A11850. Cut 'em all!

You're given a tree with $n$ vertices.

Your task is to determine the maximum possible number of edges that can be removed in such a way that all the remaining connected components will have even size.
给你一棵有 $n$ 个顶点的树。

你的任务是确定可以移除的最大边数，从而使所有剩余的连接部分大小相同。

The first line contains an integer $n$ ( $1 \le n \le 10^5$ ) denoting the size of the tree.

The next $n - 1$ lines contain two integers $u$ , $v$ ( $1 \le u, v \le n$ ) each, describing the vertices connected by the $i$ -th edge.

It's guaranteed that the given edges form a tree.
输入

第一行包含一个整数 $n$ ( $1 \le n \le 10^5$ )，表示树的大小。

接下来的 $n - 1$ 行分别包含两个整数 $u$ 、 $v$ ( $1 \le u, v \le n$ )，描述由 $i$ -th 边连接的顶点。

可以保证给定的边构成一棵树。

Output a single integer $k$ — the maximum number of edges that can be removed to leave all connected components with even size, or $-1$ if it is impossible to remove edges in order to satisfy this property.
输出

输出单个整数 $k$ - 为使所有相连的组件大小相同而可以去除的最大边数，或者 $-1$ - 如果无法去除边以满足此属性。

In the first example you can remove the edge between vertices $1$ and $4$ . The graph after that will have two connected components with two vertices in each.

In the second example you can't remove edges in such a way that all components have even number of vertices, so the answer is $-1$ .
备注

在第一个示例中，您可以删除顶点 $1$ 和 $4$ 之间的边。之后的图形将有两个相连的部分，每个部分有两个顶点。

在第二个示例中，无法通过删除边的方式使所有分量的顶点数都是偶数，因此答案是 $-1$ 。