Earthquake Damage

An earthquake has struck Farmer John's farm in Wisconsin! The quake damaged some pastures so that they can no longer be crossed. Remarkably, none of the cowpaths was damaged.

The farm is a set of $P$ pastures numbered $1 \ldots P$ ($1 \le P \le 30{,}000$), connected by $C$ undirected cowpaths numbered $1 \ldots C$ ($1 \le C \le 100{,}000$). Cowpath $i$ joins pastures $a_i$ and $b_i$ ($1 \le a_i \le P$; $1 \le b_i \le P$). A cowpath may join a pasture to itself, and two pastures may be joined by more than one cowpath. The barn is in pasture $1$.

$N$ cows, each in a different pasture ($1 \le N \le P$), phone Farmer John one after another, each reporting a single integer $\text{report}_j$ ($2 \le \text{report}_j \le P$). The report means that pasture $\text{report}_j$ is undamaged, yet the calling cow cannot get back to the barn from it because no path avoiding damaged pastures exists.

After every cow has reported in, determine the minimum number of pastures from which it is impossible to return to the barn (counting the impassable damaged pastures themselves).

• Line 1: Three space-separated integers: $P$, $C$, and $N$
• Lines $2 \ldots C+1$: Line $i+1$ describes cowpath $i$ with two integers $a_i$ and $b_i$.
• Lines $C+2 \ldots C+N+1$: Line $C+1+j$ contains a single integer $\text{report}_j$.

• Line 1: A single integer, the minimum number of pastures from which a cow cannot return to the barn (including the damaged pastures themselves).

For example, along the path $1-2-3-4$, damaging pasture $2$ leaves the cows in pastures $2$, $3$, and $4$ unable to return to the barn.