************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 The FindStatCrew * * * * This information is distributed in the hope that it will be * * useful, but WITHOUT ANY WARRANTY; without even the implied * * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ************************************************************************ ------------------------------------------------------------------------ Map identifier: Mp00204 ------------------------------------------------------------------------ Map name: LLPS ------------------------------------------------------------------------ Domain: Permutations ------------------------------------------------------------------------ Codomain: Integer partitions ------------------------------------------------------------------------ Description: The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation. An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let $$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$ Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define $A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$ where the maximum is taken over disjoint subsequences ${u_i}$ of $w$. Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation. ------------------------------------------------------------------------ References: [1] Lewis, J., Lyu, H., Pylyavskyy, P., Sen, A. Scaling limit of soliton lengths in a multicolor box-ball system [[arXiv:1911.04458]] ------------------------------------------------------------------------ Code: def mapping(pi): to_standard = sage.combinat.permutation.to_standard def llis(u): if len(u) == 1: return 1 if len(u) == 2: if u[0] < u[1]: return 2 return 1 if len(u) == 3: if u[0] < u[1] < u[2]: return 3 if u[0] > u[1] > u[2]: return 1 return 2 return to_standard(u).longest_increasing_subsequence_length() la = [] n = len(pi) t = 0 pi = pi.reverse() for k in range(1, n+1): a = 0 for p in Compositions(n, length=k): b = [sum(p[:i]) for i in range(k+1)] s = sum(llis(pi[b[i]:b[i+1]]) for i in range(k)) a = max(a, s) d = a - t if a == t: return Partition(la) la.append(d) t = a return Partition(la) ------------------------------------------------------------------------ Map images: [1] => [1] [1,2] => [1,1] [2,1] => [2] [1,2,3] => [1,1,1] [1,3,2] => [2,1] [2,1,3] => [2,1] [2,3,1] => [2,1] [3,1,2] => [2,1] [3,2,1] => [3] [1,2,3,4] => [1,1,1,1] [1,2,4,3] => [2,1,1] [1,3,2,4] => [2,1,1] [1,3,4,2] => [2,1,1] [1,4,2,3] => [2,1,1] [1,4,3,2] => [3,1] [2,1,3,4] => [2,1,1] [2,1,4,3] => [2,2] [2,3,1,4] => [2,1,1] [2,3,4,1] => [2,1,1] [2,4,1,3] => [2,1,1] [2,4,3,1] => [3,1] [3,1,2,4] => [2,1,1] [3,1,4,2] => [2,2] [3,2,1,4] => [3,1] [3,2,4,1] => [3,1] [3,4,1,2] => [2,1,1] [3,4,2,1] => [3,1] [4,1,2,3] => [2,1,1] [4,1,3,2] => [3,1] [4,2,1,3] => [3,1] [4,2,3,1] => [3,1] [4,3,1,2] => [3,1] [4,3,2,1] => [4] [1,2,3,4,5] => [1,1,1,1,1] [1,2,3,5,4] => [2,1,1,1] [1,2,4,3,5] => [2,1,1,1] [1,2,4,5,3] => [2,1,1,1] [1,2,5,3,4] => [2,1,1,1] [1,2,5,4,3] => [3,1,1] [1,3,2,4,5] => [2,1,1,1] [1,3,2,5,4] => [2,2,1] [1,3,4,2,5] => [2,1,1,1] [1,3,4,5,2] => [2,1,1,1] [1,3,5,2,4] => [2,1,1,1] [1,3,5,4,2] => [3,1,1] [1,4,2,3,5] => [2,1,1,1] [1,4,2,5,3] => [2,2,1] [1,4,3,2,5] => [3,1,1] [1,4,3,5,2] => [3,1,1] [1,4,5,2,3] => [2,1,1,1] [1,4,5,3,2] => [3,1,1] [1,5,2,3,4] => [2,1,1,1] [1,5,2,4,3] => [3,1,1] [1,5,3,2,4] => [3,1,1] [1,5,3,4,2] => [3,1,1] [1,5,4,2,3] => [3,1,1] [1,5,4,3,2] => [4,1] [2,1,3,4,5] => [2,1,1,1] [2,1,3,5,4] => [2,2,1] [2,1,4,3,5] => [2,2,1] [2,1,4,5,3] => [2,2,1] [2,1,5,3,4] => [2,2,1] [2,1,5,4,3] => [3,2] [2,3,1,4,5] => [2,1,1,1] [2,3,1,5,4] => [2,2,1] [2,3,4,1,5] => [2,1,1,1] [2,3,4,5,1] => [2,1,1,1] [2,3,5,1,4] => [2,1,1,1] [2,3,5,4,1] => [3,1,1] [2,4,1,3,5] => [2,1,1,1] [2,4,1,5,3] => [2,2,1] [2,4,3,1,5] => [3,1,1] [2,4,3,5,1] => [3,1,1] [2,4,5,1,3] => [2,1,1,1] [2,4,5,3,1] => [3,1,1] [2,5,1,3,4] => [2,1,1,1] [2,5,1,4,3] => [3,1,1] [2,5,3,1,4] => [3,1,1] [2,5,3,4,1] => [3,1,1] [2,5,4,1,3] => [3,1,1] [2,5,4,3,1] => [4,1] [3,1,2,4,5] => [2,1,1,1] [3,1,2,5,4] => [2,2,1] [3,1,4,2,5] => [2,2,1] [3,1,4,5,2] => [2,2,1] [3,1,5,2,4] => [2,2,1] [3,1,5,4,2] => [3,2] [3,2,1,4,5] => [3,1,1] [3,2,1,5,4] => [3,2] [3,2,4,1,5] => [3,1,1] [3,2,4,5,1] => [3,1,1] [3,2,5,1,4] => [3,1,1] [3,2,5,4,1] => [3,2] [3,4,1,2,5] => [2,1,1,1] [3,4,1,5,2] => [2,2,1] [3,4,2,1,5] => [3,1,1] [3,4,2,5,1] => [3,1,1] [3,4,5,1,2] => [2,1,1,1] [3,4,5,2,1] => [3,1,1] [3,5,1,2,4] => [2,1,1,1] [3,5,1,4,2] => [3,1,1] [3,5,2,1,4] => [3,1,1] [3,5,2,4,1] => [3,1,1] [3,5,4,1,2] => [3,1,1] [3,5,4,2,1] => [4,1] [4,1,2,3,5] => [2,1,1,1] [4,1,2,5,3] => [2,2,1] [4,1,3,2,5] => [3,1,1] [4,1,3,5,2] => [3,1,1] [4,1,5,2,3] => [2,2,1] [4,1,5,3,2] => [3,2] [4,2,1,3,5] => [3,1,1] [4,2,1,5,3] => [3,2] [4,2,3,1,5] => [3,1,1] [4,2,3,5,1] => [3,1,1] [4,2,5,1,3] => [3,1,1] [4,2,5,3,1] => [3,2] [4,3,1,2,5] => [3,1,1] [4,3,1,5,2] => [3,2] [4,3,2,1,5] => [4,1] [4,3,2,5,1] => [4,1] [4,3,5,1,2] => [3,1,1] [4,3,5,2,1] => [4,1] [4,5,1,2,3] => [2,1,1,1] [4,5,1,3,2] => [3,1,1] [4,5,2,1,3] => [3,1,1] [4,5,2,3,1] => [3,1,1] [4,5,3,1,2] => [3,1,1] [4,5,3,2,1] => [4,1] [5,1,2,3,4] => [2,1,1,1] [5,1,2,4,3] => [3,1,1] [5,1,3,2,4] => [3,1,1] [5,1,3,4,2] => [3,1,1] [5,1,4,2,3] => [3,1,1] [5,1,4,3,2] => [4,1] [5,2,1,3,4] => [3,1,1] [5,2,1,4,3] => [3,2] [5,2,3,1,4] => [3,1,1] [5,2,3,4,1] => [3,1,1] [5,2,4,1,3] => [3,1,1] [5,2,4,3,1] => [4,1] [5,3,1,2,4] => [3,1,1] [5,3,1,4,2] => [3,2] [5,3,2,1,4] => [4,1] [5,3,2,4,1] => [4,1] [5,3,4,1,2] => [3,1,1] [5,3,4,2,1] => [4,1] [5,4,1,2,3] => [3,1,1] [5,4,1,3,2] => [4,1] [5,4,2,1,3] => [4,1] [5,4,2,3,1] => [4,1] [5,4,3,1,2] => [4,1] [5,4,3,2,1] => [5] [1,2,3,4,5,6] => [1,1,1,1,1,1] [1,2,3,4,6,5] => [2,1,1,1,1] [1,2,3,5,4,6] => [2,1,1,1,1] [1,2,3,5,6,4] => [2,1,1,1,1] [1,2,3,6,4,5] => [2,1,1,1,1] [1,2,3,6,5,4] => [3,1,1,1] [1,2,4,3,5,6] => [2,1,1,1,1] [1,2,4,3,6,5] => [2,2,1,1] [1,2,4,5,3,6] => [2,1,1,1,1] [1,2,4,5,6,3] => [2,1,1,1,1] [1,2,4,6,3,5] => [2,1,1,1,1] [1,2,4,6,5,3] => [3,1,1,1] [1,2,5,3,4,6] => [2,1,1,1,1] [1,2,5,3,6,4] => [2,2,1,1] [1,2,5,4,3,6] => [3,1,1,1] [1,2,5,4,6,3] => [3,1,1,1] [1,2,5,6,3,4] => [2,1,1,1,1] [1,2,5,6,4,3] => [3,1,1,1] [1,2,6,3,4,5] => [2,1,1,1,1] [1,2,6,3,5,4] => [3,1,1,1] [1,2,6,4,3,5] => [3,1,1,1] [1,2,6,4,5,3] => [3,1,1,1] [1,2,6,5,3,4] => [3,1,1,1] [1,2,6,5,4,3] => [4,1,1] [1,3,2,4,5,6] => [2,1,1,1,1] [1,3,2,4,6,5] => [2,2,1,1] [1,3,2,5,4,6] => [2,2,1,1] [1,3,2,5,6,4] => [2,2,1,1] [1,3,2,6,4,5] => [2,2,1,1] [1,3,2,6,5,4] => [3,2,1] [1,3,4,2,5,6] => [2,1,1,1,1] [1,3,4,2,6,5] => [2,2,1,1] [1,3,4,5,2,6] => [2,1,1,1,1] [1,3,4,5,6,2] => [2,1,1,1,1] [1,3,4,6,2,5] => [2,1,1,1,1] [1,3,4,6,5,2] => [3,1,1,1] [1,3,5,2,4,6] => [2,1,1,1,1] [1,3,5,2,6,4] => [2,2,1,1] [1,3,5,4,2,6] => [3,1,1,1] [1,3,5,4,6,2] => [3,1,1,1] [1,3,5,6,2,4] => [2,1,1,1,1] [1,3,5,6,4,2] => [3,1,1,1] [1,3,6,2,4,5] => [2,1,1,1,1] [1,3,6,2,5,4] => [3,1,1,1] [1,3,6,4,2,5] => [3,1,1,1] [1,3,6,4,5,2] => [3,1,1,1] [1,3,6,5,2,4] => [3,1,1,1] [1,3,6,5,4,2] => [4,1,1] [1,4,2,3,5,6] => [2,1,1,1,1] [1,4,2,3,6,5] => [2,2,1,1] [1,4,2,5,3,6] => [2,2,1,1] [1,4,2,5,6,3] => [2,2,1,1] [1,4,2,6,3,5] => [2,2,1,1] [1,4,2,6,5,3] => [3,2,1] [1,4,3,2,5,6] => [3,1,1,1] [1,4,3,2,6,5] => [3,2,1] [1,4,3,5,2,6] => [3,1,1,1] [1,4,3,5,6,2] => [3,1,1,1] [1,4,3,6,2,5] => [3,1,1,1] [1,4,3,6,5,2] => [3,2,1] [1,4,5,2,3,6] => [2,1,1,1,1] [1,4,5,2,6,3] => [2,2,1,1] [1,4,5,3,2,6] => [3,1,1,1] [1,4,5,3,6,2] => [3,1,1,1] [1,4,5,6,2,3] => [2,1,1,1,1] [1,4,5,6,3,2] => [3,1,1,1] [1,4,6,2,3,5] => [2,1,1,1,1] [1,4,6,2,5,3] => [3,1,1,1] [1,4,6,3,2,5] => [3,1,1,1] [1,4,6,3,5,2] => [3,1,1,1] [1,4,6,5,2,3] => [3,1,1,1] [1,4,6,5,3,2] => [4,1,1] [1,5,2,3,4,6] => [2,1,1,1,1] [1,5,2,3,6,4] => [2,2,1,1] [1,5,2,4,3,6] => [3,1,1,1] [1,5,2,4,6,3] => [3,1,1,1] [1,5,2,6,3,4] => [2,2,1,1] [1,5,2,6,4,3] => [3,2,1] [1,5,3,2,4,6] => [3,1,1,1] [1,5,3,2,6,4] => [3,2,1] [1,5,3,4,2,6] => [3,1,1,1] [1,5,3,4,6,2] => [3,1,1,1] [1,5,3,6,2,4] => [3,1,1,1] [1,5,3,6,4,2] => [3,2,1] [1,5,4,2,3,6] => [3,1,1,1] [1,5,4,2,6,3] => [3,2,1] [1,5,4,3,2,6] => [4,1,1] [1,5,4,3,6,2] => [4,1,1] [1,5,4,6,2,3] => [3,1,1,1] [1,5,4,6,3,2] => [4,1,1] [1,5,6,2,3,4] => [2,1,1,1,1] [1,5,6,2,4,3] => [3,1,1,1] [1,5,6,3,2,4] => [3,1,1,1] [1,5,6,3,4,2] => [3,1,1,1] [1,5,6,4,2,3] => [3,1,1,1] [1,5,6,4,3,2] => [4,1,1] [1,6,2,3,4,5] => [2,1,1,1,1] [1,6,2,3,5,4] => [3,1,1,1] [1,6,2,4,3,5] => [3,1,1,1] [1,6,2,4,5,3] => [3,1,1,1] [1,6,2,5,3,4] => [3,1,1,1] [1,6,2,5,4,3] => [4,1,1] [1,6,3,2,4,5] => [3,1,1,1] [1,6,3,2,5,4] => [3,2,1] [1,6,3,4,2,5] => [3,1,1,1] [1,6,3,4,5,2] => [3,1,1,1] [1,6,3,5,2,4] => [3,1,1,1] [1,6,3,5,4,2] => [4,1,1] [1,6,4,2,3,5] => [3,1,1,1] [1,6,4,2,5,3] => [3,2,1] [1,6,4,3,2,5] => [4,1,1] [1,6,4,3,5,2] => [4,1,1] [1,