Present your Turing Machines as transition diagrams, using the notation in the HopcroftMotwani$-$Ullman textbook.

$($a$)$ Construct a Turing machine for the language $\{xay$:$x,$yin$\{a,b{\}}^{**},|x|=|y|\}.$

$($b$)$ Construct a Turing machine for the language $\{a^n{b}^{2n}{c}^{3n}$:$n1\}.$

$($c$)$ Construct a Turing machine that creates a copy of its input string to the right of the input with a blank separating the copy from the original