The worldrenowned Swedish Chef is planning a gourmet
threecourse dinner for some muppets: a starter course, a main
course, and a dessert. His famous Swedish cookbook offers a
wide variety of choices for each of these three courses, though
some of them do not go well together (for instance, you of
course cannot serve chocolate moose and sooted shreemp at the
same dinner).
Each potential dish has a list of ingredients. Each
ingredient is in turn available from a few different brands.
Each brand is of course unique in its own special way, so using
a particular brand of an ingredient will always result in a
completely different dinner experience than using another brand
of the same ingredient.
Some common ingredients such as pølårber may appear in two
of the three chosen dishes, or in all three of them. When an
ingredient is used in more than one of the three selected
dishes, Swedish Chef will use the same brand of the ingredient
in all of them.
While waiting for the meecaroo, Swedish Chef starts
wondering: how many different dinner experiences are there that
he could make, by different choices of dishes and brands for
the ingredients?
Input
The input consists of:

one line containing five integers $r$, $s$, $m$, $d$, $n$, where $1 \le r \le 1\, 000$ is the
number of different ingredients that exist, $1 \le s, m, d \le 25$ are the
number of available starter dishes, main dishes, and
desserts, respectively, and $0 \le n \le 2\, 000$ is the
number of pairs of dishes that do not go well together.

one line containing $r$ integers $b_1, \ldots , b_ r$, where
$1 \le b_ i \le 100$
is the number of different brands of ingredient
$i$.

$s+m+d$ lines
describing the $s$
starter dishes, then the $m$ main dishes, then the
$d$ desserts. Each
such line starts with an integer $1 \le k \le 20$ denoting the
number of ingredients of the dish, and is followed by
$k$ distinct integers
$i_1, \ldots , i_ k$,
where for each $1 \le j \le
k$, $1 \le i_ j \le
r$ is an ingredient.

$n$ lines each
containing two incompatible dishes. Each dish is identified
by an integer $1 \le j \le
s+m+d$, referring to the $j$’th dish given in the input (so
$1 \le j \le s$ refers
to the starter dishes, $s
< j \le s+m$ refers to the main dishes, and
$s+m < j \le s+m+d$
refers to the desserts).
Each pair of incompatible dishes in the input consists of
two dishes of different types, and any one pair of dishes is
listed at most once.
Output
If the number of different dinner experiences Swedish Chef
can make is at most $10^{18}$, then output that number.
Otherwise, output “too many”.
Sample Input 1 
Sample Output 1 
6 1 1 1 0
2 3 1 5 3 2
2 1 2
3 3 4 5
1 6

180

Sample Input 2 
Sample Output 2 
3 2 2 1 1
2 3 2
1 1
1 2
1 2
1 3
1 1
2 3

22

Sample Input 3 
Sample Output 3 
3 1 1 1 1
5 5 5
3 1 2 3
3 1 2 3
3 1 2 3
2 1

0

Sample Input 4 
Sample Output 4 
10 1 1 1 0
100 100 100 100 100 100 100 100 100 100
4 1 2 3 4
3 5 6 7
3 8 9 10

too many
