Level $2$: Line Jumpers Program the TM to simulate $$line jumpers,$$ letters at the back of the string who sneak forward to the front of the line. The simulation must process any string of X$\text{'}$s$,$ Y$$s$,$ and Z$$s$,$ from $5$ to $15$ characters long, creating a final output that matches this exact order of operations: $(1)$ the second character in the string is removed, $(2)$ the last character in the string replaces the character that was removed, $(3)$ the third character in the string is removed, $(4)$ the last character in the string replaces the character that was removed. For example, the input string: ZXYXZYXZZXY would be processed correctly if the algorithm produced this output string: ZYXXZYXZZ The set of input strings used to test your TM will not be revealed until after the assignment is due. Recommendation: Develop your own set of test strings. $2\mathrm{.}1.$ Rules $1.$ Your TM must start on the first character. $2.$ The starting state of the TM must be $0.3.$ The final state of the TM must be $$HALT$.4.$ The TM must halt on the first blank cell to the right of the last character. $5.$ After the TM has halted, the output string must be properly processed, as stated above. $6.$ The algorithm must work for any string of X$\text{'}$s$,$ Y$$s$,$ and Z$$s$,$ from $5$ to $15$ characters long.