a vertex as root vertex that satisfies the condition below. - For all vertices $ v_{1} $ and $ v_{2} $ , if $ distance $ ( $ root $ , $ v_{1} $ ) $ = distance $ ( $ root $ , $ v_{2}) $ then $ degree $ ( $ v_{1} $ ) $ = degree $ ( $ v_{2} $ ), where $ degree $ means the number of vertices connected to that vertex, and $ distance $ means the number of edges between two vertices. Determine and find if there is such root vertex in the tree. If there are multiple answers, find any of them.

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 1 \le n \le 10^{5} $ ) — the number of vertices. Each of the next $ n-1 $ lines contains two integers $ v_{i} $ and $ u_{i} $ ( $ 1 \le v_{i} \lt u_{i} \le n $ ) — it means there is an edge exist between $ v_{i} $ and $ u_{i} $ . It is guaranteed that the graph forms tree.

输出格式

If there is such root vertex exists, print any of them. Otherwise, print $ -1 $ .

输入输出样例

输入样例 #1

7
1 2
2 3
3 4
4 5
3 6
6 7

输出样例 #1

3

输入样例 #2

6
1 3
2 3
3 4
4 5
4 6

输出样例 #2

-1

说明

This is the picture for the first example. $ 1 $ , $ 5 $ , $ 7 $ also can be a valid answer. This is the picture for the second example. You can see that it's impossible to find such root vertex.