Please also note that there is an `parity` function in the Permutations package that does exactly that:
julia> using Permutations
julia> p = Permutations([3,4,5,2,1])
(1,3,5)(2,4)
julia> parity(p)
1
It returns 1 for odd permutations and 0 for even ones, and an error in case
the vector is not a permutation of [1..n]. It computes the parity/sign by
adding the length of the cycles.
