*****************************************************************************
* 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: St001375
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The pancake length of a permutation.
This is the minimal number of pancake moves needed to generate a permutation where a pancake move is a reversal of a prefix in a permutation.
-----------------------------------------------------------------------------
References: [1] Blanco, S. A., Buehrle, C. Some relations on prefix reversal generators of the symmetric and hyperoctahedral group [[arXiv:1803.01760]]
-----------------------------------------------------------------------------
Code:
@cached_function
def generate_group_from_generators(parent, gens):
gens = list(gens)
inds = range(len(gens))
assert all( gen.parent() == parent for gen in gens )
one = parent.one()
level_set_cur = set([one])
found_elements = set([one])
level_sets = []
while level_set_cur:
level_sets.append(level_set_cur)
level_set_new = set()
for x in level_set_cur:
for i in inds:
y = x * gens[i]
if y not in found_elements:
found_elements.add(y)
level_set_new.add(y)
level_set_cur = level_set_new
return level_sets
@cached_function
def pancake_gens(n):
return tuple(Permutations(n)(list(range(k,0,-1))+list(range(k+1,n+1))) for k in [2 .. n])
def statistic(sigma):
n = len(sigma)
level_sets = generate_group_from_generators(Permutations(n), pancake_gens(n))
i = 0
for level in level_sets:
if sigma not in level:
i += 1
else:
return i
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 1
[2,1,4,3] => 3
[2,3,1,4] => 2
[2,3,4,1] => 2
[2,4,1,3] => 4
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 4
[3,2,1,4] => 1
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 2
[4,1,2,3] => 2
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 4
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 0
[1,2,3,5,4] => 3
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 3
[1,3,2,4,5] => 3
[1,3,2,5,4] => 5
[1,3,4,2,5] => 3
[1,3,4,5,2] => 3
[1,3,5,2,4] => 5
[1,3,5,4,2] => 4
[1,4,2,3,5] => 3
[1,4,2,5,3] => 5
[1,4,3,2,5] => 3
[1,4,3,5,2] => 5
[1,4,5,2,3] => 3
[1,4,5,3,2] => 4
[1,5,2,3,4] => 3
[1,5,2,4,3] => 4
[1,5,3,2,4] => 5
[1,5,3,4,2] => 5
[1,5,4,2,3] => 4
[1,5,4,3,2] => 3
[2,1,3,4,5] => 1
[2,1,3,5,4] => 4
[2,1,4,3,5] => 3
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 4
[2,3,1,4,5] => 2
[2,3,1,5,4] => 4
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 4
[2,3,5,4,1] => 3
[2,4,1,3,5] => 4
[2,4,1,5,3] => 5
[2,4,3,1,5] => 3
[2,4,3,5,1] => 5
[2,4,5,1,3] => 4
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 5
[2,5,3,1,4] => 5
[2,5,3,4,1] => 4
[2,5,4,1,3] => 4
[2,5,4,3,1] => 3
[3,1,2,4,5] => 2
[3,1,2,5,4] => 4
[3,1,4,2,5] => 4
[3,1,4,5,2] => 4
[3,1,5,2,4] => 5
[3,1,5,4,2] => 5
[3,2,1,4,5] => 1
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 3
[3,4,1,5,2] => 4
[3,4,2,1,5] => 2
[3,4,2,5,1] => 4
[3,4,5,1,2] => 3
[3,4,5,2,1] => 2
[3,5,1,2,4] => 4
[3,5,1,4,2] => 5
[3,5,2,1,4] => 4
[3,5,2,4,1] => 5
[3,5,4,1,2] => 4
[3,5,4,2,1] => 3
[4,1,2,3,5] => 2
[4,1,2,5,3] => 4
[4,1,3,2,5] => 3
[4,1,3,5,2] => 5
[4,1,5,2,3] => 4
[4,1,5,3,2] => 4
[4,2,1,3,5] => 3
[4,2,1,5,3] => 4
[4,2,3,1,5] => 4
[4,2,3,5,1] => 4
[4,2,5,1,3] => 5
[4,2,5,3,1] => 5
[4,3,1,2,5] => 2
[4,3,1,5,2] => 4
[4,3,2,1,5] => 1
[4,3,2,5,1] => 3
[4,3,5,1,2] => 4
[4,3,5,2,1] => 3
[4,5,1,2,3] => 3
