Fix the Tree

A rooted tree with $N$ vertices has vertex 1 as its root. Each vertex is numbered with a distinct integer from $1$ to $N$. The tree has $M$ broken vertices. A broken vertex does not work, and neither do its descendants, whether or not they are broken. In other words, a vertex does not work if at least one of its ancestors is broken.

Repair at most $K$ broken vertices to maximize the number of vertices that work.

The first line contains three integers $N$ ($1\leq N\leq 10^5$), $M$ ($1\leq M\leq N$), and $K$ ($1\leq K\leq 10$), separated by spaces. $N$ is the number of vertices, $M$ is the number of broken vertices, and $K$ is the maximum number of vertices you can repair.

Each of the next $N-1$ lines contains two distinct vertices $u$ and $v$ ($1\leq u,v\leq N$), separated by a space, that are connected by an edge.

The line after those contains the $M$ numbers of the broken vertices, separated by spaces. All $M$ numbers are distinct.

Print the maximum number of working vertices you can get by repairing at most $K$ broken vertices.