*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000401
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The size of the symmetry class of a permutation.
The symmetry class of a permutation $\pi$ is the set of all permutations that can be obtained from $\pi$ by the three elementary operations '''inverse''' ([[Mp00066]]), '''reverse''' ([[Mp00064]]), and '''complement''' ([[Mp00069]]).
Two elements in the same symmetry class are also in the same Wilf-equivalence class, see for example [2].
-----------------------------------------------------------------------------
References: [1] Callan, D., Mansour, T. Five subsets of permutations enumerated as weak sorting permutations [[arXiv:1602.05182]]
[2] Stankova-Frenkel, Z., West, J. A New Class of Wilf-Equivalent Permutations [[arXiv:math/0103152]]
-----------------------------------------------------------------------------
Code:
def eq_class(pi):
cl = [pi]
test = [pi]
while test:
tau = test.pop()
tau1 = tau.reverse()
tau2 = tau.complement()
tau3 = tau.inverse()
if tau1 not in cl:
cl.append(tau1)
test.append(tau1)
if tau2 not in cl:
cl.append(tau2)
test.append(tau2)
if tau3 not in cl:
cl.append(tau3)
test.append(tau3)
return cl
def statistic(pi):
return len(eq_class(pi))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[1,2] => 2
[2,1] => 2
[1,2,3] => 2
[1,3,2] => 4
[2,1,3] => 4
[2,3,1] => 4
[3,1,2] => 4
[3,2,1] => 2
[1,2,3,4] => 2
[1,2,4,3] => 4
[1,3,2,4] => 2
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 4
[2,1,3,4] => 4
[2,1,4,3] => 2
[2,3,1,4] => 8
[2,3,4,1] => 4
[2,4,1,3] => 2
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 2
[3,2,1,4] => 4
[3,2,4,1] => 8
[3,4,1,2] => 2
[3,4,2,1] => 4
[4,1,2,3] => 4
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 2
[4,3,1,2] => 4
[4,3,2,1] => 2
[1,2,3,4,5] => 2
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 8
[1,2,5,3,4] => 8
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 8
[1,3,5,2,4] => 8
[1,3,5,4,2] => 8
[1,4,2,3,5] => 4
[1,4,2,5,3] => 8
[1,4,3,2,5] => 2
[1,4,3,5,2] => 8
[1,4,5,2,3] => 4
[1,4,5,3,2] => 8
[1,5,2,3,4] => 8
[1,5,2,4,3] => 8
[1,5,3,2,4] => 8
[1,5,3,4,2] => 4
[1,5,4,2,3] => 8
[1,5,4,3,2] => 4
[2,1,3,4,5] => 4
[2,1,3,5,4] => 2
[2,1,4,3,5] => 4
[2,1,4,5,3] => 8
[2,1,5,3,4] => 8
[2,1,5,4,3] => 4
[2,3,1,4,5] => 8
[2,3,1,5,4] => 8
[2,3,4,1,5] => 8
[2,3,4,5,1] => 4
[2,3,5,1,4] => 8
[2,3,5,4,1] => 8
[2,4,1,3,5] => 8
[2,4,1,5,3] => 4
[2,4,3,1,5] => 8
[2,4,3,5,1] => 4
[2,4,5,1,3] => 8
[2,4,5,3,1] => 8
[2,5,1,3,4] => 8
[2,5,1,4,3] => 8
[2,5,3,1,4] => 2
[2,5,3,4,1] => 8
[2,5,4,1,3] => 8
[2,5,4,3,1] => 8
[3,1,2,4,5] => 8
[3,1,2,5,4] => 8
[3,1,4,2,5] => 8
[3,1,4,5,2] => 8
[3,1,5,2,4] => 4
[3,1,5,4,2] => 8
[3,2,1,4,5] => 4
[3,2,1,5,4] => 4
[3,2,4,1,5] => 8
[3,2,4,5,1] => 8
[3,2,5,1,4] => 8
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 8
[3,4,2,1,5] => 8
[3,4,2,5,1] => 8
[3,4,5,1,2] => 4
[3,4,5,2,1] => 4
[3,5,1,2,4] => 8
[3,5,1,4,2] => 4
[3,5,2,1,4] => 8
[3,5,2,4,1] => 8
[3,5,4,1,2] => 8
[3,5,4,2,1] => 8
[4,1,2,3,5] => 8
[4,1,2,5,3] => 8
[4,1,3,2,5] => 8
[4,1,3,5,2] => 2
[4,1,5,2,3] => 8
[4,1,5,3,2] => 8
[4,2,1,3,5] => 8
[4,2,1,5,3] => 8
[4,2,3,1,5] => 4
[4,2,3,5,1] => 8
[4,2,5,1,3] => 4
[4,2,5,3,1] => 8
[4,3,1,2,5] => 8
[4,3,1,5,2] => 8
[4,3,2,1,5] => 4
[4,3,2,5,1] => 8
[4,3,5,1,2] => 8
