Consider a permutation $\left( \begin{smallmatrix} 1&2&...&n \\ j_1&j_2&...&j_n \end{smallmatrix} \right)$. A disorder is pair $(k,l)$ with $1\leqslant k< l\leqslant n$ such that $j_k>j_l$. A permutation is called even if the number of disorders is even and odd otherwise.