Enumerating Oriented Gene Orderings

Problem

A signed permutation of length n is some ordering of the positive integers {1,2,…,n} in which each integer is then provided with either a positive or negative sign (for the sake of simplicity, we omit the positive sign). For example, π=(5,−3,−2,1,4) is a signed permutation of length 5.

Given: A positive integer n≤6.

Return: The total number of signed permutations of length n, followed by a list of all such permutations (you may list the signed permutations in any order).