[4,3,5,2,1] => 8
[4,5,1,2,3] => 4
[4,5,1,3,2] => 8
[4,5,2,1,3] => 8
[4,5,2,3,1] => 4
[4,5,3,1,2] => 2
[4,5,3,2,1] => 4
[5,1,2,3,4] => 4
[5,1,2,4,3] => 8
[5,1,3,2,4] => 4
[5,1,3,4,2] => 8
[5,1,4,2,3] => 8
[5,1,4,3,2] => 8
[5,2,1,3,4] => 8
[5,2,1,4,3] => 4
[5,2,3,1,4] => 8
[5,2,3,4,1] => 2
[5,2,4,1,3] => 8
[5,2,4,3,1] => 4
[5,3,1,2,4] => 8
[5,3,1,4,2] => 8
[5,3,2,1,4] => 8
[5,3,2,4,1] => 4
[5,3,4,1,2] => 4
[5,3,4,2,1] => 4
[5,4,1,2,3] => 4
[5,4,1,3,2] => 8
[5,4,2,1,3] => 8
[5,4,2,3,1] => 4
[5,4,3,1,2] => 4
[5,4,3,2,1] => 2
[1,2,3,4,5,6] => 2
[1,2,3,4,6,5] => 4
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 8
[1,2,3,6,4,5] => 8
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 2
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 8
[1,2,4,5,6,3] => 8
[1,2,4,6,3,5] => 8
[1,2,4,6,5,3] => 8
[1,2,5,3,4,6] => 8
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 4
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 8
[1,2,6,3,4,5] => 8
[1,2,6,3,5,4] => 8
[1,2,6,4,3,5] => 8
[1,2,6,4,5,3] => 4
[1,2,6,5,3,4] => 8
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 4
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 8
[1,3,2,6,4,5] => 8
[1,3,2,6,5,4] => 4
[1,3,4,2,5,6] => 8
[1,3,4,2,6,5] => 8
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 8
[1,3,4,6,2,5] => 8
[1,3,4,6,5,2] => 8
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 8
[1,3,5,4,2,6] => 8
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 8
[1,3,5,6,4,2] => 8
[1,3,6,2,4,5] => 8
[1,3,6,2,5,4] => 8
[1,3,6,4,2,5] => 8
[1,3,6,4,5,2] => 8
[1,3,6,5,2,4] => 8
[1,3,6,5,4,2] => 8
[1,4,2,3,5,6] => 8
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 4
[1,4,2,5,6,3] => 8
[1,4,2,6,3,5] => 8
[1,4,2,6,5,3] => 8
[1,4,3,2,5,6] => 4
[1,4,3,2,6,5] => 4
[1,4,3,5,2,6] => 8
[1,4,3,5,6,2] => 8
[1,4,3,6,2,5] => 8
[1,4,3,6,5,2] => 8
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 8
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 8
[1,4,5,6,2,3] => 8
[1,4,5,6,3,2] => 8
[1,4,6,2,3,5] => 8
[1,4,6,2,5,3] => 4
[1,4,6,3,2,5] => 8
[1,4,6,3,5,2] => 8
[1,4,6,5,2,3] => 8
[1,4,6,5,3,2] => 8
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 8
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 8
[1,5,2,6,4,3] => 8
[1,5,3,2,4,6] => 8
[1,5,3,2,6,4] => 8
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 4
[1,5,3,6,4,2] => 8
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 8
[1,5,4,3,2,6] => 2
[1,5,4,3,6,2] => 8
[1,5,4,6,2,3] => 8
[1,5,4,6,3,2] => 8
[1,5,6,2,3,4] => 8
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 8
[1,5,6,3,4,2] => 8
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 8
[1,6,2,3,4,5] => 8
[1,6,2,3,5,4] => 8
[1,6,2,4,3,5] => 8
[1,6,2,4,5,3] => 8
[1,6,2,5,3,4] => 8
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 8
[1,6,3,2,5,4] => 8
[1,6,3,4,2,5] => 8
[1,6,3,4,5,2] => 4
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 8
[1,6,4,2,5,3] => 8
[1,6,4,3,2,5] => 8
[1,6,4,3,5,2] => 4
[1,6,4,5,2,3] => 8
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 8
[1,6,5,2,4,3] => 8
[1,6,5,3,2,4] => 8
[1,6,5,3,4,2] => 8
[1,6,5,4,2,3] => 8
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 4
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 8
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 2
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 8
[2,1,4,6,3,5] => 8
[2,1,4,6,5,3] => 8
[2,1,5,3,4,6] => 8
[2,1,5,3,6,4] => 8
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 4
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 8
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 8
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 8
[2,3,1,4,6,5] => 8
[2,3,1,5,4,6] => 8
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 8
[2,3,4,1,5,6] => 8
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 8
[2,3,4,5,6,1] => 4
[2,3,4,6,1,5] => 8
[2,3,4,6,5,1] => 8
[2,3,5,1,4,6] => 8
[2,3,5,1,6,4] => 8
[2,3,5,4,1,6] => 8
[2,3,5,4,6,1] => 8
[2,3,5,6,1,4] => 8
[2,3,5,6,4,1] => 8
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 8
[2,3,6,4,1,5] => 8
[2,3,6,4,5,1] => 8
[2,3,6,5,1,4] => 8
[2,3,6,5,4,1] => 8
[2,4,1,3,5,6] => 8
[2,4,1,3,6,5] => 8
[2,4,1,5,3,6] => 8
[2,4,1,5,6,3] => 8
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 8
[2,4,3,1,5,6] => 8
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 8
[2,4,3,5,6,1] => 8
[2,4,3,6,1,5] => 8
[2,4,3,6,5,1] => 8
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 4
[2,4,5,3,1,6] => 8
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 8
[2,4,5,6,3,1] => 8
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 8
[2,4,6,3,1,5] => 8
[2,4,6,3,5,1] => 8
[2,4,6,5,1,3] => 8
[2,4,6,5,3,1] => 8
[2,5,1,3,4,6] => 8
[2,5,1,3,6,4] => 4
[2,5,1,4,3,6] => 8
[2,5,1,4,6,3] => 8
[2,5,1,6,3,4] => 8
[2,5,1,6,4,3] => 8
[2,5,3,1,4,6] => 8
[2,5,3,1,6,4] => 8
[2,5,3,4,1,6] => 8
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 8
[2,5,3,6,4,1] => 8
[2,5,4,1,3,6] => 8
[2,5,4,1,6,3] => 4
[2,5,4,3,1,6] => 8
[2,5,4,3,6,1] => 4
[2,5,4,6,1,3] => 8
[2,5,4,6,3,1] => 8
[2,5,6,1,3,4] => 8
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 8
[2,5,6,3,4,1] => 8
[2,5,6,4,1,3] => 8
[2,5,6,4,3,1] => 8
[2,6,1,3,4,5] => 8
[2,6,1,3,5,4] => 8
[2,6,1,4,3,5] => 8
[2,6,1,4,5,3] => 8
[2,6,1,5,3,4] => 8
[2,6,1,5,4,3] => 8
[2,6,3,1,4,5] => 8
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 8
[2,6,3,5,1,4] => 8
[2,6,3,5,4,1] => 8
[2,6,4,1,3,5] => 8
[2,6,4,1,5,3] => 8
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 8
[2,6,4,5,1,3] => 8
[2,6,4,5,3,1] => 8
[2,6,5,1,3,4] => 8
[2,6,5,1,4,3] => 8
[2,6,5,3,1,4] => 8
[2,6,5,3,4,1] => 8
[2,6,5,4,1,3] => 8
[2,6,5,4,3,1] => 8
[3,1,2,4,5,6] => 8
[3,1,2,4,6,5] => 8
[3,1,2,5,4,6] => 8
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 8
[3,1,4,2,5,6] => 8
[3,1,4,2,6,5] => 8
[3,1,4,5,2,6] => 8
[3,1,4,5,6,2] => 8
[3,1,4,6,2,5] => 4
[3,1,4,6,5,2] => 8
[3,1,5,2,4,6] => 8
[3,1,5,2,6,4] => 4
[3,1,5,4,2,6] => 8
[3,1,5,4,6,2] => 8
[3,1,5,6,2,4] => 8
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 8
[3,1,6,2,5,4] => 8
[3,1,6,4,2,5] => 8
[3,1,6,4,5,2] => 8
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 8
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 4
[3,2,1,5,4,6] => 4
[3,2,1,5,6,4] => 8
[3,2,1,6,4,5] => 8
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 8
[3,2,4,1,6,5] => 8
[3,2,4,5,1,6] => 8
[3,2,4,5,6,1] => 8
[3,2,4,6,1,5] => 8
[3,2,4,6,5,1] => 4
[3,2,5,1,4,6] => 8
[3,2,5,1,6,4] => 8
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 8
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 8
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 8
[3,2,6,5,1,4] => 8
