Let $\displaystyle x_1,x_2,\dots,x_{n}$ be real numbers such that $\displaystyle \sum_{k = 1}^{n}\frac {1}{x_k^2 + 1} = n-1$......Find the maximum value of
$\displaystyle x_{1}x_{2}\cdots x_{n}+\sum\limits_{1 \leqslant i < j \leqslant n} {x_i x_j }-\sum_{k = 1}^{n}x_{k}^{2}$