CF1029E.Tree with Small Distances

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.

给你一棵包含 $n$ 个顶点的无向树。无向树是一种具有 $n - 1$ 条边的连通无向图。

你的任务是添加最少数量的边，使得顶点 $1$ 到任意其他顶点的最短路径长度至多为 $2$。注意：不允许添加自环（loop）和重边（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.

第一行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）——树中顶点的数量。

接下来的 $n - 1$ 行描述边：第 $i$ 条边以一对顶点 $u_i, v_i$（$1 \le u_i, v_i \le n$）给出。保证所给边构成一棵树。保证所给边中不存在自环和重边。

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.

输出一个整数——为使顶点 $1$ 到任意其他顶点的最短距离至多为 $2$，所需添加的最少边数。注意：不允许添加自环边和重边。

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 $(1, 3)$.

第一个示例对应的树： 答案为 $2$，其中一些可能的答案如下：$[(1, 5), (1, 6)]$、$[(1, 4), (1, 7)]$、$[(1, 6), (1, 7)]$。

第二个示例对应的树： 答案为 $0$。

第三个示例对应的树： 答案为 $1$，唯一能达到该答案的方式是添加边 $(1, 3)$。