[3,2,6,5,4,1] => 8
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 4
[3,4,1,5,2,6] => 8
[3,4,1,5,6,2] => 8
[3,4,1,6,2,5] => 8
[3,4,1,6,5,2] => 8
[3,4,2,1,5,6] => 8
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 8
[3,4,2,5,6,1] => 8
[3,4,2,6,1,5] => 8
[3,4,2,6,5,1] => 8
[3,4,5,1,2,6] => 8
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 8
[3,4,5,2,6,1] => 8
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 4
[3,4,6,1,2,5] => 8
[3,4,6,1,5,2] => 8
[3,4,6,2,1,5] => 8
[3,4,6,2,5,1] => 8
[3,4,6,5,1,2] => 8
[3,4,6,5,2,1] => 8
[3,5,1,2,4,6] => 8
[3,5,1,2,6,4] => 8
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 8
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 8
[3,5,2,1,4,6] => 8
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 8
[3,5,2,4,6,1] => 8
[3,5,2,6,1,4] => 8
[3,5,2,6,4,1] => 4
[3,5,4,1,2,6] => 8
[3,5,4,1,6,2] => 8
[3,5,4,2,1,6] => 8
[3,5,4,2,6,1] => 8
[3,5,4,6,1,2] => 4
[3,5,4,6,2,1] => 4
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 8
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 8
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 8
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 8
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 8
[3,6,2,1,5,4] => 8
[3,6,2,4,1,5] => 8
[3,6,2,4,5,1] => 8
[3,6,2,5,1,4] => 4
[3,6,2,5,4,1] => 8
[3,6,4,1,2,5] => 8
[3,6,4,1,5,2] => 8
[3,6,4,2,1,5] => 8
[3,6,4,2,5,1] => 8
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 8
[3,6,5,1,2,4] => 8
[3,6,5,1,4,2] => 8
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 8
[3,6,5,4,2,1] => 8
[4,1,2,3,5,6] => 8
[4,1,2,3,6,5] => 8
[4,1,2,5,3,6] => 8
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 8
[4,1,2,6,5,3] => 8
[4,1,3,2,5,6] => 8
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 8
[4,1,3,5,6,2] => 8
[4,1,3,6,2,5] => 8
[4,1,3,6,5,2] => 8
[4,1,5,2,3,6] => 8
[4,1,5,2,6,3] => 4
[4,1,5,3,2,6] => 8
[4,1,5,3,6,2] => 8
[4,1,5,6,2,3] => 8
[4,1,5,6,3,2] => 8
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 8
[4,1,6,3,2,5] => 4
[4,1,6,3,5,2] => 8
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 8
[4,2,1,3,5,6] => 8
[4,2,1,3,6,5] => 8
[4,2,1,5,3,6] => 8
[4,2,1,5,6,3] => 8
[4,2,1,6,3,5] => 8
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 4
[4,2,3,5,1,6] => 8
[4,2,3,5,6,1] => 8
[4,2,3,6,1,5] => 8
[4,2,3,6,5,1] => 8
[4,2,5,1,3,6] => 4
[4,2,5,1,6,3] => 8
[4,2,5,3,1,6] => 8
[4,2,5,3,6,1] => 8
[4,2,5,6,1,3] => 8
[4,2,5,6,3,1] => 8
[4,2,6,1,3,5] => 8
[4,2,6,1,5,3] => 2
[4,2,6,3,1,5] => 8
[4,2,6,3,5,1] => 4
[4,2,6,5,1,3] => 8
[4,2,6,5,3,1] => 8
[4,3,1,2,5,6] => 8
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 8
[4,3,1,5,6,2] => 8
[4,3,1,6,2,5] => 8
[4,3,1,6,5,2] => 8
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 8
[4,3,2,5,6,1] => 8
[4,3,2,6,1,5] => 8
[4,3,2,6,5,1] => 8
[4,3,5,1,2,6] => 8
[4,3,5,1,6,2] => 8
[4,3,5,2,1,6] => 8
[4,3,5,2,6,1] => 8
[4,3,5,6,1,2] => 8
[4,3,5,6,2,1] => 8
[4,3,6,1,2,5] => 8
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 8
[4,3,6,5,1,2] => 4
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 8
[4,5,1,2,6,3] => 8
[4,5,1,3,2,6] => 8
[4,5,1,3,6,2] => 8
[4,5,1,6,2,3] => 4
[4,5,1,6,3,2] => 8
[4,5,2,1,3,6] => 8
[4,5,2,1,6,3] => 8
[4,5,2,3,1,6] => 8
[4,5,2,3,6,1] => 8
[4,5,2,6,1,3] => 8
[4,5,2,6,3,1] => 8
