In the city of Pandaville, the predominant black and white
colours of the inhabitants have somehow made chess a very
popular game in the area. There are a total of $N$ chess players in the city and they
are very competitive. Recently, the annual Panda Chess
Tournament has just ended where a total of $M$ matches have been played among the
players to decide who is the best chess player. This has
resulted in a unique ranking among the players such that for
every match, the winner has a higher rank than the loser. The
ranking will be published on The Daily
Chess tomorrow.
Each chess player is identified by his/her unique IC number
which is a number containing at most $D$ digits from $0$ to $9$. The ranking is a list of IC
numbers ordered by their relative ranks with the top player
being the first in the list.
The ranking list published is typed by a panda writer using
a typewriter. Due to his fat paws, the panda writer makes a lot
of mistakes. You are asked to amend the ranking list.
$1$ edit is defined as
either removing an IC number or inserting an IC number into the
list. You aim to find out what is the least number of edits
required to correct the ranking list.
Input
The input consists of:

One line with three integers $N$ ($2 \le N \le 100\, 000$),
$M$ ($1 \le M \le 200\, 000$) and
$D$ ($1 \le D \le 10$), where
$N$ is the number of
chess players, $M$ is
the number of matches played, and $D$ is the maximum number of
digits for each IC number;

$M$ lines each with
two IC numbers $A$ and
$B$, indicating that
panda A wins over panda B;

$N$ lines each with
one IC number $C$,
representing the ranking list typed by the panda
writer;
It is guaranteed that the $M$ matches define one unique ranking
for the $N$ pandas and
every match will be played between $2$ different players. However,
$2$ players can play more
than once.
Output
Output one line with a single integer: the minimum number of
edits required to obtain the actual ranking list from the
original ranking list typed by the panda writer.
Sample Input 1 
Sample Output 1 
4 4 3
345 678
12 345
345 678
678 999
999
12
824
999

4
