It was time for the 7th
Nordic Cinema Popcorn
Convention, and this year the manager Ian had a brilliant
idea. In addition to the traditional film program, there would
be a surprise room where a small group of people could stream a
random movie from a large collection, while enjoying popcorn
and martinis.
However, it turned out that some people were extremely
disappointed, because they got to see movies like Ghosts of
Mars, which instead caused them to tear out their hair in
despair and horror.
To avoid this problem for the next convention, Ian has come
up with a solution, but he needs your help to implement it.
When the group enters the surprise room, they will type in a
list of movies in a computer. This is the socalled horror
list, which consists of bad movies that no one in the
group would ever like to see. Of course, this list varies from
group to group.
You also have access to the database Awesome Comparison
of Movies which tells you which movies are directly
similar to which. You can assume that movies that are similar
to bad movies will be almost as bad. More specificly, we define
the Horror index as follows:
\[ HI = \left\{ \begin{array}{ll} 0 &
\textrm{if movie is on horror list. This overrides the other
definitions.} \\ Q+1 & \textrm{if the worst directly
similar movie has $HI = Q$} \\ +\infty & \textrm{if not
similar at all to a horrible movie} \end{array} \right.
\]
Input
The first line of input contains three positive integers
$N$, $H$, $L$ ($1
\leq H < N \leq 1\, 000,0 \leq L \leq 10\, 000$),
where $N$ is the number of
movies (represented by IDs, ranging from $0$ to $N1$), $H$ is the number of movies on the
horror list and $L$ is the
number of similarities in the database.
The second line contains $H$ unique spaceseparated integers
$x_ i$ ($0 \leq x_ i <N$) denoting the ID
of the movies on the horror list.
The following $L$ lines
contains two spaceseparated integers $a_ i,b_ i$ ($0 \leq a_ i < b_ i < N$),
denoting that movie with ID $a_
i$ is similar to movie with ID $b_ i$ (and vice versa).
Output
Output the ID of the movie in the collection with the
highest Horror Index. In case of a tie, output the movie with
the lowest ID.
Sample Input 1 
Sample Output 1 
6 3 5
0 5 2
0 1
1 2
4 5
3 5
0 2

1

Sample Input 2 
Sample Output 2 
6 2 3
5 2
0 5
0 1
3 4

3
