A D0L (Deterministic Lindenmayer system without interaction) system consists
of a finite set of symbols (the alphabet), a finite
set *P* of productions and a starting string .
The productions in *P* are of the form
, where and
(*u* is called the right side of the production),
is the set of all strings of symbols from
excluding the empty string. Such productions represent the transformation of the
symbol *x* into the string *u*. For each symbol
, *P* contains exactly one production of the form
. Direct derivation from string to
consists of replacing each occurrence of the symbol
in by the string on the right side of
the production for that symbol. The language of the D0L system consists of all
strings which can be derived from the starting string
by a sequence of the direct derivations.

Suppose that the alphabet consists of two symbols ` a` and

The input file of the program consists of several blocks of lines. Each block
includes four lines. There are no empty lines between any successive two blocks.
The first line of a block contains the right side of the production for the
symbol `a`. The second one contains the right side of the production for
the symbol `b` and the third one contains the starting string and the fourth line the given string
*z*. The right sides of the productions, the given string *z* and the
starting string are at most 15 characters long.

For each block in the input file there is one line in the output file
containing `YES` or `NO` according to the solution of the given
problem.

aa bb ab aaabb a b ab ba

YES NO