What is the coefficient $c$ of the term $x_1^2x_2^2x_3^2\cdots x_{12}^2$ in the expansion of the following multivariable polynomial:
$(x_1-x_2)(x_1-x_3)(x_1-x_4)(x_1-x_{10})(x_2-x_3)(x_2-x_5)(x_2-x_{11})(x_3-x_6)(x_3-x_{12})(x_4-x_5)(x_4-x_6)(x_4-x_7)(x_5-x_6)(x_5-x_8)(x_6-x_9)(x_7-x_8)(x_7-x_9)(x_7-x_{10})(x_8-x_9)(x_8-x_{11})(x_9-x_{12})(x_{10}-x_{11})(x_{10}-x_{12})(x_{11}-x_{12})$
I wish to know the theoretical methods to find the coefficient $c$, although I know the coefficient $c=-36$ which can be obtained by Mathematica or Maple . I hope the answers. Thank you very much!