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 should contain an even number of vertices.

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

Input Format
The first line of input contains two integers N and M. N is the number of vertices and M is the number of edges.
The next M lines contain two integers ui and vi which specifies an edge of the tree. (1-based index)

Output Format
Print the answer, a single integer.

Constraints
2 <= N <= 100.

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

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