Tree with Small Distances
Description
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.
Input
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.
Output
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.
Samples
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
Note
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 $(1, 3)$.