## Even Tree

You are given a tree (a simple connected graph with no cycles). The tree has nodes numbered from to and is rooted at node .

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.

**Input Format**

The first line of input contains two integers and . is the number of nodes, and is the number of edges.

The next lines contain two integers and which specifies an edge of the tree.

**Constraints**

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

**Output Format**

Print the number of removed edges.

**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 edges and , we can get the desired result.

Original tree:

Decomposed tree: