Let x_1,x_2,\dots,x_{n} be real numbers such that \sum_{k = 1}^{n}\frac {1}{x_k^2 + 1} = n-1......Find the maximum value of
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}