[4,5,1,3,2] => 4
[4,5,2,1,3] => 4
[4,5,2,3,1] => 4
[4,5,3,1,2] => 3
[4,5,3,2,1] => 2
[5,1,2,3,4] => 2
[5,1,2,4,3] => 3
[5,1,3,2,4] => 5
[5,1,3,4,2] => 4
[5,1,4,2,3] => 4
[5,1,4,3,2] => 3
[5,2,1,3,4] => 3
[5,2,1,4,3] => 4
[5,2,3,1,4] => 4
[5,2,3,4,1] => 4
[5,2,4,1,3] => 5
[5,2,4,3,1] => 4
[5,3,1,2,4] => 4
[5,3,1,4,2] => 5
[5,3,2,1,4] => 3
[5,3,2,4,1] => 4
[5,3,4,1,2] => 4
[5,3,4,2,1] => 4
[5,4,1,2,3] => 2
[5,4,1,3,2] => 3
[5,4,2,1,3] => 3
[5,4,2,3,1] => 4
[5,4,3,1,2] => 2
[5,4,3,2,1] => 1
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 3
[1,2,3,5,4,6] => 3
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 3
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 5
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 4
[1,2,4,6,3,5] => 6
[1,2,4,6,5,3] => 5
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 6
[1,2,5,4,3,6] => 3
[1,2,5,4,6,3] => 5
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 4
[1,2,6,3,4,5] => 4
[1,2,6,3,5,4] => 5
[1,2,6,4,3,5] => 5
[1,2,6,4,5,3] => 6
[1,2,6,5,3,4] => 4
[1,2,6,5,4,3] => 3
[1,3,2,4,5,6] => 3
[1,3,2,4,6,5] => 6
[1,3,2,5,4,6] => 5
[1,3,2,5,6,4] => 5
[1,3,2,6,4,5] => 5
[1,3,2,6,5,4] => 5
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 5
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 3
[1,3,4,6,2,5] => 5
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 5
[1,3,5,2,6,4] => 6
[1,3,5,4,2,6] => 4
[1,3,5,4,6,2] => 6
[1,3,5,6,2,4] => 5
[1,3,5,6,4,2] => 5
[1,3,6,2,4,5] => 5
[1,3,6,2,5,4] => 6
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 6
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 5
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 5
[1,4,2,6,3,5] => 6
[1,4,2,6,5,3] => 6
[1,4,3,2,5,6] => 3
[1,4,3,2,6,5] => 5
[1,4,3,5,2,6] => 5
[1,4,3,5,6,2] => 5
[1,4,3,6,2,5] => 6
[1,4,3,6,5,2] => 6
[1,4,5,2,3,6] => 3
[1,4,5,2,6,3] => 5
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 4
[1,4,6,2,3,5] => 5
[1,4,6,2,5,3] => 6
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 6
[1,4,6,5,2,3] => 4
[1,4,6,5,3,2] => 5
[1,5,2,3,4,6] => 3
[1,5,2,3,6,4] => 5
[1,5,2,4,3,6] => 4
[1,5,2,4,6,3] => 6
[1,5,2,6,3,4] => 5
[1,5,2,6,4,3] => 6
[1,5,3,2,4,6] => 5
[1,5,3,2,6,4] => 6
[1,5,3,4,2,6] => 5
[1,5,3,4,6,2] => 5
[1,5,3,6,2,4] => 6
[1,5,3,6,4,2] => 6
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 6
[1,5,4,3,2,6] => 3
[1,5,4,3,6,2] => 5
[1,5,4,6,2,3] => 5
[1,5,4,6,3,2] => 5
[1,5,6,2,3,4] => 3
[1,5,6,2,4,3] => 4
[1,5,6,3,2,4] => 5
[1,5,6,3,4,2] => 5
[1,5,6,4,2,3] => 5
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 3
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 6
[1,6,2,4,5,3] => 5
[1,6,2,5,3,4] => 5
[1,6,2,5,4,3] => 4
[1,6,3,2,4,5] => 5
[1,6,3,2,5,4] => 6
[1,6,3,4,2,5] => 5
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 6
[1,6,3,5,4,2] => 6
[1,6,4,2,3,5] => 5
[1,6,4,2,5,3] => 6
[1,6,4,3,2,5] => 5
[1,6,4,3,5,2] => 6
[1,6,4,5,2,3] => 5
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 4
[1,6,5,2,4,3] => 5
[1,6,5,3,2,4] => 5
[1,6,5,3,4,2] => 5
[1,6,5,4,2,3] => 4
[1,6,5,4,3,2] => 3
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 5
[2,1,3,6,4,5] => 5
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 3
[2,1,4,3,6,5] => 5
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 5
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 5
[2,1,5,6,3,4] => 3
[2,1,5,6,4,3] => 4
[2,1,6,3,4,5] => 3
