Alex likes solving fillwords. Fillword is a word game with very simple rules. The author of the fillword takes rectangular grid (M cells width, N cells height) and P words. Then he writes letters in the cells of the grid (one letter in one cell) so that each word can be found on the grid and the following conditions are met:
- no cell belongs to more than one word
- no cell belongs to any word more than once
Some word W (let us consider its length being k) is found on the grid if you can find such sequence of cells (x1
), …, (xk
- (xi, yi) and (xi+1, yi+1) are neighbors (|xi-xi+1| + |yi-yi+1| = 1) for each i = 1, 2, …, k-1
- W[i] is written in the cell with coordinates (xi, yi).
The task is to find all the words on the grid. After they are found, you see that the letters in some cells are not used (they do not belong to any found word). You make up a secret word using these letters and win a big prize.
Your task is to help Alex to solve fillwords. You should find out which letters will be left after he finds all the words on the grid. The most difficult task - to make up a secret word out of them - we still reserve to Alex.
The first line contains three integers - N, M (2 ≤ M, N ≤ 10) and P (P ≤ 100). Next N lines contain M characters each, and represent the grid. The following P lines contain words that are to be found on the fillword grid.
Fillword will always have at least one solution. All characters occurring in fillword will be capital English letters.
Output letters from, which a secret word should be made up. Letters should be output in lexicographical order.
3 3 2
Problem Author: Alex Selivanov
Problem Source: ACM ICPC 2001. Northeastern European Region, Northern Subregion