Implement a Deterministic Stack Automata $($DAS$)$ that

recognizes expressions consisting of the characters $\text{'}$x$\text{'}$ and $\text{'}$y$\text{'},$ in such a way that:

$-$ as many $\text{'}$x$\text{'}$ characters appear in total, as many $\text{'}$y$\text{'}$ characters appear

in total

$-$ looking at the expression from left to right, the characters $\text{'}$y$\text{'}$ are never

more than the characters $\text{'}$x$\text{'}.$

Print the sequence of steps that led to recognition $($or rejection$)$

of expression.