Even Tree problem & my solution

You are given a tree (a simple connected graph with no cycles).You have to remove as many edges from the tree as possible to obtain a forest with the condition that : Each connected component of the forest contains even number of vertices

Your task is to calculate the number of removed edges in such a forest.

Input:
The first line of input contains two integers N and M. N is the number of vertices and M is the number of edges. 2 <= N <= 100.
Next M lines contains two integers u_i and v_i which specifies an edge of the tree. (1-based index)

Output:
Print a single integer which is the answer

Sample Input 

10 9

2 1

3 1

4 3

5 2

6 1

7 2

8 6

9 8

10 8

 

Sample Output :

2

 

Explanation : On removing the edges (1, 3) and (1, 6), we can get the desired result.

Original tree:


Decomposed tree:

Note: The tree in the input will be such that it can always be decomposed into components containing even number of nodes. 

My solution is on pastebin - clickhere