# Cut 'em all!

## 题目描述

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.

## 输入输出格式

### 输入格式

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.

### 输出格式

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.

## 输入输出样例

### 输入样例 #1

``````4
2 4
4 1
3 1
``````

### 输出样例 #1

``1``

### 输入样例 #2

``````3
1 2
1 3
``````

### 输出样例 #2

``-1``

### 输入样例 #3

``````10
7 1
8 4
8 10
4 7
6 5
9 3
3 5
2 10
2 5
``````

### 输出样例 #3

``4``

### 输入样例 #4

``````2
1 2
``````

### 输出样例 #4

``0``

## 说明

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 \$ .