In a confrontation with battle droids, twelve Jedi engage in combat. Each Jedi can destroy 10 droids per minute. At the end of each minute, four Jedi retreat and are replaced by four Padawans, each of whom can destroy half as many droids as a Jedi per minute. After the last four Jedi retreat, the Padawans continue fighting the droids alone. At the end of the confrontation, a total of 720 battle droids are destroyed. Throughout the confrontation, all Jedi and Padawans fight at their full rates, with none incapacitated. How many minutes did the Padawans fight alone after the last Jedi retreated?