You are given a tree (a simple connected graph without cycles).
Find the maximum number of edges you can remove from the tree to get a forest such that each connected component of the forest contains an even number of nodes.
As an example, the following tree with 4 nodes can be cut at most 1 time to create an even forest.
The first line contains two integers n (2≤n≤100,n is even) and m — the number of nodes and edges. The next m lines contain two integers which specify the nodes connected by an edge of the tree. The root of the tree is node 1.
Print the maximum number of removed edges.