Let $\displaystyle n \in \mathbb{N}$. Let's definite $\displaystyle A_n=\left \{ 1,2,\ldots , n\right \}$. Let $\displaystyle x_1<x_2<\ldots<x_n$ and $\displaystyle x_i \in \mathbb{R}$. Determinate the major quantity of pairs $\displaystyle (i,j) \in A_n \times A_n$ with $\displaystyle i\neq j$ that satisfy $\displaystyle 1<|x_i-x_j|<2$