Time Limit:1000ms Memory Limit:65536KB

Description

Wisconsin has had an earthquake that has struck Farmer John's farm! 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 <= 3,000) pastures
conveniently numbered 1..P which are connected by a set of C (1 <= C <= 20,000)
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 contacts
Farmer John 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 that are
damaged.

Input

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

Output

Line 1: One number, the minimum number of damaged pastures. 

Sample Input

5 5 2
1 2
2 3
3 5
2 4
4 5
4
5

Sample Output

1

Hint


Author

Source

USACO MAR09