CF982C Cut 'em all!

You're given a tree with $ n $ vertices. Your task is to determine the maximum possible number of edges that can be removed in such a way that all the remaining connected components will have even size.

The first line contains an integer $ n $ ( $ 1 \le n \le 10^5 $ ) denoting the size of the tree. The next $ n - 1 $ lines contain two integers $ u $ , $ v $ ( $ 1 \le u, v \le n $ ) each, describing the vertices connected by the $ i $ -th edge. It's guaranteed that the given edges form a tree.

Output a single integer $ k $ — the maximum number of edges that can be removed to leave all connected components with even size, or $ -1 $ if it is impossible to remove edges in order to satisfy this property.

In the first example you can remove the edge between vertices $ 1 $ and $ 4 $ . The graph after that will have two connected components with two vertices in each. In the second example you can't remove edges in such a way that all components have even number of vertices, so the answer is $ -1 $ .