CF982C.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.

给你一棵包含 $n$ 个顶点的树。

你的任务是确定最多可以删除多少条边，使得剩余的所有连通分量的大小均为偶数。

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.

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 $n - 1$ 行每行包含两个整数 $u$、$v$（$1 \le u, v \le n$），描述第 $i$ 条边所连接的两个顶点。

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.

输出一个整数 $k$ —— 满足删除后所有连通分量的大小均为偶数的最大可删除边数；若无法通过删边使所有连通分量的大小均为偶数，则输出 $-1$。

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 $-1$.

在第一个例子中，你可以删除顶点 $1$ 和 $4$ 之间的边。删除后，图将分为两个连通分量，每个分量包含两个顶点。

在第二个例子中，无法通过删除边使得所有连通分量均包含偶数个顶点，因此答案为 $-1$。