Greg is volunteering at the school charity basketball game. He is in charge of providing bottled water. Greg knows these facts: The event meet will last 3 hours. There will be 117 athletes, 7 coaches, and 4 judges attending the charity game. One case of bottled water contains 24 bottles. The number of bottles of water each athlete, coach, and a judge will get for each hour of the event: athletes (4), coaches (3), and judges (2). What is the fewest number of cases of bottled water Greg will need to provide for all the athletes, coaches, and judges at the game?