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 8
[4,5,3,2,1,6] => 8
[4,5,3,2,6,1] => 8
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 8
[4,5,6,1,2,3] => 2
[4,5,6,1,3,2] => 8
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 4
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 8
[4,6,1,2,5,3] => 8
[4,6,1,3,2,5] => 8
[4,6,1,3,5,2] => 8
[4,6,1,5,2,3] => 8
[4,6,1,5,3,2] => 8
[4,6,2,1,3,5] => 8
[4,6,2,1,5,3] => 8
[4,6,2,3,1,5] => 8
[4,6,2,3,5,1] => 8
[4,6,2,5,1,3] => 4
[4,6,2,5,3,1] => 8
[4,6,3,1,2,5] => 8
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 8
[4,6,3,2,5,1] => 8
[4,6,3,5,1,2] => 8
[4,6,3,5,2,1] => 8
[4,6,5,1,2,3] => 8
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 4
[4,6,5,2,3,1] => 8
[4,6,5,3,1,2] => 8
[4,6,5,3,2,1] => 8
[5,1,2,3,4,6] => 8
[5,1,2,3,6,4] => 8
[5,1,2,4,3,6] => 8
[5,1,2,4,6,3] => 8
[5,1,2,6,3,4] => 8
[5,1,2,6,4,3] => 8
[5,1,3,2,4,6] => 8
[5,1,3,2,6,4] => 8
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 8
[5,1,3,6,4,2] => 8
[5,1,4,2,3,6] => 8
[5,1,4,2,6,3] => 8
[5,1,4,3,2,6] => 8
[5,1,4,3,6,2] => 4
[5,1,4,6,2,3] => 8
[5,1,4,6,3,2] => 8
[5,1,6,2,3,4] => 8
[5,1,6,2,4,3] => 8
[5,1,6,3,2,4] => 8
[5,1,6,3,4,2] => 8
[5,1,6,4,2,3] => 8
[5,1,6,4,3,2] => 8
[5,2,1,3,4,6] => 8
[5,2,1,3,6,4] => 8
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 8
[5,2,1,6,3,4] => 8
[5,2,1,6,4,3] => 8
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 8
[5,2,3,4,1,6] => 4
[5,2,3,4,6,1] => 8
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 8
[5,2,4,1,3,6] => 8
[5,2,4,1,6,3] => 8
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 8
[5,2,4,6,1,3] => 8
[5,2,4,6,3,1] => 8
[5,2,6,1,3,4] => 8
[5,2,6,1,4,3] => 8
[5,2,6,3,1,4] => 8
[5,2,6,3,4,1] => 8
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 8
[5,3,1,2,4,6] => 8
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 8
[5,3,1,4,6,2] => 8
[5,3,1,6,2,4] => 8
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 8
[5,3,2,1,6,4] => 8
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 8
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 8
[5,3,4,1,2,6] => 8
[5,3,4,1,6,2] => 8
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 8
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 8
[5,3,6,1,2,4] => 8
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 8
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 8
[5,4,1,2,3,6] => 8
[5,4,1,2,6,3] => 8
[5,4,1,3,2,6] => 8
[5,4,1,3,6,2] => 8
[5,4,1,6,2,3] => 8
[5,4,1,6,3,2] => 4
[5,4,2,1,3,6] => 8
[5,4,2,1,6,3] => 8
[5,4,2,3,1,6] => 8
[5,4,2,3,6,1] => 8
[5,4,2,6,1,3] => 8
[5,4,2,6,3,1] => 8
[5,4,3,1,2,6] => 8
[5,4,3,1,6,2] => 8
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 8
[5,4,3,6,1,2] => 8
[5,4,3,6,2,1] => 8
[5,4,6,1,2,3] => 8
[5,4,6,1,3,2] => 4
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 8
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 8
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 8
[5,6,1,3,2,4] => 4
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 8
[5,6,1,4,3,2] => 8
[5,6,2,1,3,4] => 8
[5,6,2,1,4,3] => 4
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 4
[5,6,2,4,1,3] => 8
[5,6,2,4,3,1] => 8
[5,6,3,1,2,4] => 8
[5,6,3,1,4,2] => 8
[5,6,3,2,1,4] => 8
[5,6,3,2,4,1] => 8
[5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 4
[5,6,4,1,3,2] => 8
