2015 AIME II Problem 5

Two unit squares are selected at random without replacement from an n \times n grid of unit squares. Find the least positive integer n such that the probability that the two selected unit squares are horizontally or vertically adjacent is less than \frac{1}{2015}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.