On the board are written n consecutive integers. Maria has n labels of the form
“This number is not divisible by i” for i = 2, 3, \dots, n+1.
She places each label next to one number on the board, so that each number has exactly one label. For every true statement on the labels, Maria receives one piece of candy.
Determine the maximum number of candies Maria can guarantee to obtain, regardless of the specific n consecutive integers written on the board, if she plays optimally.