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.

Input

The first line contains one integer n (2 ≤ n ≤ 2 * 105) — the number of vertices in the tree.

The following n − 1 lines contain edges: edge i is given as a pair of vertices ui, vi (1 ≤ ui, vi ≤ 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.