Book Replacement

The deadline for Professor Hachioji's assignment is tomorrow. To finish it, students must copy pages from many reference books in the library. Every reference book is kept in a storeroom that only the librarian may enter, so a student who wants a copy must ask the librarian, who fetches the requested book from the storeroom and makes the copy.

Students wait in a single queue in front of the counter. A student may request only one book at a time. After a request has been served, if the student still has more books to request, the student goes to the back of the queue.

The overall situation is shown in Figure 1 (The Library).

The storeroom contains $m$ desks $D_1, D_2, \dots, D_m$ and one shelf, placed in a line in that order from the door toward the back of the room. Each desk holds at most $c$ books. Initially every desk is empty (all books start on the shelf), and no new students arrive after the library opens.

To serve a request, the librarian looks for the book on $D_1, D_2, \dots, D_m$ in that order and finally on the shelf. After finding the book, the librarian takes it and gives a copy of the page to the student. The librarian then returns the book to $D_1$ using the following procedure.

• If $D_1$ is not full (it currently holds fewer than $c$ books), put the requested book on $D_1$.
• If $D_1$ is full, the librarian:
  1. temporarily puts the requested book on the non-full desk closest to the entrance, or on the shelf if every desk is full;
  2. takes from $D_1$ the book that has not been requested for the longest time (the least recently used book);
  3. puts that book on the non-full desk other than $D_1$ closest to the entrance, or on the shelf if every desk other than $D_1$ is full;
  4. takes the requested book back from its temporary place;
  5. finally puts the requested book on $D_1$.

Cost. Only accesses to a desk or the shelf cost anything: each time a book is put onto or taken from a location, that counts as one access. An access to desk $D_i$ costs $i$, and an access to the shelf costs $m + 1$. Every other action is free. Simulate the students and the librarian and report the total cost of processing all requests.

Cost accounting example. Suppose there are $3$ desks, each holding at most $1$ book, and two students: the first requests books $60, 61, 62$ and the second requests $70, 60$. Because a student who still has requests rejoins the back of the queue, the books are served in the order $60, 70, 61, 60, 62$. Serving book $60$ first costs $5$ (take it from the shelf for $4$, put it on $D_1$ for $1$). Serving $70$ then costs $13$, and serving $61, 60, 62$ costs $14, 12, 14$ respectively, for a total of $5 + 13 + 14 + 12 + 14 = 58$.

The input consists of several datasets. Each dataset has the following form.

m c n
k1
b11 ... b1k1
...
kn
bn1 ... bnkn

All values are positive integers. $m$ is the number of desks with $m \le 10$. $c$ is the maximum number of books allowed on one desk with $c \le 30$. $n$ is the number of students with $n \le 100$. For the $i$-th student, $k_i$ is the number of books requested with $k_i \le 50$, and $b_{i1}, \dots, b_{ik_i}$ are the IDs of the requested books, given in request order. Every book has a distinct ID, and each ID is less than $100$; a student may request the same book more than once.

The end of the input is a line containing three zeros separated by spaces (0 0 0); it is not a dataset.

For each dataset, output the total cost of processing all of its requests on its own line.