Construct Turing machines with input alphabet $\{a, b\}$ that compute the specified functions. The symbols $u$ and $v$ represent arbitrary strings over $\{a, b\}^*$.
a) $f(u)=$ aaa
b) $f(u)= \begin{cases}a & \text { if length }(u) \text { is even } \\ b & \text { otherwise }\end{cases}$
c) $f(u)=u^R$
d) $f(u, v)= \begin{cases}u & \text { if length }(u)>\text { length }(v) \\ v & \text { otherwise }\end{cases}$