We have proved that the Bakery algorithm is First-Come, First-Served (FCFS), and satisfies mutual exclusion. In the Bakery lock algorithm, we use lexicographic ordering (amounting to some arbitrary, permanent ordering of threads) to determine the order in which two or more threads that both received the same label enter the critical section. Let's say we made a change so that, if two or more threads both receive the same label, the losing thread instead gets a new label. Would this violate anything that was true about the previous version of the Bakery lock? Why or why not?