Wilbur the pig now wants to play with strings. He has found an n by m table consisting only of the digits from 0 to 9 where the rows are numbered 1 to n and the columns are numbered 1 to m . Wilbur starts at some square and makes certain moves. If he is at square ( x , y ) and the digit d ( 0 ≤ d ≤ 9 ) is written at position ( x , y ), then he must move to the square ( x + a d , y + b d ), if that square lies within the table, and he stays in the square ( x , y ) otherwise. Before Wilbur makes a move, he can choose whether or not to write the digit written in this square on the white board. All digits written on the whiteboard form some string. Every time a new digit is written, it goes to the end of the current string. Wilbur has q strings that he is worried about. For each string s i , Wilbur wants to know whether there exists a starting position ( x , y ) so that by making finitely many moves, Wilbur can end up with the string s i written on the white board. The first line of the input consists of three integers n , m , and q ( 1 ≤ n , m , q ≤ 200 ) — the dimensions of the table and the number of strings to process, respectively. Each of the next n lines contains m digits from 0 and 9 giving the table itself. Then follow 10 lines. The i -th of them contains the values a i - 1 and b i - 1 ( - 200 ≤ a i , b i ≤ 200 ), i.e. the vector that Wilbur uses to make a move from the square with a digit i - 1 in it. There are q lines that follow. The i -th of them will contain a string s i consisting only of digits from 0 to 9 . It is guaranteed that the total length of these q strings won't exceed 1 000 000 . For each of the q strings, print " YES " if Wilbur can choose x and y in order to finish with this string after some finite number of moves. If it's impossible, than print " NO " for the corresponding string. In the first sample, there is a 1 by 1 table consisting of the only digit 0 . The only move that can be made is staying on the square. The first string