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Ingrid is solving the Saturday newspaper Hidden Words in a Grid puzzle, but is finding it a bit tedious to do by hand. Luckily Ingrid knows how to program, and has written a neat image recognition routine that converts a picture of the puzzle into a nice text-based format. However, she is struggling with writing the program that actually solves the puzzle – can you help her out?
A word is contained within a h by w grid if the word can be constructed by starting in a cell in the grid and walking from there to neighboring unvisited cells. A cell neighbors another cell if it is adjacent, not including diagonal movement. Given such a grid and a list of words, decide how many of the words in the list are contained in the grid.
The first line consists of two integers h and w (1 ≤ h, w ≤ 10), the height and width of the grid. Then h lines follow, each containing a string of length w consisting exclusively of uppercase letters describing one row of the grid. Then follows a line with a single integer n (1 ≤ n ≤ 100 000), indicating the number of words Ingrid is looking for. Finally the n words follow, each on a separate line. None of these words are longer than 10 characters.
The output consists of a single number, the number of words underneath the grid that are contained in the grid.
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