You are given a tree (a simple connected graph with no 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.

Function Description

Complete the evenForest function in the editor below. It should return an integer as described.

evenForest has the following parameter(s):

t_nodes: the number of nodes in the tree
t_edges: the number of undirected edges in the tree
t_from: start nodes for each edge
t_to: end nodes for each edge, (Match by index to t_from.)

Input Format

The first line of input contains two integers $t_{n}odes$ and $t_e dges$, the number of nodes and edges.

The next $t_e dges$ lines contain two integers $t_{f}rom[i]$ and $t_to[i]$ which specify nodes connected by an edge of the tree. The root of the tree is node $1$.

Constraints

$2\leq n\leq100$
$n\in\mathbb{Z}^+_{\text{even}}$

Note: The tree in the input will be such that it can always be decomposed into components containing an even number of nodes. $\mathbb{Z}_{\text{even}}^{+}$ is the set of positive even integers.

Output Format

Print the number of removed edges.

Sample Input 1

10 9
2 1
3 1
4 3
5 2
6 1
7 2
8 6
9 8
10 8

Sample Output 1

2

Explanation 1

Remove edges ${(1,3)}$ and ${(1,6)}$ to get the desired result.

No more edges can be removed.

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