Bokstavstärningar

문제

Klara has $NN$ dices with letters written on them. Each die has a letter on each of its $KK$ sides. By throwing the dice and rearranging them in some arbitrary order, you can make construct a word with $NN$ 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 $MM$ valid $NN$-letter words.

[이미지 1]

Figure 1: An illustration of the first example. Since $K=3K\; =\; 3$, each die has three sides. You can also write STOL and MASK, but not NATT or KOST.

입력

The first line of input contains three space-separated integers $NN$, $KK$ and $MM$.

The next $NN$ lines each describe a die. Line $ii$ will contain $KK$ letters, the letters on the sides of the $ii$:th die.

Finally, there will be $MM$ lines, the valid words. Each line will contain an $NN$-letter word.

All words will only capital letters A-Z.

No letter will appear on more than one side of a die.

출력

Your program should print a single integer: the number of valid words that can be written.