6,4,5,2,3] => [3,1,1,1] [1,6,4,5,3,2] => [4,1,1] [1,6,5,2,3,4] => [3,1,1,1] [1,6,5,2,4,3] => [4,1,1] [1,6,5,3,2,4] => [4,1,1] [1,6,5,3,4,2] => [4,1,1] [1,6,5,4,2,3] => [4,1,1] [1,6,5,4,3,2] => [5,1] [2,1,3,4,5,6] => [2,1,1,1,1] [2,1,3,4,6,5] => [2,2,1,1] [2,1,3,5,4,6] => [2,2,1,1] [2,1,3,5,6,4] => [2,2,1,1] [2,1,3,6,4,5] => [2,2,1,1] [2,1,3,6,5,4] => [3,2,1] [2,1,4,3,5,6] => [2,2,1,1] [2,1,4,3,6,5] => [2,2,2] [2,1,4,5,3,6] => [2,2,1,1] [2,1,4,5,6,3] => [2,2,1,1] [2,1,4,6,3,5] => [2,2,1,1] [2,1,4,6,5,3] => [3,2,1] [2,1,5,3,4,6] => [2,2,1,1] [2,1,5,3,6,4] => [2,2,2] [2,1,5,4,3,6] => [3,2,1] [2,1,5,4,6,3] => [3,2,1] [2,1,5,6,3,4] => [2,2,1,1] [2,1,5,6,4,3] => [3,2,1] [2,1,6,3,4,5] => [2,2,1,1] [2,1,6,3,5,4] => [3,2,1] [2,1,6,4,3,5] => [3,2,1] [2,1,6,4,5,3] => [3,2,1] [2,1,6,5,3,4] => [3,2,1] [2,1,6,5,4,3] => [4,2] [2,3,1,4,5,6] => [2,1,1,1,1] [2,3,1,4,6,5] => [2,2,1,1] [2,3,1,5,4,6] => [2,2,1,1] [2,3,1,5,6,4] => [2,2,1,1] [2,3,1,6,4,5] => [2,2,1,1] [2,3,1,6,5,4] => [3,2,1] [2,3,4,1,5,6] => [2,1,1,1,1] [2,3,4,1,6,5] => [2,2,1,1] [2,3,4,5,1,6] => [2,1,1,1,1] [2,3,4,5,6,1] => [2,1,1,1,1] [2,3,4,6,1,5] => [2,1,1,1,1] [2,3,4,6,5,1] => [3,1,1,1] [2,3,5,1,4,6] => [2,1,1,1,1] [2,3,5,1,6,4] => [2,2,1,1] [2,3,5,4,1,6] => [3,1,1,1] [2,3,5,4,6,1] => [3,1,1,1] [2,3,5,6,1,4] => [2,1,1,1,1] [2,3,5,6,4,1] => [3,1,1,1] [2,3,6,1,4,5] => [2,1,1,1,1] [2,3,6,1,5,4] => [3,1,1,1] [2,3,6,4,1,5] => [3,1,1,1] [2,3,6,4,5,1] => [3,1,1,1] [2,3,6,5,1,4] => [3,1,1,1] [2,3,6,5,4,1] => [4,1,1] [2,4,1,3,5,6] => [2,1,1,1,1] [2,4,1,3,6,5] => [2,2,1,1] [2,4,1,5,3,6] => [2,2,1,1] [2,4,1,5,6,3] => [2,2,1,1] [2,4,1,6,3,5] => [2,2,1,1] [2,4,1,6,5,3] => [3,2,1] [2,4,3,1,5,6] => [3,1,1,1] [2,4,3,1,6,5] => [3,2,1] [2,4,3,5,1,6] => [3,1,1,1] [2,4,3,5,6,1] => [3,1,1,1] [2,4,3,6,1,5] => [3,1,1,1] [2,4,3,6,5,1] => [3,2,1] [2,4,5,1,3,6] => [2,1,1,1,1] [2,4,5,1,6,3] => [2,2,1,1] [2,4,5,3,1,6] => [3,1,1,1] [2,4,5,3,6,1] => [3,1,1,1] [2,4,5,6,1,3] => [2,1,1,1,1] [2,4,5,6,3,1] => [3,1,1,1] [2,4,6,1,3,5] => [2,1,1,1,1] [2,4,6,1,5,3] => [3,1,1,1] [2,4,6,3,1,5] => [3,1,1,1] [2,4,6,3,5,1] => [3,1,1,1] [2,4,6,5,1,3] => [3,1,1,1] [2,4,6,5,3,1] => [4,1,1] [2,5,1,3,4,6] => [2,1,1,1,1] [2,5,1,3,6,4] => [2,2,1,1] [2,5,1,4,3,6] => [3,1,1,1] [2,5,1,4,6,3] => [3,1,1,1] [2,5,1,6,3,4] => [2,2,1,1] [2,5,1,6,4,3] => [3,2,1] [2,5,3,1,4,6] => [3,1,1,1] [2,5,3,1,6,4] => [3,2,1] [2,5,3,4,1,6] => [3,1,1,1] [2,5,3,4,6,1] => [3,1,1,1] [2,5,3,6,1,4] => [3,1,1,1] [2,5,3,6,4,1] => [3,2,1] [2,5,4,1,3,6] => [3,1,1,1] [2,5,4,1,6,3] => [3,2,1] [2,5,4,3,1,6] => [4,1,1] [2,5,4,3,6,1] => [4,1,1] [2,5,4,6,1,3] => [3,1,1,1] [2,5,4,6,3,1] => [4,1,1] [2,5,6,1,3,4] => [2,1,1,1,1] [2,5,6,1,4,3] => [3,1,1,1] [2,5,6,3,1,4] => [3,1,1,1] [2,5,6,3,4,1] => [3,1,1,1] [2,5,6,4,1,3] => [3,1,1,1] [2,5,6,4,3,1] => [4,1,1] [2,6,1,3,4,5] => [2,1,1,1,1] [2,6,1,3,5,4] => [3,1,1,1] [2,6,1,4,3,5] => [3,1,1,1] [2,6,1,4,5,3] => [3,1,1,1] [2,6,1,5,3,4] => [3,1,1,1] [2,6,1,5,4,3] => [4,1,1] [2,6,3,1,4,5] => [3,1,1,1] [2,6,3,1,5,4] => [3,2,1] [2,6,3,4,1,5] => [3,1,1,1] [2,6,3,4,5,1] => [3,1,1,1] [2,6,3,5,1,4] => [3,1,1,1] [2,6,3,5,4,1] => [4,1,1] [2,6,4,1,3,5] => [3,1,1,1] [2,6,4,1,5,3] => [3,2,1] [2,6,4,3,1,5] => [4,1,1] [2,6,4,3,5,1] => [4,1,1] [2,6,4,5,1,3] => [3,1,1,1] [2,6,4,5,3,1] => [4,1,1] [2,6,5,1,3,4] => [3,1,1,1] [2,6,5,1,4,3] => [4,1,1] [2,6,5,3,1,4] => [4,1,1] [2,6,5,3,4,1] => [4,1,1] [2,6,5,4,1,3] => [4,1,1] [2,6,5,4,3,1] => [5,1] [3,1,2,4,5,6] => [2,1,1,1,1] [3,1,2,4,6,5] => [2,2,1,1] [3,1,2,5,4,6] => [2,2,1,1] [3,1,2,5,6,4] => [2,2,1,1] [3,1,2,6,4,5] => [2,2,1,1] [3,1,2,6,5,4] => [3,2,1] [3,1,4,2,5,6] => [2,2,1,1] [3,1,4,2,6,5] => [2,2,2] [3,1,4,5,2,6] => [2,2,1,1] [3,1,4,5,6,2] => [2,2,1,1] [3,1,4,6,2,5] => [2,2,1,1] [3,1,4,6,5,2] => [3,2,1] [3,1,5,2,4,6] => [2,2,1,1] [3,1,5,2,6,4] => [2,2,2] [3,1,5,4,2,6] => [3,2,1] [3,1,5,4,6,2] => [3,2,1] [3,1,5,6,2,4] => [2,2,1,1] [3,1,5,6,4,2] => [3,2,1] [3,1,6,2,4,5] => [2,2,1,1] [3,1,6,2,5,4] => [3,2,1] [3,1,6,4,2,5] => [3,2,1] [3,1,6,4,5,2] => [3,2,1] [3,1,6,5,2,4] => [3,2,1] [3,1,6,5,4,2] => [4,2] [3,2,1,4,5,6] => [3,1,1,1] [3,2,1,4,6,5] => [3,2,1] [3,2,1,5,4,6] => [3,2,1] [3,2,1,5,6,4] => [3,2,1] [3,2,1,6,4,5] => [3,2,1] [3,2,1,6,5,4] => [3,3] [3,2,4,1,5,6] => [3,1,1,1] [3,2,4,1,6,5] => [3,2,1] [3,2,4,5,1,6] => [3,1,1,1] [3,2,4,5,6,1] => [3,1,1,1] [3,2,4,6,1,5] => [3,1,1,1] [3,2,4,6,5,1] => [3,2