A10143. Wilbur and Strings

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 $1000000$ .

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 can be written on the white board by writing $0$ repeatedly. The second string cannot be written as there is no $2$ on the table.