Sequential consistency model. Consider a data store with five replicas each having a process associated with it$.$ The processes are denoted as P$1-$P$5.$

For each of the following executions, check if the executions are possible when the data store implements sequential consistency model? If yes, find out one sequential order of all the write executions. If not, try to reorder some read operations to make executions conform to sequential consistency, and show one sequential order of all the write executions.

$(1)$

P$1$: W$1($x$)$a W$1($x$)$b W$1($x$)$c

P$2$: W$2($x$)$d W$2($x$)$e R$2($x$)$b R$2($x$)$f

P$3$: R$3($x$)$a R$3($x$)$d R$3($x$)$b W$3($x$)$f

P$4$: R$4($x$)$a R$4($x$)$f R$4($x$)$c

P$5$: R$5($x$)$d R$5($x$)$b R$5($x$)$f

$(2)$

P$1$: R$1($x$)$a W$1($x$)$c R$1($x$)$b R$1($x$)$e

P$2$: R$2($x$)$b R$2($x$)$c R$2($x$)$e R$2($x$)$d

P$3$: W$3($x$)$b R$3($x$)$b R$3($x$)$d R$3($x$)$e

P$4$: R$4($x$)$c W$4($x$)$d W$4($x$)$e R$4($x$)$e

P$5$: W$5($x$)$a R$5($x$)$c R$5($x$)$b R$5($x$)$d

$(3)$

P$1$: W$1($x$)$a R$1($x$)$a R$1($x$)$c R$1($y$)$d W$1($y$)$b R$2($y$)$b

P$2$: W$2($x$)$c R$2($x$)$c R$2($y$)$e W$2($y$)$d R$2($y$)$d R$2($y$)$b

P$3$: R$3($x$)$a R$3($y$)$b R$3($x$)$c

P$4$: R$4($y$)$e R$4($y$)$b R$4($x$)$c

P$5$: R$5($x$)$c W$5($y$)$e R$5($y$)$d R$5($y$)$b