Design a queue management system in $C++$ that calculates how long it will take for each roller coaster to handle its line based on its ride capacity and duration per cycle.

$3\mathrm{.}1$ Prompt the user to enter the number of riders waiting in line for each roller coaster:

Coaster A: "Red Rail" Maximum Occupancy:$10$ Ride Duration:$3$ Minutes

Coaster B: "Blue Rail" Maximum Occupancy:$15$ Ride Duration:$2$ Minutes

Coaster C: "Green Line Maximum Occupancy:$10$ Ride Duration: $5$ Minutes

$(15$ Marks$)$

$3\mathrm{.}2$ Calculate the total number of ride cycles required for each coaster to clear its entire queue, considering that each cycle should accommodate up to the maximum capacity or the remaining number of riders, whichever is less.

$(15$ Marks$)$

$3\mathrm{.}3$ Multiply the number of cycles by the ride duration per cycle to calculate the total wait time $($in minutes$)$ required for each coaster to process all its riders.

$(15$ Marks$)$

$3\mathrm{.}4$ At the end of the calculation, print the total wait time $($in minutes$)$ for each coaster to process all riders in its queue.

$(5$ Marks$)$