You are given a tree consisting of $n$ nodes.
A matching is a set of edges where each node is an endpoint of at most one edge. What is the maximum number of edges in a matching?
The first input line contains an integer $n$ : the number of nodes. The nodes are numbered $1,2,\ldots,n$ .
Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ .
Print one integer: the maximum number of pairs.
5 1 2 1 3 3 4 3 5\n · \n · \n · \n · \n
2\n
One possible matching is $(1,2)$ and $(3,4)$ .