Even Tree

You are given a tree, which is a simple connected graph without cycles.

Find the maximum number of edges that can be removed from the tree to obtain a forest where each connected component contains an even number of nodes.

For example, in the tree with $4$ nodes shown below, you can remove at most $1$ edge to create an even forest.

Input

The first line contains two integers $n(2\le n\le 100,n$ is even) and $m$ — the number of nodes and edges. Each of the next $m$ lines contains two integers representing the nodes connected by an edge in the tree. The root of the tree is node $1$.

Output

Print the maximum number of edges that can be removed.

Examples