You are designing a geartrain with three spur gears: one input gear, one idler gear, and one output gear. The diametral pitch for the geartrain is 16. The diameter of the input gear needs to be twice the diameter of the idler gear and three times the diameter of the output gear. The entire geartrain needs to fit into a rectangular footprint of no larger than 16 in. high and 24 in. long. Determine an appropriate number of teeth and diameter of each gear.