In a recent survey, 62 students reported whether they liked their potatoes Mashed, French-fried, or Twice-baked. 30 liked them mashed, 35 liked French fried, and 44 liked twice baked potatoes. Additionally, 15 students liked both mashed and fried potatoes, 17 liked French fries and twice baked potatoes, 25 liked mashed and baked, and 13 liked all three styles. How many students hate potatoes? Explain why your answer is correct