,1] [3,2,5,1,4,6] => [3,1,1,1] [3,2,5,1,6,4] => [3,2,1] [3,2,5,4,1,6] => [3,2,1] [3,2,5,4,6,1] => [3,2,1] [3,2,5,6,1,4] => [3,1,1,1] [3,2,5,6,4,1] => [3,2,1] [3,2,6,1,4,5] => [3,1,1,1] [3,2,6,1,5,4] => [3,2,1] [3,2,6,4,1,5] => [3,2,1] [3,2,6,4,5,1] => [3,2,1] [3,2,6,5,1,4] => [3,2,1] [3,2,6,5,4,1] => [4,2] [3,4,1,2,5,6] => [2,1,1,1,1] [3,4,1,2,6,5] => [2,2,1,1] [3,4,1,5,2,6] => [2,2,1,1] [3,4,1,5,6,2] => [2,2,1,1] [3,4,1,6,2,5] => [2,2,1,1] [3,4,1,6,5,2] => [3,2,1] [3,4,2,1,5,6] => [3,1,1,1] [3,4,2,1,6,5] => [3,2,1] [3,4,2,5,1,6] => [3,1,1,1] [3,4,2,5,6,1] => [3,1,1,1] [3,4,2,6,1,5] => [3,1,1,1] [3,4,2,6,5,1] => [3,2,1] [3,4,5,1,2,6] => [2,1,1,1,1] [3,4,5,1,6,2] => [2,2,1,1] [3,4,5,2,1,6] => [3,1,1,1] [3,4,5,2,6,1] => [3,1,1,1] [3,4,5,6,1,2] => [2,1,1,1,1] [3,4,5,6,2,1] => [3,1,1,1] [3,4,6,1,2,5] => [2,1,1,1,1] [3,4,6,1,5,2] => [3,1,1,1] [3,4,6,2,1,5] => [3,1,1,1] [3,4,6,2,5,1] => [3,1,1,1] [3,4,6,5,1,2] => [3,1,1,1] [3,4,6,5,2,1] => [4,1,1] [3,5,1,2,4,6] => [2,1,1,1,1] [3,5,1,2,6,4] => [2,2,1,1] [3,5,1,4,2,6] => [3,1,1,1] [3,5,1,4,6,2] => [3,1,1,1] [3,5,1,6,2,4] => [2,2,1,1] [3,5,1,6,4,2] => [3,2,1] [3,5,2,1,4,6] => [3,1,1,1] [3,5,2,1,6,4] => [3,2,1] [3,5,2,4,1,6] => [3,1,1,1] [3,5,2,4,6,1] => [3,1,1,1] [3,5,2,6,1,4] => [3,1,1,1] [3,5,2,6,4,1] => [3,2,1] [3,5,4,1,2,6] => [3,1,1,1] [3,5,4,1,6,2] => [3,2,1] [3,5,4,2,1,6] => [4,1,1] [3,5,4,2,6,1] => [4,1,1] [3,5,4,6,1,2] => [3,1,1,1] [3,5,4,6,2,1] => [4,1,1] [3,5,6,1,2,4] => [2,1,1,1,1] [3,5,6,1,4,2] => [3,1,1,1] [3,5,6,2,1,4] => [3,1,1,1] [3,5,6,2,4,1] => [3,1,1,1] [3,5,6,4,1,2] => [3,1,1,1] [3,5,6,4,2,1] => [4,1,1] [3,6,1,2,4,5] => [2,1,1,1,1] [3,6,1,2,5,4] => [3,1,1,1] [3,6,1,4,2,5] => [3,1,1,1] [3,6,1,4,5,2] => [3,1,1,1] [3,6,1,5,2,4] => [3,1,1,1] [3,6,1,5,4,2] => [4,1,1] [3,6,2,1,4,5] => [3,1,1,1] [3,6,2,1,5,4] => [3,2,1] [3,6,2,4,1,5] => [3,1,1,1] [3,6,2,4,5,1] => [3,1,1,1] [3,6,2,5,1,4] => [3,1,1,1] [3,6,2,5,4,1] => [4,1,1] [3,6,4,1,2,5] => [3,1,1,1] [3,6,4,1,5,2] => [3,2,1] [3,6,4,2,1,5] => [4,1,1] [3,6,4,2,5,1] => [4,1,1] [3,6,4,5,1,2] => [3,1,1,1] [3,6,4,5,2,1] => [4,1,1] [3,6,5,1,2,4] => [3,1,1,1] [3,6,5,1,4,2] => [4,1,1] [3,6,5,2,1,4] => [4,1,1] [3,6,5,2,4,1] => [4,1,1] [3,6,5,4,1,2] => [4,1,1] [3,6,5,4,2,1] => [5,1] [4,1,2,3,5,6] => [2,1,1,1,1] [4,1,2,3,6,5] => [2,2,1,1] [4,1,2,5,3,6] => [2,2,1,1] [4,1,2,5,6,3] => [2,2,1,1] [4,1,2,6,3,5] => [2,2,1,1] [4,1,2,6,5,3] => [3,2,1] [4,1,3,2,5,6] => [3,1,1,1] [4,1,3,2,6,5] => [3,2,1] [4,1,3,5,2,6] => [3,1,1,1] [4,1,3,5,6,2] => [3,1,1,1] [4,1,3,6,2,5] => [3,1,1,1] [4,1,3,6,5,2] => [3,2,1] [4,1,5,2,3,6] => [2,2,1,1] [4,1,5,2,6,3] => [2,2,2] [4,1,5,3,2,6] => [3,2,1] [4,1,5,3,6,2] => [3,2,1] [4,1,5,6,2,3] => [2,2,1,1] [4,1,5,6,3,2] => [3,2,1] [4,1,6,2,3,5] => [2,2,1,1] [4,1,6,2,5,3] => [3,2,1] [4,1,6,3,2,5] => [3,2,1] [4,1,6,3,5,2] => [3,2,1] [4,1,6,5,2,3] => [3,2,1] [4,1,6,5,3,2] => [4,2] [4,2,1,3,5,6] => [3,1,1,1] [4,2,1,3,6,5] => [3,2,1] [4,2,1,5,3,6] => [3,2,1] [4,2,1,5,6,3] => [3,2,1] [4,2,1,6,3,5] => [3,2,1] [4,2,1,6,5,3] => [3,3] [4,2,3,1,5,6] => [3,1,1,1] [4,2,3,1,6,5] => [3,2,1] [4,2,3,5,1,6] => [3,1,1,1] [4,2,3,5,6,1] => [3,1,1,1] [4,2,3,6,1,5] => [3,1,1,1] [4,2,3,6,5,1] => [3,2,1] [4,2,5,1,3,6] => [3,1,1,1] [4,2,5,1,6,3] => [3,2,1] [4,2,5,3,1,6] => [3,2,1] [4,2,5,3,6,1] => [3,2,1] [4,2,5,6,1,3] => [3,1,1,1] [4,2,5,6,3,1] => [3,2,1] [4,2,6,1,3,5] => [3,1,1,1] [4,2,6,1,5,3] => [3,2,1] [4,2,6,3,1,5] => [3,2,1] [4,2,6,3,5,1] => [3,2,1] [4,2,6,5,1,3] => [3,2,1] [4,2,6,5,3,1] => [4,2] [4,3,1,2,5,6] => [3,1,1,1] [4,3,1,2,6,5] => [3,2,1] [4,3,1,5,2,6] => [3,2,1] [4,3,1,5,6,2] => [3,2,1] [4,3,1,6,2,5] => [3,2,1] [4,3,1,6,5,2] => [3,3] [4,3,2,1,5,6] => [4,1,1] [4,3,2,1,6,5] => [4,2] [4,3,2,5,1,6] => [4,1,1] [4,3,2,5,6,1] => [4,1,1] [4,3,2,6,1,5] => [4,1,1] [4,3,2,6,5,1] => [4,2] [4,3,5,1,2,6] => [3,1,1,1] [4,3,5,1,6,2] => [3,2,1] [4,3,5,2,1,6] => [4,1,1] [4,3,5,2,6,1] => [4,1,1] [4,3,5,6,1,2] => [3,1,1,1] [4,3,5,6,2,1] => [4,1,1] [4,3,6,1,2,5] => [3,1,1,1] [4,3,6,1,5,2] => [3,2,1] [4,3,6,2,1,5] => [4,1,1] [4,3,6,2,5,1] => [4,1,1] [4,3,6,5,1,2] => [3,2,1] [4,3,6,5,2,1] => [4,2] [4,5,1,2,3,6] => [2,1,1,1,1] [4,5,1,2,6,3] => [2,2,1,1] [4,5,1,3,2,6] => [3,1,1,1] [4,5,1,3,6,2] => [3,1,1,1] [4,5,1,6,2,3] => [2,2,1,1] [4,5,1,6,3,2] => [3,2,1] [4,5,2,1,3,6] => [3,1,1,1] [4,5,2,1,6,3] => [3,2,1] [4,5,2,3,1,6] => [3,1,1,1] [4,5,2,3,6,1] => [3,1,1,1] [4,5,2,6,1,3] => [3,1,1,1] [4,5,2,6,3,1] => [3,2,1] [4,5,3,1,2,6] => [3,1,1,1] [4,5,3,1,6,2] => [3,2,1] [4,5,3,2,1,6] => [4,1,1] [4,5,3,2,6,1] => [4,1,1] [4,5,3,6,1,2] => [3,1,1,1] [4,5,3,6,2,1] => [4,1,1] [4,5,6,1,2,3] => [2,1,1,1,1] [4,5,6,1,3,2] => [3,1,1,1] [4,5,6,2,1,3] => [3,1,1,1] [4,5,6,2,3,1] => [3,1,1,1] [4,5,6,3,1,2] => [3,1,1,1] [4,5,6,3,2,1] => [4,1,1] [4,6,1,2,3,5] => [2,1,1,1,1] [4,6,1,2,5,3] => [3,1,1,1] [4,6,1,3,2,5] => [3,1,1,1] [4,6,1,3,5,2] => [3,1,1,1] [4,6,1,5,2,3] => [3,1,1,1] [4,6,1,5,3,2] => [4,1,1] [4,6,2,1,3,5] => [3,1,1,1] [4,6,2,1,5,3] => [3,2,1] [4,6,2,3,1,5] => [3,1,1,1] [4,6,2,3,5,1] => [3,1,1,1] [4,6,2,5,1,3] => [3,1,1,1] [4,6,2,5,3,1] => [4,1,1] [4,6,3,1,2,5] => [3,1,1,1] [4,6,3,1,5,2] => [3,2,1] [4,6,3,2,1,5] => [4,1,1] [4,6,3,2,5,1] => [4,1,1] [4,6,3,5,1,2] => [3,1,1,1] [4,6,3,5,2,1] => [4,1,1] [4,6,5,1,2,3] => [3,1,1,1] [4,6,5,1,3,2] => [4,1,1] [4,6,5,2,1,3] => [4,1,1] [4,6,5,2,3,1] => [4,1,1] [4,6,5,3,1,2] => [4,1,1] [4,6,5,3,2,1] => [5,1] [5,1,2,3,4,6] => [2,1,1,1,1] [5,1,2,3,6,4] => [2,2,1,1] [5,1,2,4,3,6] => [3,1,1,1] [5,1,2,4,6,3] => [3,1,1,1] [5,1,2,6,3,4] => [2,2,1,1] [5,1,2,6,4,3] => [3,2,1] [5,1,3,2,4,6] => [3,1,1,1] [5,1,3,2,6,4] => [3,2,1] [5,1,3,4,2,6] => [3,1,1,1] [5,1,3,4,6,2] => [3,1,1,1] [5,1,3,6,2,4] => [3,1,1,1] [5,1,3,6,4,2] => [3,2,1] [5,1,4,2,3,6] => [3,1,1,1] [5,1,4,2,6,3] => [3,2,1] [5,1,4,3,2,6] => [4,1,1] [5,1,4,3,6,2] => [4,1,1] [5,1,4,6,2,3] => [3,1,1,1] [5,1,4,6,3,2] => [4,1,1] [5,1,6,2,3,4] => [2,2,1,1] [5,1,6,2,4,3] => [3,2,1] [5,1,6,3,2,4] => [3,2,1] [5,1,6,3,4,2] => [3,2,1] [5,1,6,4,2,3] => [3,2,1] [5,1,6,4,3,2] => [4,2] [5,2,1,3,4,6] => [3,1,1,1] [5,2,1,3,6,4] => [3,2,1] [5,2,1,4,3,6] => [3,2,1] [5,2,1,4,6,3] => [3,2,1] [5,2,1,6,3,4] => [3,2,1] [5,2,1,6,4,3] => [3,3] [5,2,3,1,4,6] => [3,1,1,1] [5,2,3,1,6,4] => [3,2,1] [5,2,3,4,1,6] => [3,1,1,1] [5,2,3,4,6,1] => [3,1,1,1] [5,2,3,6,1,4] => [3,1,1,1] [5,2,3,6,4,1] => [3,2,1] [5,2,4,1,3,6] => [3,1,1,1] [5,2,4,1,6,3] => [3,2,1] [5,2,4,3,1,6] => [4,1,1] [5,2,4,3,6,1] => [4,1,1] [5,2,4,6,1,3] => [3,1,1,1] [5,2,4,6,3,1] => [4,1,1] [5,2,6,1,3,4] => [3,1,1,1] [5,2,6,1,4,3] => [3,2,1] [5,2,6,3,1,4] => [3,2,1] [5,2,6,3,4,1] => [3,2,1] [5,2,6,4,1,3] => [3,2,1] [5,2,6,4,3,1] => [4,2] [5,3,1,2,4,6] => [3,1,1,1] [5,3,1,2,6,4] => [3,2,1] [5,3,1,4,2,6] => [3,2,1] [5,3,1,4,6,2] => [3,2,1] [5,3,1,6,2,4] => [3,2,1] [5,3,1,6,4,2] => [3,3] [5,3,2,1,4,6] => [4,1,1] [5,3,2,1,6,4] => [4,2] [5,3,2,4,1,6] => [4,1,1] [5,3,2,4,6,1] => [4,1,1] [5,3,2,6,1,4] => [4,1,1] [5,3,2,6,4,1] => [4,2] [5,3,4,1,2,6] => [3,1,1,1] [5,3,4,1,6,2] => [3,2,1] [5,3,4,2,1,6] => [4,1,1] [5,3,4,2,6,1] => [4,1,1] [5,3,4,6,1,2] => [3,1,1,1] [5,3,4,6,2,1] => [4,1,1] [5,3,6,1,2,4] => [3,1,1,1] [5,3,6,1,4,2] => [3,2,1] [5,3,6,2,1,4] => [4,1,1] [5,3,6,2,4,1] => [4,1,1] [5,3,6,4,1,2] => [3,2,1] [5,3,6,4,2,1] => [4,2] [5,4,1,2,3,6] => [3,1,1,1] [5,4,1,2,6,3] => [3,2,1] [5,4,1,3,2,6] => [4,1,1] [5,4,1,3,6,2] => [4,1,1] [5,4,1,6,2,3] => [3,2,1] [5,4,1,6,3,2] => [4,2] [5,4,2,1,3,6] => [4,1,1] [5,4,2,1,6,3] => [4,2] [5,4,2,3,1,6] => [4,1,1] [5,4,2,3,6,1] => [4,1,1] [5,4,2,6,1,3] => [4,1,1] [5,4,2,6,3,1] => [4,2] [5,4,3,1,2,6] => [4,1,1] [5,4,3,1,6,2] => [4,2] [5,4,3,2,1,6] => [5,1] [5,4,3,2,6,1] => [5,1] [5,4,3,6,1,2] => [4,1,1] [5,4,3,6,2,1] => [5,1] [5,4,6,1,2,3] => [3,1,1,1] [5,4,6,1,3,2] => [4,1,1] [5,4,6,2,1,3] => [4,1,1] [5,4,6,2,3,1] => [4,1,1] [5,4,6,3,1,2] => [4,1,1] [5,4,6,3,2,1] => [5,1] [5,6,1,2,3,4] => [2,1,1,1,1] [5,6,1,2,4,3] => [3,1,1,1] [5,6,1,3,2,4] => [3,1,1,1] [5,6,1,3,4,2] => [3,1,1,1] [5,6,1,4,2,3] => [3,1,1,1] [5,6,1,4,3,2] => [4,1,1] [5,6,2,1,3,4] => [3,1,1,1] [5,6,2,1,4,3] => [3,2,1] [5,6,2,3,1,4] => [3,1,1,1] [5,6,2,3,4,1] => [3,1,1,1] [5,6,2,4,1,3] => [3,1,1,1] [5,6,2,4,3,1] => [4,1,1] [5,6,3,1,2,4] => [3,1,1,1] [5,6,3,1,4,2] => [3,2,1] [5,6,3,2,1,4] => [4,1,1] [5,6,3,2,4,1] => [4,1,1] [5,6,3,4,1,2] => [3,1,1,1] [5,6,3,4,2,1] => [4,1,1] [5,6,4,1,2,3] => [3,1,1,1] [5,6,4,1,3,2] => [4,1,1] [5,6,4,2,1,3] => [4,1,1] [5,6,4,2,3,1] => [4,1,1] [5,6,4,3,1,2] => [4,1,1] [5,6,4,3,2,1] => [5,1] [6,1,2,3,4,5] => [2,1,1,1,1] [6,1,2,3,5,4] => [3,1,1,1] [6,1,2,4,3,5] => [3,1,1,1] [6,1,2,4,5,3] => [3,1,1,1] [6,1,2,5,3,4] => [3,1,1,1] [6,1,2,5,4,3] => [4,1,1] [6,1,3,2,4,5] => [3,1,1,1] [6,1,3,2,5,4] => [3,2,1] [6,1,3,4,2,5] => [3,1,1,1] [6,1,3,4,5,2] => [3,1,1,1] [6,1,3,5,2,4