[5,6,4,2,1,3] => 8
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 4
[6,1,2,3,4,5] => 4
[6,1,2,3,5,4] => 8
[6,1,2,4,3,5] => 8
[6,1,2,4,5,3] => 8
[6,1,2,5,3,4] => 8
[6,1,2,5,4,3] => 8
[6,1,3,2,4,5] => 8
[6,1,3,2,5,4] => 8
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 8
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 8
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 8
[6,1,4,3,2,5] => 4
[6,1,4,3,5,2] => 8
[6,1,4,5,2,3] => 8
[6,1,4,5,3,2] => 8
[6,1,5,2,3,4] => 8
[6,1,5,2,4,3] => 8
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 8
[6,1,5,4,2,3] => 8
[6,1,5,4,3,2] => 8
[6,2,1,3,4,5] => 8
[6,2,1,3,5,4] => 4
[6,2,1,4,3,5] => 8
[6,2,1,4,5,3] => 8
[6,2,1,5,3,4] => 8
[6,2,1,5,4,3] => 8
[6,2,3,1,4,5] => 8
[6,2,3,1,5,4] => 8
[6,2,3,4,1,5] => 8
[6,2,3,4,5,1] => 2
[6,2,3,5,1,4] => 8
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 8
[6,2,4,1,5,3] => 4
[6,2,4,3,1,5] => 8
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 8
[6,2,4,5,3,1] => 8
[6,2,5,1,3,4] => 8
[6,2,5,1,4,3] => 8
[6,2,5,3,1,4] => 8
[6,2,5,3,4,1] => 8
[6,2,5,4,1,3] => 8
[6,2,5,4,3,1] => 4
[6,3,1,2,4,5] => 8
[6,3,1,2,5,4] => 8
[6,3,1,4,2,5] => 8
[6,3,1,4,5,2] => 8
[6,3,1,5,2,4] => 4
[6,3,1,5,4,2] => 8
[6,3,2,1,4,5] => 8
[6,3,2,1,5,4] => 8
[6,3,2,4,1,5] => 8
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 8
[6,3,2,5,4,1] => 2
[6,3,4,1,2,5] => 8
[6,3,4,1,5,2] => 8
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 4
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 8
[6,3,5,1,4,2] => 8
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 8
[6,3,5,4,2,1] => 8
[6,4,1,2,3,5] => 8
[6,4,1,2,5,3] => 8
[6,4,1,3,2,5] => 8
[6,4,1,3,5,2] => 8
[6,4,1,5,2,3] => 8
[6,4,1,5,3,2] => 8
[6,4,2,1,3,5] => 8
[6,4,2,1,5,3] => 8
[6,4,2,3,1,5] => 8
[6,4,2,3,5,1] => 8
[6,4,2,5,1,3] => 8
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 8
[6,4,3,1,5,2] => 8
[6,4,3,2,1,5] => 8
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 8
[6,4,3,5,2,1] => 8
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 8
[6,4,5,2,1,3] => 8
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 4
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 4
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 8
[6,5,1,4,3,2] => 8
[6,5,2,1,3,4] => 8
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 8
[6,5,2,4,3,1] => 8
[6,5,3,1,2,4] => 8
[6,5,3,1,4,2] => 8
[6,5,3,2,1,4] => 8
[6,5,3,2,4,1] => 8
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 4
[6,5,4,1,3,2] => 8
[6,5,4,2,1,3] => 8
[6,5,4,2,3,1] => 4
[6,5,4,3,1,2] => 4
[6,5,4,3,2,1] => 2
[1,2,3,4,5,6,7] => 2
[1,2,3,4,5,7,6] => 4
[1,2,3,4,6,5,7] => 4
[1,2,3,4,6,7,5] => 8
[1,2,3,4,7,5,6] => 8
[1,2,3,4,7,6,5] => 4
[1,2,3,5,4,6,7] => 4
[1,2,3,5,4,7,6] => 4
[1,2,3,5,6,4,7] => 8
[1,2,3,5,6,7,4] => 8
[1,2,3,5,7,4,6] => 8
[1,2,3,5,7,6,4] => 8
[1,2,3,6,4,5,7] => 8
[1,2,3,6,4,7,5] => 8
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 8
[1,2,3,6,7,4,5] => 4
[1,2,3,6,7,5,4] => 8
[1,2,3,7,4,5,6] => 8
[1,2,3,7,4,6,5] => 8
[1,2,3,7,5,4,6] => 8
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 8
[1,2,3,7,6,5,4] => 4
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 4
[1,2,4,3,6,5,7] => 4
[1,2,4,3,6,7,5] => 8
[1,2,4,3,7,5,6] => 8
[1,2,4,3,7,6,5] => 4
[1,2,4,5,3,6,7] => 4
[1,2,4,5,3,7,6] => 8
[1,2,4,5,6,3,7] => 8
[1,2,4,5,6,7,3] => 8
