If possible, show how a Two$-$Phase Locking might execute following history. $($Hint: A transaction might first obtain a shared lock and then upgrade it to an exclusive lock during its growth phase.$)$

R$1($A$)$; R$2($A$)$; R$3($B$)$; W$1($A$)$; R$2($C$)$; R$2($B$)$; W$2($B$)$; W$1($C$)$;

T$1$ T$2$ T$3$