Tree with small distances

You are given an undirected tree consisting of $n$ vertices. An undirected tree is a connected 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 vertex $1$ to any other vertex is at most $2$. Note that you are not allowed to add loops or 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 next $n-1$ lines describe the edges: the $i$-th edge is specified as a pair of vertices $u_i,v_i(1\le u_i,v_i\le n)$. It is guaranteed that the given graph is a tree. It is guaranteed that there are no loops or multiple edges among the given edges.

Output

Print a single integer — the minimum number of edges that need to be added in order to ensure that the length of the shortest path from vertex $1$ to any other vertex does not exceed $2$. Note that you cannot add loops or multiple edges.

Examples