[1,2,4,5,7,3,6] => 8
[1,2,4,5,7,6,3] => 8
[1,2,4,6,3,5,7] => 8
[1,2,4,6,3,7,5] => 8
[1,2,4,6,5,3,7] => 8
[1,2,4,6,5,7,3] => 8
[1,2,4,6,7,3,5] => 8
[1,2,4,6,7,5,3] => 8
[1,2,4,7,3,5,6] => 8
[1,2,4,7,3,6,5] => 8
[1,2,4,7,5,3,6] => 8
[1,2,4,7,5,6,3] => 8
[1,2,4,7,6,3,5] => 8
[1,2,4,7,6,5,3] => 8
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 8
[1,2,5,3,6,4,7] => 8
[1,2,5,3,6,7,4] => 8
[1,2,5,3,7,4,6] => 8
[1,2,5,3,7,6,4] => 8
[1,2,5,4,3,6,7] => 2
[1,2,5,4,3,7,6] => 4
[1,2,5,4,6,3,7] => 8
[1,2,5,4,6,7,3] => 8
[1,2,5,4,7,3,6] => 8
[1,2,5,4,7,6,3] => 8
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 8
[1,2,5,6,4,3,7] => 8
[1,2,5,6,4,7,3] => 8
[1,2,5,6,7,3,4] => 8
[1,2,5,6,7,4,3] => 8
[1,2,5,7,3,4,6] => 8
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 8
[1,2,5,7,4,6,3] => 8
[1,2,5,7,6,3,4] => 8
[1,2,5,7,6,4,3] => 8
[1,2,6,3,4,5,7] => 8
[1,2,6,3,4,7,5] => 8
[1,2,6,3,5,4,7] => 8
[1,2,6,3,5,7,4] => 8
[1,2,6,3,7,4,5] => 8
[1,2,6,3,7,5,4] => 8
[1,2,6,4,3,5,7] => 8
[1,2,6,4,3,7,5] => 8
[1,2,6,4,5,3,7] => 4
[1,2,6,4,5,7,3] => 8
[1,2,6,4,7,3,5] => 4
[1,2,6,4,7,5,3] => 8
[1,2,6,5,3,4,7] => 8
[1,2,6,5,3,7,4] => 8
[1,2,6,5,4,3,7] => 4
[1,2,6,5,4,7,3] => 8
[1,2,6,5,7,3,4] => 8
[1,2,6,5,7,4,3] => 8
[1,2,6,7,3,4,5] => 8
[1,2,6,7,3,5,4] => 8
[1,2,6,7,4,3,5] => 8
[1,2,6,7,4,5,3] => 8
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 8
[1,2,7,3,4,5,6] => 8
[1,2,7,3,4,6,5] => 8
[1,2,7,3,5,4,6] => 8
[1,2,7,3,5,6,4] => 8
[1,2,7,3,6,4,5] => 8
[1,2,7,3,6,5,4] => 8
[1,2,7,4,3,5,6] => 8
[1,2,7,4,3,6,5] => 8
[1,2,7,4,5,3,6] => 8
[1,2,7,4,5,6,3] => 4
[1,2,7,4,6,3,5] => 8
[1,2,7,4,6,5,3] => 4
[1,2,7,5,3,4,6] => 8
[1,2,7,5,3,6,4] => 8
[1,2,7,5,4,3,6] => 8
[1,2,7,5,4,6,3] => 4
[1,2,7,5,6,3,4] => 8
[1,2,7,5,6,4,3] => 8
[1,2,7,6,3,4,5] => 8
[1,2,7,6,3,5,4] => 8
[1,2,7,6,4,3,5] => 8
[1,2,7,6,4,5,3] => 8
[1,2,7,6,5,3,4] => 8
[1,2,7,6,5,4,3] => 4
[1,3,2,4,5,6,7] => 4
[1,3,2,4,5,7,6] => 4
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 8
[1,3,2,4,7,5,6] => 8
[1,3,2,4,7,6,5] => 4
[1,3,2,5,4,6,7] => 4
[1,3,2,5,4,7,6] => 4
[1,3,2,5,6,4,7] => 8
[1,3,2,5,6,7,4] => 8
[1,3,2,5,7,4,6] => 8
[1,3,2,5,7,6,4] => 8
[1,3,2,6,4,5,7] => 8
[1,3,2,6,4,7,5] => 8
[1,3,2,6,5,4,7] => 4
[1,3,2,6,5,7,4] => 8
[1,3,2,6,7,4,5] => 4
[1,3,2,6,7,5,4] => 8
[1,3,2,7,4,5,6] => 8
[1,3,2,7,4,6,5] => 8
[1,3,2,7,5,4,6] => 8
[1,3,2,7,5,6,4] => 4
[1,3,2,7,6,4,5] => 8
[1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => 8
[1,3,4,2,5,7,6] => 8
[1,3,4,2,6,5,7] => 8
[1,3,4,2,6,7,5] => 8
[1,3,4,2,7,5,6] => 8
[1,3,4,2,7,6,5] => 8
[1,3,4,5,2,6,7] => 8
[1,3,4,5,2,7,6] => 8
[1,3,4,5,6,2,7] => 4
[1,3,4,5,6,7,2] => 8
[1,3,4,5,7,2,6] => 8
[1,3,4,5,7,6,2] => 8
[1,3,4,6,2,5,7] => 8
[1,3,4,6,2,7,5] => 8
[1,3,4,6,5,2,7] => 8
[1,3,4,6,5,7,2] => 8
[1,3,4,6,7,2,5] => 8
[1,3,4,6,7,5,2] => 8
[1,3,4,7,2,5,6] => 8
[1,3,4,7,2,6,5] => 8
[1,3,4,7,5,2,6] => 8
[1,3,4,7,5,6,2] => 8
[1,3,4,7,6,2,5] => 8
[1,3,4,7,6,5,2] => 8
[1,3,5,2,4,6,7] => 8
[1,3,5,2,4,7,6] => 8
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 8
[1,3,5,2,7,4,6] => 8
[1,3,5,2,7,6,4] => 8
[1,3,5,4,2,6,7] => 8
[1,3,5,4,2,7,6] => 8
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 8
[1,3,5,4,7,2,6] => 8
[1,3,5,4,7,6,2] => 8
[1,3,5,6,2,4,7] => 8
[1,3,5,6,2,7,4] => 8
[1,3,5,6,4,2,7] => 8
[1,3,5,6,4,7,2] => 8
[1,3,5,6,7,2,4] => 8
