Model the following token$-$based mutual exclusion

algorithm that works on a bidirectional array. There are N processes $\{0,...,$ N $1\}$ in an array.

Each process i$,$ has a single variable s$[$i$]$ that takes values in the set $\{0,1,2,3\}$ independent of the

size of the array. The two processes $0$ and N $1$ behave differently from the rest, they can take

two values each: s$[0]$ can take values $\{1,3\}$ and s$[$N $1]$ can take values $\{0,2\}.$ Let Nbrs$($i$)$ be the

set of neighboring processes for process i$.$