] => [3,1,1,1] [6,1,3,5,4,2] => [4,1,1] [6,1,4,2,3,5] => [3,1,1,1] [6,1,4,2,5,3] => [3,2,1] [6,1,4,3,2,5] => [4,1,1] [6,1,4,3,5,2] => [4,1,1] [6,1,4,5,2,3] => [3,1,1,1] [6,1,4,5,3,2] => [4,1,1] [6,1,5,2,3,4] => [3,1,1,1] [6,1,5,2,4,3] => [4,1,1] [6,1,5,3,2,4] => [4,1,1] [6,1,5,3,4,2] => [4,1,1] [6,1,5,4,2,3] => [4,1,1] [6,1,5,4,3,2] => [5,1] [6,2,1,3,4,5] => [3,1,1,1] [6,2,1,3,5,4] => [3,2,1] [6,2,1,4,3,5] => [3,2,1] [6,2,1,4,5,3] => [3,2,1] [6,2,1,5,3,4] => [3,2,1] [6,2,1,5,4,3] => [4,2] [6,2,3,1,4,5] => [3,1,1,1] [6,2,3,1,5,4] => [3,2,1] [6,2,3,4,1,5] => [3,1,1,1] [6,2,3,4,5,1] => [3,1,1,1] [6,2,3,5,1,4] => [3,1,1,1] [6,2,3,5,4,1] => [4,1,1] [6,2,4,1,3,5] => [3,1,1,1] [6,2,4,1,5,3] => [3,2,1] [6,2,4,3,1,5] => [4,1,1] [6,2,4,3,5,1] => [4,1,1] [6,2,4,5,1,3] => [3,1,1,1] [6,2,4,5,3,1] => [4,1,1] [6,2,5,1,3,4] => [3,1,1,1] [6,2,5,1,4,3] => [4,1,1] [6,2,5,3,1,4] => [4,1,1] [6,2,5,3,4,1] => [4,1,1] [6,2,5,4,1,3] => [4,1,1] [6,2,5,4,3,1] => [5,1] [6,3,1,2,4,5] => [3,1,1,1] [6,3,1,2,5,4] => [3,2,1] [6,3,1,4,2,5] => [3,2,1] [6,3,1,4,5,2] => [3,2,1] [6,3,1,5,2,4] => [3,2,1] [6,3,1,5,4,2] => [4,2] [6,3,2,1,4,5] => [4,1,1] [6,3,2,1,5,4] => [4,2] [6,3,2,4,1,5] => [4,1,1] [6,3,2,4,5,1] => [4,1,1] [6,3,2,5,1,4] => [4,1,1] [6,3,2,5,4,1] => [4,2] [6,3,4,1,2,5] => [3,1,1,1] [6,3,4,1,5,2] => [3,2,1] [6,3,4,2,1,5] => [4,1,1] [6,3,4,2,5,1] => [4,1,1] [6,3,4,5,1,2] => [3,1,1,1] [6,3,4,5,2,1] => [4,1,1] [6,3,5,1,2,4] => [3,1,1,1] [6,3,5,1,4,2] => [4,1,1] [6,3,5,2,1,4] => [4,1,1] [6,3,5,2,4,1] => [4,1,1] [6,3,5,4,1,2] => [4,1,1] [6,3,5,4,2,1] => [5,1] [6,4,1,2,3,5] => [3,1,1,1] [6,4,1,2,5,3] => [3,2,1] [6,4,1,3,2,5] => [4,1,1] [6,4,1,3,5,2] => [4,1,1] [6,4,1,5,2,3] => [3,2,1] [6,4,1,5,3,2] => [4,2] [6,4,2,1,3,5] => [4,1,1] [6,4,2,1,5,3] => [4,2] [6,4,2,3,1,5] => [4,1,1] [6,4,2,3,5,1] => [4,1,1] [6,4,2,5,1,3] => [4,1,1] [6,4,2,5,3,1] => [4,2] [6,4,3,1,2,5] => [4,1,1] [6,4,3,1,5,2] => [4,2] [6,4,3,2,1,5] => [5,1] [6,4,3,2,5,1] => [5,1] [6,4,3,5,1,2] => [4,1,1] [6,4,3,5,2,1] => [5,1] [6,4,5,1,2,3] => [3,1,1,1] [6,4,5,1,3,2] => [4,1,1] [6,4,5,2,1,3] => [4,1,1] [6,4,5,2,3,1] => [4,1,1] [6,4,5,3,1,2] => [4,1,1] [6,4,5,3,2,1] => [5,1] [6,5,1,2,3,4] => [3,1,1,1] [6,5,1,2,4,3] => [4,1,1] [6,5,1,3,2,4] => [4,1,1] [6,5,1,3,4,2] => [4,1,1] [6,5,1,4,2,3] => [4,1,1] [6,5,1,4,3,2] => [5,1] [6,5,2,1,3,4] => [4,1,1] [6,5,2,1,4,3] => [4,2] [6,5,2,3,1,4] => [4,1,1] [6,5,2,3,4,1] => [4,1,1] [6,5,2,4,1,3] => [4,1,1] [6,5,2,4,3,1] => [5,1] [6,5,3,1,2,4] => [4,1,1] [6,5,3,1,4,2] => [4,2] [6,5,3,2,1,4] => [5,1] [6,5,3,2,4,1] => [5,1] [6,5,3,4,1,2] => [4,1,1] [6,5,3,4,2,1] => [5,1] [6,5,4,1,2,3] => [4,1,1] [6,5,4,1,3,2] => [5,1] [6,5,4,2,1,3] => [5,1] [6,5,4,2,3,1] => [5,1] [6,5,4,3,1,2] => [5,1] [6,5,4,3,2,1] => [6] [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] [1,2,3,4,5,7,6] => [2,1,1,1,1,1] [1,2,3,4,6,5,7] => [2,1,1,1,1,1] [1,2,3,4,6,7,5] => [2,1,1,1,1,1] [1,2,3,4,7,5,6] => [2,1,1,1,1,1] [1,2,3,4,7,6,5] => [3,1,1,1,1] [1,2,3,5,4,6,7] => [2,1,1,1,1,1] [1,2,3,5,4,7,6] => [2,2,1,1,1] [1,2,3,5,6,4,7] => [2,1,1,1,1,1] [1,2,3,5,6,7,4] => [2,1,1,1,1,1] [1,2,3,5,7,4,6] => [2,1,1,1,1,1] [1,2,3,5,7,6,4] => [3,1,1,1,1] [1,2,3,6,4,5,7] => [2,1,1,1,1,1] [1,2,3,6,4,7,5] => [2,2,1,1,1] [1,2,3,6,5,4,7] => [3,1,1,1,1] [1,2,3,6,5,7,4] => [3,1,1,1,1] [1,2,3,6,7,4,5] => [2,1,1,1,1,1] [1,2,3,6,7,5,4] => [3,1,1,1,1] [1,2,3,7,4,5,6] => [2,1,1,1,1,1] [1,2,3,7,4,6,5] => [3,1,1,1,1] [1,2,3,7,5,4,6] => [3,1,1,1,1] [1,2,3,7,5,6,4] => [3,1,1,1,1] [1,2,3,7,6,4,5] => [3,1,1,1,1] [1,2,3,7,6,5,4] => [4,1,1,1] [1,2,4,3,5,6,7] => [2,1,1,1,1,1] [1,2,4,3,5,7,6] => [2,2,1,1,1] [1,2,4,3,6,5,7] => [2,2,1,1,1] [1,2,4,3,6,7,5] => [2,2,1,1,1] [1,2,4,3,7,5,6] => [2,2,1,1,1] [1,2,4,3,7,6,5] => [3,2,1,1] [1,2,4,5,3,6,7] => [2,1,1,1,1,1] [1,2,4,5,3,7,6] => [2,2,1,1,1] [1,2,4,5,6,3,7] => [2,1,1,1,1,1] [1,2,4,5,6,7,3] => [2,1,1,1,1,1] [1,2,4,5,7,3,6] => [2,1,1,1,1,1] [1,2,4,5,7,6,3] => [3,1,1,1,1] [1,2,4,6,3,5,7] => [2,1,1,1,1,1] [1,2,4,6,3,7,5] => [2,2,1,1,1] [1,2,4,6,5,3,7] => [3,1,1,1,1] [1,2,4,6,5,7,3] => [3,1,1,1,1] [1,2,4,6,7,3,5] => [2,1,1,1,1,1] [1,2,4,6,7,5,3] => [3,1,1,1,1] [1,2,4,7,3,5,6] => [2,1,1,1,1,1] [1,2,4,7,3,6,5] => [3,1,1,1,1] [1,2,4,7,5,3,6] => [3,1,1,1,1] [1,2,4,7,5,6,3] => [3,1,1,1,1] [1,2,4,7,6,3,5] => [3,1,1,1,1] [1,2,4,7,6,5,3] => [4,1,1,1] [1,2,5,3,4,6,7] => [2,1,1,1,1,1] [1,2,5,3,4,7,6] => [2