Get rid of them all

Input

The first line contains a single integer $n$ (1 \leq n \leq 10^5).

The following n - 1 lines each contain two integers $u$ and $v$ (1 \leq u, v \leq n), representing an edge between vertices $u$ and $v$.

It is guaranteed that the input describes a valid tree.

Output

Print a single integer $k$, which is the maximum number of edges that can be removed to ensure all connected components have an even number of vertices. If it is not possible to achieve this, print $-1$.

Examples