3. Among the twelve employees of the accounting firm ABACUS, a quar- rel has broken out over vacation times. Abacus can only spare one employee at a time and therefore has a strict policy of assigning a different employee to each month for vacation. Here are each employees' top five preferred months: Jenny | Fabio Martha | April | Maybelline | June 1st Dec Jun Jun Apr Dec May 2nd Sep May Dec May Aug Oct 3rd Jul Jul Mar Jul Jul Jun 4th Mar Dec Aug Jun Jan Sep 5th Jun Oct May Aug Jun Jul 6th Jan Feb Jul Mar May Apr Jules Audrey Sebastian | Otto-Per | Novalee | Dexter 1st Dec Jun Jul Jul Sep Oct 2nd Sep Apr Jun Nov May Dec 3rd May Mar Oct Dec Apr Aug 4th Jul Sep Aug Apr Dec May 5th Jun Feb Dec Sep Aug Jul 6th Aug Dec Nov Oct Jun Sep To settle the issue in an impartial manner, management decided to use the top trading cycle algorithm to determine who can vacation when. 2 (i) If months are initially assigned in the order in which employees are listed above (i.e. Jenny | January, Fabio | February, etc.), what are the matches that result in the first round of the algorithm? (ii) Which matches are made in the second round? (iii) Which matches are made in the third round? Which months are the remaining employees matched to? (iv) Can Jenny report a different ordering from her true preferences and get a better match? Why or why not? (v) Suppose Fabio gets a chance to chat with Maybelline in the break room, and they talk about vacations. Maybelline trusts Fabio: she will request her vacation in the month he suggests. How could he affect her preferences in a way that allows him to get his top choice in the top cycle trading algorithm?