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 5
[2,1,6,4,5,3] => 5
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 5
[2,3,1,5,4,6] => 4
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 5
[2,3,4,1,5,6] => 2
[2,3,4,1,6,5] => 4
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 2
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 3
[2,3,5,1,4,6] => 4
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 5
[2,3,6,4,1,5] => 5
[2,3,6,4,5,1] => 4
[2,3,6,5,1,4] => 5
[2,3,6,5,4,1] => 3
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 6
[2,4,1,5,3,6] => 5
[2,4,1,5,6,3] => 5
[2,4,1,6,3,5] => 6
[2,4,1,6,5,3] => 6
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 5
[2,4,3,5,1,6] => 5
[2,4,3,5,6,1] => 5
[2,4,3,6,1,5] => 5
[2,4,3,6,5,1] => 5
[2,4,5,1,3,6] => 4
[2,4,5,1,6,3] => 5
[2,4,5,3,1,6] => 4
[2,4,5,3,6,1] => 5
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 6
[2,4,6,3,5,1] => 6
[2,4,6,5,1,3] => 5
[2,4,6,5,3,1] => 5
[2,5,1,3,4,6] => 4
[2,5,1,3,6,4] => 6
[2,5,1,4,3,6] => 5
[2,5,1,4,6,3] => 6
[2,5,1,6,3,4] => 5
[2,5,1,6,4,3] => 5
[2,5,3,1,4,6] => 5
[2,5,3,1,6,4] => 6
[2,5,3,4,1,6] => 4
[2,5,3,4,6,1] => 5
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 6
[2,5,4,1,3,6] => 4
[2,5,4,1,6,3] => 5
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 6
[2,5,4,6,3,1] => 5
[2,5,6,1,3,4] => 4
[2,5,6,1,4,3] => 5
[2,5,6,3,1,4] => 5
[2,5,6,3,4,1] => 5
[2,5,6,4,1,3] => 5
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 4
[2,6,1,3,5,4] => 5
[2,6,1,4,3,5] => 6
[2,6,1,4,5,3] => 5
[2,6,1,5,3,4] => 5
[2,6,1,5,4,3] => 5
[2,6,3,1,4,5] => 5
[2,6,3,1,5,4] => 6
[2,6,3,4,1,5] => 5
[2,6,3,4,5,1] => 4
[2,6,3,5,1,4] => 6
[2,6,3,5,4,1] => 5
[2,6,4,1,3,5] => 6
[2,6,4,1,5,3] => 6
[2,6,4,3,1,5] => 5
[2,6,4,3,5,1] => 5
[2,6,4,5,1,3] => 6
[2,6,4,5,3,1] => 6
[2,6,5,1,3,4] => 4
[2,6,5,1,4,3] => 5
[2,6,5,3,1,4] => 5
[2,6,5,3,4,1] => 4
[2,6,5,4,1,3] => 4
[2,6,5,4,3,1] => 3
[3,1,2,4,5,6] => 2
[3,1,2,4,6,5] => 5
[3,1,2,5,4,6] => 4
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 5
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 6
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 6
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 5
[3,1,5,2,6,4] => 6
[3,1,5,4,2,6] => 5
[3,1,5,4,6,2] => 6
[3,1,5,6,2,4] => 5
[3,1,5,6,4,2] => 5
[3,1,6,2,4,5] => 5
[3,1,6,2,5,4] => 6
[3,1,6,4,2,5] => 6
[3,1,6,4,5,2] => 5
[3,1,6,5,2,4] => 5
[3,1,6,5,4,2] => 5
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 4
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 5
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 5
[3,2,4,6,5,1] => 4
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 5
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 5
[3,2,5,6,1,4] => 5
[3,2,5,6,4,1] => 5
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 5
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 5
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 4
[3,4,1,2,5,6] => 3
[3,4,1,2,6,5] => 5
[3,4,1,5,2,6] => 4
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 5
[3,4,2,1,5,6] => 2
[3,4,2,1,6,5] => 4
[3,4,2,5,1,6] => 4
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 5
[3,4,2,6,5,1] => 5
[3,4,5,1,2,6] => 3
[3,4,5,1,6,2] => 4
[3,4,5,2,1,6] => 2
[3,4,5,2,6,1] => 4
[3,4,5,6,1,2] => 3
[3,4,5,6,2,1] => 2
[3,4,6,1,2,5] => 5
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 4
[3,4,6,2,5,1] => 5
[3,4,6,5,1,2] => 4
[3,4,6,5,2,1] => 3
