Mathematics · Time and Work

A team of A, B, and C was supposed to complete a piece of work. Working alone, A could have completed the work in 190 hours, B in 285 hours, and C in 342 hours. They decided that only one person would work at any point in time. In the first cycle of three days, A worked for 2 hours on Day 1, B worked for 2 hours on Day 2, and C worked for 2 hours on Day 3. In the second cycle of three days, A worked for 4 hours on Day 1, B worked for 4 hours on Day 2, and C worked for 4 hours on Day 3. In general, each person works for 2n hours on their respective day in Cycle n. This continued until the work was completed, with a potential mid-cycle exception in the last cycle. What was the total number of days needed for the work to be completed?