Earthquake Damage    damage.X

Wisconsin has had an earthquake that has struck Farmer Tom's farm!
Farmer Tom is a distant relative of Farmer Ran - about as distant
as Wisconsin is from Claremont, CA. The earthquake has damaged some
of the pastures so that they are unpassable. Remarkably, none of the
cowpaths was damaged.

As usual, the farm is modeled as a set of P (1 <= P <= 30,000)
pastures conveniently numbered 1..P which are connected by a set
of C (1 <= C <= 100,000) non-directional cowpaths conveniently
numbered 1..C. Cowpath i connects pastures a_i and b_i (1 <= a_i
<= P; 1 <= b_i <= P). Cowpaths might connect a_i to itself or perhaps
might connect two pastures more than once.  The barn is located in
pasture 1.

A total of N (1 <= N <= P) cows (in different pastures) sequentially
contact Farmer Tom via moobile phone with an integer message
report_j (2 <= report_j <= P) that indicates that pasture report_j
is undamaged but that the calling cow is unable to return to the
barn from pasture report_j because she could not find a path that
does not go through damaged pastures.

After all the cows report in, determine the minimum number of
pastures (including ones that are uncrossable) from which it is not
possible to return to the barn.

PROBLEM NAME: damage.X

INPUT FORMAT:

* Line 1: Three space-separated integers: P, C, and N

* Lines 2..C+1: Line i+1 describes cowpath i with two integers: a_i
        and b_i

* Lines C+2..C+N+1: Line C+1+j contains a single integer: report_j

SAMPLE INPUT:

4 3 1
1 2
2 3
3 4
3

OUTPUT FORMAT:

* Line 1: A single integer that is the minimum count of pastures from
        which a cow can not return to the barn (including the damaged
        pastures themselves)

SAMPLE OUTPUT:

3

OUTPUT DETAILS:

Pasture 2 is damaged, resulting in cows in pastures 2, 3, 4 not being able to
return to the barn.