Vertex Cover

You are given an unweighted, undirected tree. Write a program to find a vertex set of minimum size in this tree such that each edge has as least one of its end-points in that set.

Input

The first line contains one integer $n(0<n\le 10^5)$ — number of nodes in the tree. Next $n-1$ lines contain $n-1$ edges of that tree. Each line contains a pair $(u,v)$ means there is an edge between node $u$ and node $v(1\le u,v\le n)$.

Output

Print number of nodes in the satisfied vertex set on one line.

Examples