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

`b`. So the set of productions includes two productions of the form

`a`,

`b`, where

*u*and , and the starting string . Can you answer whether there exists a string in the language of the D0L system of the form

*xzy*for a given string

*z*? (

*x*and

*y*are some strings from , is the set of all strings of symbols from , including the empty string.). Certainly you can. Write the program which will solve this problem.