$[20$ points$]$ Give a high$-$level description of a TM $($how it moves its head around, etc.$)$ that takes a bit string xin$\{0,1{\}}^{**}$ and halts with $x$#$\stackrel{}{x}$ written on the tape, where $\stackrel{}{x}$ denotes the bitwise negation of $x($and # is a single symbol$).$ For example, if the input $x$ is $01101$ then the output should be $01101$#$10010.$ Do not give a state diagram. Use the "marking" idea to keep track of where the TM left off.