Amal and Vimal together can complete a task in $150$ days, while Vimal and Sunil together can complete the same task in $100$ days. Amal starts working on the task and works for $75$ days, then Vimal takes over and works for $135$ days. Finally, Sunil takes over and completes the remaining task in $45$ days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been