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.

Input

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 $1 000 000$.

Output

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.

Note

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.