[1,3,5,6,7,4,2] => 8
[1,3,5,7,2,4,6] => 8
[1,3,5,7,2,6,4] => 8
[1,3,5,7,4,2,6] => 8
[1,3,5,7,4,6,2] => 8
[1,3,5,7,6,2,4] => 8
[1,3,5,7,6,4,2] => 8
[1,3,6,2,4,5,7] => 8
[1,3,6,2,4,7,5] => 8
[1,3,6,2,5,4,7] => 8
[1,3,6,2,5,7,4] => 8
[1,3,6,2,7,4,5] => 8
[1,3,6,2,7,5,4] => 8
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 8
[1,3,6,4,5,2,7] => 8
[1,3,6,4,5,7,2] => 8
[1,3,6,4,7,2,5] => 8
[1,3,6,4,7,5,2] => 8
[1,3,6,5,2,4,7] => 8
[1,3,6,5,2,7,4] => 8
[1,3,6,5,4,2,7] => 8
[1,3,6,5,4,7,2] => 8
[1,3,6,5,7,2,4] => 8
[1,3,6,5,7,4,2] => 8
[1,3,6,7,2,4,5] => 8
[1,3,6,7,2,5,4] => 8
[1,3,6,7,4,2,5] => 8
[1,3,6,7,4,5,2] => 8
[1,3,6,7,5,2,4] => 8
[1,3,6,7,5,4,2] => 8
[1,3,7,2,4,5,6] => 8
[1,3,7,2,4,6,5] => 8
[1,3,7,2,5,4,6] => 8
[1,3,7,2,5,6,4] => 8
[1,3,7,2,6,4,5] => 8
[1,3,7,2,6,5,4] => 8
[1,3,7,4,2,5,6] => 8
[1,3,7,4,2,6,5] => 8
[1,3,7,4,5,2,6] => 8
[1,3,7,4,5,6,2] => 8
[1,3,7,4,6,2,5] => 8
[1,3,7,4,6,5,2] => 8
[1,3,7,5,2,4,6] => 8
[1,3,7,5,2,6,4] => 8
[1,3,7,5,4,2,6] => 8
[1,3,7,5,4,6,2] => 8
[1,3,7,5,6,2,4] => 8
[1,3,7,5,6,4,2] => 8
[1,3,7,6,2,4,5] => 8
[1,3,7,6,2,5,4] => 8
[1,3,7,6,4,2,5] => 8
[1,3,7,6,4,5,2] => 8
[1,3,7,6,5,2,4] => 8
[1,3,7,6,5,4,2] => 8
[1,4,2,3,5,6,7] => 8
[1,4,2,3,5,7,6] => 8
[1,4,2,3,6,5,7] => 8
[1,4,2,3,6,7,5] => 8
[1,4,2,3,7,5,6] => 8
[1,4,2,3,7,6,5] => 8
[1,4,2,5,3,6,7] => 8
[1,4,2,5,3,7,6] => 8
[1,4,2,5,6,3,7] => 8
[1,4,2,5,6,7,3] => 8
[1,4,2,5,7,3,6] => 8
[1,4,2,5,7,6,3] => 8
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 8
[1,4,2,6,5,3,7] => 8
[1,4,2,6,5,7,3] => 8
[1,4,2,6,7,3,5] => 8
[1,4,2,6,7,5,3] => 8
[1,4,2,7,3,5,6] => 8
[1,4,2,7,3,6,5] => 8
[1,4,2,7,5,3,6] => 8
[1,4,2,7,5,6,3] => 8
[1,4,2,7,6,3,5] => 8
[1,4,2,7,6,5,3] => 8
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 4
[1,4,3,2,6,5,7] => 4
[1,4,3,2,6,7,5] => 8
[1,4,3,2,7,5,6] => 8
[1,4,3,2,7,6,5] => 4
[1,4,3,5,2,6,7] => 8
[1,4,3,5,2,7,6] => 8
[1,4,3,5,6,2,7] => 8
[1,4,3,5,6,7,2] => 8
[1,4,3,5,7,2,6] => 8
[1,4,3,5,7,6,2] => 8
[1,4,3,6,2,5,7] => 8
[1,4,3,6,2,7,5] => 8
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 8
[1,4,3,6,7,2,5] => 8
[1,4,3,6,7,5,2] => 8
[1,4,3,7,2,5,6] => 8
[1,4,3,7,2,6,5] => 8
[1,4,3,7,5,2,6] => 8
[1,4,3,7,5,6,2] => 8
[1,4,3,7,6,2,5] => 8
[1,4,3,7,6,5,2] => 8
[1,4,5,2,3,6,7] => 4
[1,4,5,2,3,7,6] => 4
[1,4,5,2,6,3,7] => 8
[1,4,5,2,6,7,3] => 8
[1,4,5,2,7,3,6] => 8
[1,4,5,2,7,6,3] => 8
[1,4,5,3,2,6,7] => 8
[1,4,5,3,2,7,6] => 8
[1,4,5,3,6,2,7] => 8
[1,4,5,3,6,7,2] => 8
[1,4,5,3,7,2,6] => 8
[1,4,5,3,7,6,2] => 8
[1,4,5,6,2,3,7] => 4
[1,4,5,6,2,7,3] => 8
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 8
[1,4,5,6,7,2,3] => 8
[1,4,5,6,7,3,2] => 8
[1,4,5,7,2,3,6] => 8
[1,4,5,7,2,6,3] => 8
[1,4,5,7,3,2,6] => 8
[1,4,5,7,3,6,2] => 8
[1,4,5,7,6,2,3] => 8
[1,4,5,7,6,3,2] => 8
[1,4,6,2,3,5,7] => 8
[1,4,6,2,3,7,5] => 8
[1,4,6,2,5,3,7] => 4
[1,4,6,2,5,7,3] => 8
[1,4,6,2,7,3,5] => 4
[1,4,6,2,7,5,3] => 8
[1,4,6,3,2,5,7] => 8
[1,4,6,3,2,7,5] => 8
[1,4,6,3,5,2,7] => 8
[1,4,6,3,5,7,2] => 8
[1,4,6,3,7,2,5] => 8
[1,4,6,3,7,5,2] => 8
[1,4,6,5,2,3,7] => 8
[1,4,6,5,2,7,3] => 8
[1,4,6,5,3,2,7] => 8
[1,4,6,5,3,7,2] => 8
-----------------------------------------------------------------------------
Created: Feb 23, 2016 at 18:09 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: May 10, 2019 at 17:30 by Henning Ulfarsson