Let $ n \in N $. Let's define $ S_n = \{1, ..., n \} $. Let $ x_1 <x_2 <\cdots <x_n $ be any real. Determine the largest possible number of pairs $ (i, j) \in S_n \times S_n $ with $ i \not = j $, for which it is true that $ 1 <| x_i-x_j | <2 $ and justify why said value cannot be higher.