CF1182D.Complete Mirror

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.

你有一棵包含 $n$ 个顶点的树。请选出一个顶点作为根节点，使其满足以下条件：

• 对于任意两个顶点 $v_{1}$ 和 $v_{2}$，若 $distance$($root$, $v_{1}$) $= distance$($root$, $v_{2}$)，则必有 $degree$($v_{1}$) $= degree$($v_{2}$)，其中 $degree$ 表示与该顶点相连的顶点数（即度数），$distance$ 表示两个顶点之间边的数量（即距离）。

请判断并找出树中是否存在满足上述条件的根节点。若存在多个解，输出任意一个即可。

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.

第一行包含一个整数 $n$（$1 \le n \le 10^{5}$）—— 表示顶点的数量。

接下来的 $n-1$ 行中，每行包含两个整数 $v_{i}$ 和 $u_{i}$（$1 \le v_{i} \lt u_{i} \le n$）—— 表示顶点 $v_{i}$ 与 $u_{i}$ 之间存在一条边。保证该图构成一棵树。

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

如果存在这样的根顶点，则输出其中任意一个；否则，输出 $-1$。

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.

这是第一个示例的图示。$1$、$5$、$7$ 同样可以是有效的答案。

这是第二个示例的图示。可以看出，无法找到满足条件的根顶点。