Create Permutation

Consider a list $L$ of permutations, where a *permutation with length* $x$ denotes a permutation of integers $1$ through $x$ and the elements of this list are indexed starting from $1$. Initially, the list contains a single permutation with length $1$ (i.e. $L_1 = (1)$). You may create new permutations and append them to $L$ using operations with the following form: - Choose two (not necessari