\problemname{Transportation Delegation}

You have just been hired by Amalgamated, Inc.\ in the country of Acmania to
oversee the transportation of raw materials to the company's factories.  Each
supplier of raw materials and each factory resides in one of Acmania's states.
No state has both a factory and a supplier (and never more than one of either)
and there are arcane laws governing which transportation companies can transport
materials across state lines.  Because of the fierce competition between
factories and between suppliers each transportation company handles the output
of at most one raw material site and delivers to at most one factory (or to
another transportation company).  Each supplier can produce enough material to
contract with at most one factory and no factory will contract with more than
one supplier.  Your job is to determine the maximum number of factories that can
be supplied with raw materials.

For example, suppose that there are three suppliers in states A, B and C, and
three factories in states D, E and F.  Let's say you contract three
transportation firms: firm $1$ can transport between states A, E and G; firm $2$
can transport between states A, C and E; and firm $3$ can transport between
states B, D and F.  In this case, you can supply at most two factories
(for example, factory E can be supplied from supplier A using firm $1$, and
factory F can be supplied from supplier B using firm $3$). If you find a fourth
firm that transports between states G and F then you can supply all three
factories: factory D can be supplied from B using firm $3$, factory E can be
supplied from C using firm $2$, and factory F can be supplied from A using
firms $1$ and $4$.

\section*{Input}

The input will start with four positive integers $s$ $r$ $f$ $t$ indicating
the number of states, raw material sites, factories and transportation
companies, where $1 \leq r,f \leq 200$, $r+f \leq s \leq 600$ and
$1 \leq t \leq 1000$.

Next will follow a line containing $r$ state names, one for each raw material
site.

The next line will contain $f$ state names, one for each factory site.

Finally there will be $t$ lines, one for each transportation company.  Each of
these lines will start with an integer  $n$, $1 \leq n \leq s$, indicating the
number of states the company is allowed to work in, followed by  $n$ state
names. No state will contain both a raw material site and a factory site.

All state names will be alphabetic strings with no blanks.
\newpage
\section*{Output}

Output the maximum number of factories that can be supplied with raw materials.