,2,1,1,1] [1,2,5,3,6,4,7] => [2,2,1,1,1] [1,2,5,3,6,7,4] => [2,2,1,1,1] [1,2,5,3,7,4,6] => [2,2,1,1,1] [1,2,5,3,7,6,4] => [3,2,1,1] [1,2,5,4,3,6,7] => [3,1,1,1,1] [1,2,5,4,3,7,6] => [3,2,1,1] [1,2,5,4,6,3,7] => [3,1,1,1,1] [1,2,5,4,6,7,3] => [3,1,1,1,1] [1,2,5,4,7,3,6] => [3,1,1,1,1] [1,2,5,4,7,6,3] => [3,2,1,1] [1,2,5,6,3,4,7] => [2,1,1,1,1,1] [1,2,5,6,3,7,4] => [2,2,1,1,1] [1,2,5,6,4,3,7] => [3,1,1,1,1] [1,2,5,6,4,7,3] => [3,1,1,1,1] [1,2,5,6,7,3,4] => [2,1,1,1,1,1] [1,2,5,6,7,4,3] => [3,1,1,1,1] [1,2,5,7,3,4,6] => [2,1,1,1,1,1] [1,2,5,7,3,6,4] => [3,1,1,1,1] [1,2,5,7,4,3,6] => [3,1,1,1,1] [1,2,5,7,4,6,3] => [3,1,1,1,1] [1,2,5,7,6,3,4] => [3,1,1,1,1] [1,2,5,7,6,4,3] => [4,1,1,1] [1,2,6,3,4,5,7] => [2,1,1,1,1,1] [1,2,6,3,4,7,5] => [2,2,1,1,1] [1,2,6,3,5,4,7] => [3,1,1,1,1] [1,2,6,3,5,7,4] => [3,1,1,1,1] [1,2,6,3,7,4,5] => [2,2,1,1,1] [1,2,6,3,7,5,4] => [3,2,1,1] [1,2,6,4,3,5,7] => [3,1,1,1,1] [1,2,6,4,3,7,5] => [3,2,1,1] [1,2,6,4,5,3,7] => [3,1,1,1,1] [1,2,6,4,5,7,3] => [3,1,1,1,1] [1,2,6,4,7,3,5] => [3,1,1,1,1] [1,2,6,4,7,5,3] => [3,2,1,1] [1,2,6,5,3,4,7] => [3,1,1,1,1] [1,2,6,5,3,7,4] => [3,2,1,1] [1,2,6,5,4,3,7] => [4,1,1,1] [1,2,6,5,4,7,3] => [4,1,1,1] [1,2,6,5,7,3,4] => [3,1,1,1,1] [1,2,6,5,7,4,3] => [4,1,1,1] [1,2,6,7,3,4,5] => [2,1,1,1,1,1] [1,2,6,7,3,5,4] => [3,1,1,1,1] [1,2,6,7,4,3,5] => [3,1,1,1,1] [1,2,6,7,4,5,3] => [3,1,1,1,1] [1,2,6,7,5,3,4] => [3,1,1,1,1] [1,2,6,7,5,4,3] => [4,1,1,1] [1,2,7,3,4,5,6] => [2,1,1,1,1,1] [1,2,7,3,4,6,5] => [3,1,1,1,1] [1,2,7,3,5,4,6] => [3,1,1,1,1] [1,2,7,3,5,6,4] => [3,1,1,1,1] [1,2,7,3,6,4,5] => [3,1,1,1,1] [1,2,7,3,6,5,4] => [4,1,1,1] [1,2,7,4,3,5,6] => [3,1,1,1,1] [1,2,7,4,3,6,5] => [3,2,1,1] [1,2,7,4,5,3,6] => [3,1,1,1,1] [1,2,7,4,5,6,3] => [3,1,1,1,1] [1,2,7,4,6,3,5] => [3,1,1,1,1] [1,2,7,4,6,5,3] => [4,1,1,1] [1,2,7,5,3,4,6] => [3,1,1,1,1] [1,2,7,5,3,6,4] => [3,2,1,1] [1,2,7,5,4,3,6] => [4,1,1,1] [1,2,7,5,4,6,3] => [4,1,1,1] [1,2,7,5,6,3,4] => [3,1,1,1,1] [1,2,7,5,6,4,3] => [4,1,1,1] [1,2,7,6,3,4,5] => [3,1,1,1,1] [1,2,7,6,3,5,4] => [4,1,1,1] [1,2,7,6,4,3,5] => [4,1,1,1] [1,2,7,6,4,5,3] => [4,1,1,1] [1,2,7,6,5,3,4] => [4,1,1,1] [1,2,7,6,5,4,3] => [5,1,1] [1,3,2,4,5,6,7] => [2,1,1,1,1,1] [1,3,2,4,5,7,6] => [2,2,1,1,1] [1,3,2,4,6,5,7] => [2,2,1,1,1] [1,3,2,4,6,7,5] => [2,2,1,1,1] [1,3,2,4,7,5,6] => [2,2,1,1,1] [1,3,2,4,7,6,5] => [3,2,1,1] [1,3,2,5,4,6,7] => [2,2,1,1,1] [1,3,2,5,4,7,6] => [2,2,2,1] [1,3,2,5,6,4,7] => [2,2,1,1,1] [1,3,2,5,6,7,4] => [2,2,1,1,1] [1,3,2,5,7,4,6] => [2,2,1,1,1] [1,3,2,5,7,6,4] => [3,2,1,1] [1,3,2,6,4,5,7] => [2,2,1,1,1] [1,3,2,6,4,7,5] => [2,2,2,1] [1,3,2,6,5,4,7] => [3,2,1,1] [1,3,2,6,5,7,4] => [3,2,1,1] [1,3,2,6,7,4,5] => [2,2,1,1,1] [1,3,2,6,7,5,4] => [3,2,1,1] [1,3,2,7,4,5,6] => [2,2,1,1,1] [1,3,2,7,4,6,5] => [3,2,1,1] [1,3,2,7,5,4,6] => [3,2,1,1] [1,3,2,7,5,6,4] => [3,2,1,1] [1,3,2,7,6,4,5] => [3,2,1,1] [1,3,2,7,6,5,4] => [4,2,1] [1,3,4,2,5,6,7] => [2,1,1,1,1,1] [1,3,4,2,5,7,6] => [2,2,1,1,1] [1,3,4,2,6,5,7] => [2,2,1,1,1] [1,3,4,2,6,7,5] => [2,2,1,1,1] [1,3,4,2,7,5,6] => [2,2,1,1,1] [1,3,4,2,7,6,5] => [3,2,1,1] [1,3,4,5,2,6,7] => [2,1,1,1,1,1] [1,3,4,5,2,7,6] => [2,2,1,1,1] [1,3,4,5,6,2,7] => [2,1,1,1,1,1] [1,3,4,5,6,7,2] => [2,1,1,1,1,1] [1,3,4,5,7,2,6] => [2,1,1,1,1,1] [1,3,4,5,7,6,2] => [3,1,1,1,1] [1,3,4,6,2,5,7] => [2,1,1,1,1,1] [1,3,4,6,2,7,5] => [2,2,1,1,1] [1,3,4,6,5,2,7] => [3,1,1,1,1] [1,3,4,6,5,7,2] => [3,1,1,1,1] [1,3,4,6,7,2,5] => [2,1,1,1,1,1] [1,3,4,6,7,5,2] => [3,1,1,1,1] [1,3,4,7,2,5,6] => [2,1,1,1,1,1] [1,3,4,7,2,6,5] => [3,1,1,1,1] [1,3,4,7,5,2,6] => [3,1,1,1,1] [1,3,4,7,5,6,2] => [3,1,1,1,1] [1,3,4,7,6,2,5] => [3,1,1,1,1] [1,3,4,7,6,5,2] => [4,1,1,1] [1,3,5,2,4,6,7] => [2,1,1,1,1,1] [1,3,5,2,4,7,6] => [2,2,1,1,1] [1,3,5,2,6,4,7] => [2,2,1,1,1] [1,3,5,2,6,7,4] => [2,2,1,1,1] [1,3,5,2,7,4,6] => [2,2,1,1,1] [1,3,5,2,7,6,4] => [3,2,1,1] [1,3,5,4,2,6,7] => [3,1,1,1,1] [1,3,5,4,2,7,6] => [3,2,1,1] [1,3,5,4,6,2,7] => [3,1,1,1,1] [1,3,5,4,6,7,2] => [3,1,1,1,1] [1,3,5,4,7,2,6] => [3,1,1,1,1] [1,3,5,4,7,6,2] => [3,2,1,1] [1,3,5,6,2,4,7] => [2,1,1,1,1,1] [1,3,5,6,2,7,4] => [2,2,1,1,1] [1,3,5,6,4,2,7] => [3,1,1,1,1] [1,3,5,6,4,7,2] => [3,1,1,1,1] [1,3,5,6,7,2,4] => [2,1,1,1,1,1] [1,3,5,6,7,4,2] => [3,1,1,1,1] [1,3,5,7,2,4,6] => [2,1,1,1,1,1] [1,3,5,7,2,6,4] => [3,1,1,1,1] [1,3,5,7,4,2,6] => [3,1,1,1,1] [1,3,5,7,4,6,2] => [3,1,1,1,1] [1,3,5,7,6,2,4] => [3,1,1,1,1] [1,3,5,7,6,4,2] => [4,1,1,1] [1,3,6,2,4,5,7] => [2,1,1,1,1,1] [1,3,6,2,4,7,5] => [2,2,1,1,1] [1,3,6,2,5,4,7] => [3,1,1,1,1] [1,3,6,2,5,7,4] => [3,1,1,1,1] [1,3,6,2,7,4,5] => [2,2,1,1,1] [1,3,6,2,7,5,4] => [3,2,1,1] [1,3,6,4,2,5,7] => [3,1,1,1,1] [1,3,6,4,2,7,5] => [3,2,1,1] [1,3,6,4,5,2,7] => [3,1,1,1,1] [1,3,6,4,5,7,2] => [3,1,1,1,1] [1,3,6,4,7,2,5] => [3,1,1,1,1] [1,3,6,4,7,5,2] => [3,2,1,1] [1,3,6,5,2,4,7] => [3,1,1,1,1] [1,3,6,5,2,7,4] => [3,2,1,1] [1,3,6,5,4,2,7] => [4,1,1,1] [1,3,6,5,4,7,2] => [4,1,1,1] [1,3,6,5,7,2,4] => [3,1,1,1,1] [1,3,6,5,7,4,2] => [4,1,1,1] [1,3,6,7,2,4,5] => [2,1,1,1,1,1] [1,3,6,7,2,5,4] => [3,1,1,1,1] [1,3,6,7,4,2,5] => [3,1,1,1,1] [1,3,6,7,4,5,2] => [3,1,1,1,1] [1,3,6,7,5,2,4] => [3,1,1,1,1] [1,3,6,7,5,4,2] => [4,1,1,1] [1,3,7,2,4,5,6] => [2,1,1,1,1,1] [1,3,7,2,4,6,5] => [3,1,1,1,1] [1,3,7,2,5,4,6] => [3,1,1,1,1] [1,3,7,2,5,6,4] => [3,1,1,1,1] [1,3,7,2,6,4,5] => [3,1,1,1,1] [1,3,7,2,6,5,4] => [4,1,1,1] [1,3,7,4,2,5,6] => [3,1,1,1,1] [1,3,7,4,2,6,5] => [3,2,1,1] [1,3,7,4,5,2,6] => [3,1,1,1,1] [1,3,7,4,5,6,2] => [3,1,1,1,1] [1,3,7,4,6,2,5] => [3,1,1,1,1] [1,3,7,4,6,5,2] => [4,1,1,1] [1,3,7,5,2,4,6] => [3,1,1,1,1] [1,3,7,5,2,6,4] => [3,2,1,1] [1,3,7,5,4,2,6] => [4,1,1,1] [1,3,7,5,4,6,2] => [4,1,1,1] [1,3,7,5,6,2,4] => [3,1,1,1,1] [1,3,7,5,6,4,2] => [4,1,1,1] [1,3,7,6,2,4,5] => [3,1,1,1,1] [1,3,7,6,2,5,4] => [4,1,1,1] [1,3,7,6,4,2,5] => [4,1,1,1] [1,3,7,6,4,5,2] => [4,1,1,1] [1,3,7,6,5,2,4] => [4,1,1,1] [1,3,7,6,5,4,2] => [5,1,1] [1,4,2,3,5,6,7] => [2,1,1,1,1,1] [1,4,2,3,5,7,6] => [2,2,1,1,1] [1,4,2,3,6,5,7] => [2,2,1,1,1] [1,4,2,3,6,7,5] => [2,2,1,1,1] [1,4,2,3,7,5,6] => [2,2,1,1,1] [1,4,2,3,7,6,5] => [3,2,1,1] [1,4,2,5,3,6,7] => [2,2,1,1,1] [1,4,2,5,3,7,6] => [2,2,2,1] [1,4,2,5,6,3,7] => [2,2,1,1,1] [1,4,2,5,6,7,3] => [2,2,1,1,1] [1,4,2,5,7,3,6] => [2,2,1,1,1] [1,4,2,5,7,6,3] => [3,2,1,1] [1,4,2,6,3,5,7] => [2,2,1,1,1] [1,4,2,6,3,7,5] => [2,2,2,1] [1,4,2,6,5,3,7] => [3,2,1,1] [1,4,2,6,5,7,3] => [3,2,1,1] [1,4,2,6,7,3,5] => [2,2,1,1,1] [1,4,2,6,7,5,3] => [3,2,1,1] [1,4,2,7,3,5,6] => [2,2,1,1,1] [1,4,2,7,3,6,5] => [3,2,1,1] [1,4,2,7,5,3,6] => [3,2,1,1] [1,4,2,7,5,6,3] => [3,2,1,1] [1,4,2,7,6,3,5] => [3,2,1,1] [1,4,2,7,6,5,3] => [4,2,1] [1,4,3,2,5,6,7] => [3,1,1,1,1] [1,4,3,2,5,7,6] => [3,2,1,1] [1,4,3,2,6,5,7] => [3,2,1,1] [1,4,3,2,6,7,5] => [3,2,1,1] [1,4,3,2,7,5,6] => [3,2,1,1] [1,4,3,2,7,6,5] => [3,3,1] [1,4,3,5,2,6,7] => [3,1,1,1,1] [1,4,3,5,2,7,6] => [3,2,1,1] [1,4,3,5,6,2,7] => [3,1,1,1,1] [1,4,3,5,6,7,2] => [3,1,1,1,1] [1,4,3,5,7,2,6] => [3,1,1,1,1] [1,4,3,5,7,6,2] => [3,2,1,1] [1,4,3,6,2,5,7] => [3,1,1,1,1] [1,4,3,6,2,7,5] => [3,2,1,1] [1,4,3,6,5,2,7] => [3,2,1,1] [1,4,3,6,5,7,2] => [3,2,1,1] [1,4,3,6,7,2,5] => [3,1,1,1,1] [1,4,3,6,7,5,2] => [3,2,1,1] [1,4,3,7,2,5,6] => [3,1,1,1,1] [1,4,3,7,2,6,5] => [3,2,1,1] [1,4,3,7,5,2,6] => [3,2,1,1] [1,4,3,7,5,6,2] => [3,2,1,1] [1,4,3,7,6,2,5] => [3,2,1,1] [1,4,3,7,6,5,2] => [4,2,1] [1,4,5,2,3,6,7] => [2,1,1,1,1,1] [1,4,5,2,3,7,6] => [2,2,1,1,1] [1,4,5,2,6,3,7] => [2,2,1,1,1] [1,4,5,2,6,7,3] => [2,2,1,1,1] [1,4,5,2,7,3,6] => [2,2,1,1,1] [1,4,5,2,7,6,3] => [3,2,1,1] [1,4,5,3,2,6,7] => [3,1,1,1,1] [1,4,5,3,2,7,6] => [3,2,1,1] [1,4,5,3,6,2,7] => [3,1,1,1,1] [1,4,5,3,6,7,2] => [3,1,1,1,1] [1,4,5,3,7,2,6] => [3,1,1,1,1] [1,4,5,3,7,6,2] => [3,2,1,1] [1,4,5,6,2,3,7] => [2,1,1,1,1,1] [1,4,5,6,2,7,3] => [2,2,1,1,1] [1,4,5,6,3,2,7] => [3,1,1,1,1] [1,4,5,6,3,7,2] => [3,1,1,1,1] [1,4,5,6,7,2,3] => [2,1,1,1,1,1] [1,4,5,6,7,3,2] => [3,1,1,1,1] [1,4,5,7,2,3,6] => [2,1,1,1,1,1] [1,4,5,7,2,6,3] => [3,1,1,1,1] [1,4,5,7,3,2,6] => [3,1,1,1,1] [1,4,5,7,3,6,2] => [3,1,1,1,1] [1,4,5,7,6,2,3] => [3,1,1,1,1] [1,4,5,7,6,3,2] => [4,1,1,1] [1,4,6,2,3,5,7] => [2,1,1,1,1,1] [1,4,6,2,3,7,5] => [2,2,1,1,1] [1,4,6,2,5,3,7] => [3,1,1,1,1] [1,4,6,2,5,7,3] => [3,1,1,1,1] [1,4,6,2,7,3,5] => [2,2,1,1,1] [1,4,6,2,7,5,3] => [3,2,1,1] [1,4,6,3,2,5,7] => [3,1,1,1,1] [1,4,6,3,2,7,5] => [3,2,1,1] [1,4,6,3,5,2,7] => [3,1,1,1,1] [1,4,6,3,5,7,2] => [3,1,1,1,1] [1,4,6,3,7,2,5] => [3,1,1,1,1] [1,4,6,3,7,5,2] => [3,2,1,1] [1,4,6,5,2,3,7] => [3,1,1,1,1] [1,4,6,5,2,7,3] => [3,2,1,1] [1,4,6,5,3,2,7] => [4,1,1,1] ----------------------------------------------------------------------------- Created: Jan 28, 2021 at 12:18 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 01, 2021 at 12:27 by Martin Rubey