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Klara has $N$ dices with letters written on them. Each die has a letter on each of its $K$ sides. By throwing the dice and rearranging them in some arbitrary order, you can make construct a word with $N$ letters.
Write a program to count the number of valid words that can be constructed using Klara's dice. You will get a wordlist, that contains all the $M$ valid $N$-letter words.
Figure 1: An illustration of the first example. Since $K = 3$, each die has three sides. You can also write
MASK, but not
The first line of input contains three space-separated integers $N$, $K$ and $M$.
The next $N$ lines each describe a die. Line $i$ will contain $K$ letters, the letters on the sides of the $i$:th die.
Finally, there will be $M$ lines, the valid words. Each line will contain an $N$-letter word.
All words will only capital letters
No letter will appear on more than one side of a die.
Your program should print a single integer: the number of valid words that can be written.
$K = 2, N \le 4, M \le 100$
$K \le 6, N \le 5, M \le 100$
$K \le 20, N \le 6, M \le 1000$
$K \le 15, N \le 6, M \le 10\,000$
$K \le 20, N \le 6, M \le 100\,000$
$K \le 10, N \le 13, M \le 500$
4 3 5 TSU NKT KMO LJA KATT NATT STOL MASK KOST