Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. if an integer is displayed, pressing the $\textcolor{blue}{\bf\circledast}$ key chops off the first digit and moves it to the end. for example, if $6138$ is on the screen, then pressing the $\textcolor{blue}{\bf\circledast}$ key changes the display to $1386$. thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again. after all these steps, the calculator displays $243$. what number did thea originally enter?