Tree with Small Distances

Description:

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.

Sample Input:

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

Sample Output:

2

Sample Input:

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

Sample Output:

0

Sample Input:

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

Sample Output:

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 $$$(1, 3)$$$.