Tree with Small Distances

### 题目描述 给定一颗有根树（根节点为 $1$）。要求往树中加入一些边使得从根节点到其他节点的距离至多是 $2$。 求加入边的最小数量。(边全部都是无向的) ### 输入格式 第一行一个整数 $n$，表示树中的节点个数。 接下来 $n−1$ 行，每行两个整数 $x,y$，表示 $x,y$ 之间有一条连边。 ### 输出格式 一个整数，表示加入边的最小数量。 ### 数据范围 $2 \le n \le 2\times 10^5$

You are given an undirected tree consisting of $ n $ vertices. An undirected tree is a connected undirected graph with $ n - 1 $ edges. Your task is to add the minimum number of edges in such a way that the length of the shortest path from the vertex $ 1 $ to any other vertex is at most $ 2 $ . Note that you are not allowed to add loops and multiple edges.

The first line contains one integer $ n $ ( $ 2 \le n \le 2 \cdot 10^5 $ ) — the number of vertices in the tree. The following $ n - 1 $ lines contain edges: edge $ i $ is given as a pair of vertices $ u_i, v_i $ ( $ 1 \le u_i, v_i \le n $ ). It is guaranteed that the given edges form a tree. It is guaranteed that there are no loops and multiple edges in the given edges.

Print a single integer — the minimum number of edges you have to add in order to make the shortest distance from the vertex $ 1 $ to any other vertex at most $ 2 $ . Note that you are not allowed to add loops and multiple edges.

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

2

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

0

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

1

The tree corresponding to the first example:  The answer is $ 2 $ , some of the possible answers are the following: $ [(1, 5), (1, 6)] $ , $ [(1, 4), (1, 7)] $ , $ [(1, 6), (1, 7)] $ . The tree corresponding to the second example:  The answer is $ 0 $ . The tree corresponding to the third example:  The answer is $ 1 $ , only one possible way to reach it is to add the edge $ (1, 3) $ .