Thea has a key on her calculator marked blue star. If an integer is displayed, pressing the blue star key chops off the first digit and moves it to the end. For example, if 6138 is on the screen, then pressing the blue star key changes the display to 1386.
Thea enters a positive integer into her calculator, then squares it, then presses the blue star key, then squares the result, then presses the blue star key again. After all these steps, the calculator displays 1372. What number did Thea originally enter?