[3,5,1,2,4,6] => 4
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 5
[3,5,1,4,6,2] => 6
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 6
[3,5,2,1,4,6] => 4
[3,5,2,1,6,4] => 5
[3,5,2,4,1,6] => 5
[3,5,2,4,6,1] => 6
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 4
[3,5,4,1,6,2] => 5
[3,5,4,2,1,6] => 3
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 5
[3,5,6,1,2,4] => 5
[3,5,6,1,4,2] => 6
[3,5,6,2,1,4] => 4
[3,5,6,2,4,1] => 5
[3,5,6,4,1,2] => 5
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 5
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 6
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 5
[3,6,2,1,4,5] => 4
[3,6,2,1,5,4] => 5
[3,6,2,4,1,5] => 6
[3,6,2,4,5,1] => 5
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 5
[3,6,4,1,2,5] => 6
[3,6,4,1,5,2] => 6
[3,6,4,2,1,5] => 5
[3,6,4,2,5,1] => 6
[3,6,4,5,1,2] => 5
[3,6,4,5,2,1] => 4
[3,6,5,1,2,4] => 4
[3,6,5,1,4,2] => 5
[3,6,5,2,1,4] => 5
[3,6,5,2,4,1] => 5
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 3
[4,1,2,3,5,6] => 2
[4,1,2,3,6,5] => 4
[4,1,2,5,3,6] => 4
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 5
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 5
[4,1,3,5,2,6] => 5
[4,1,3,5,6,2] => 5
[4,1,3,6,2,5] => 6
[4,1,3,6,5,2] => 6
[4,1,5,2,3,6] => 4
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 4
[4,1,5,3,6,2] => 6
[4,1,5,6,2,3] => 4
[4,1,5,6,3,2] => 4
[4,1,6,2,3,5] => 5
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 5
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 5
[4,1,6,5,3,2] => 5
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 5
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 5
[4,2,1,6,5,3] => 5
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 6
[4,2,3,5,1,6] => 4
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 6
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 5
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 5
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 5
[4,2,5,6,3,1] => 5
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 5
[4,2,6,5,3,1] => 5
[4,3,1,2,5,6] => 2
[4,3,1,2,6,5] => 4
[4,3,1,5,2,6] => 4
[4,3,1,5,6,2] => 4
[4,3,1,6,2,5] => 5
[4,3,1,6,5,2] => 5
[4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => 3
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 3
[4,3,2,6,1,5] => 4
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 4
[4,3,5,1,6,2] => 5
[4,3,5,2,1,6] => 3
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 4
[4,3,5,6,2,1] => 3
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 6
[4,3,6,2,1,5] => 5
[4,3,6,2,5,1] => 5
[4,3,6,5,1,2] => 4
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 3
[4,5,1,2,6,3] => 5
[4,5,1,3,2,6] => 4
[4,5,1,3,6,2] => 6
[4,5,1,6,2,3] => 5
[4,5,1,6,3,2] => 4
[4,5,2,1,3,6] => 4
[4,5,2,1,6,3] => 4
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 5
[4,5,2,6,1,3] => 5
[4,5,2,6,3,1] => 5
[4,5,3,1,2,6] => 3
[4,5,3,1,6,2] => 5
[4,5,3,2,1,6] => 2
[4,5,3,2,6,1] => 4
[4,5,3,6,1,2] => 5
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 4
[4,5,6,2,1,3] => 4
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 3
[4,5,6,3,2,1] => 2
[4,6,1,2,3,5] => 4
[4,6,1,2,5,3] => 5
[4,6,1,3,2,5] => 5
[4,6,1,3,5,2] => 6
[4,6,1,5,2,3] => 6
[4,6,1,5,3,2] => 5
[4,6,2,1,3,5] => 5
[4,6,2,1,5,3] => 6
[4,6,2,3,1,5] => 6
[4,6,2,3,5,1] => 6
[4,6,2,5,1,3] => 7
[4,6,2,5,3,1] => 6
[4,6,3,1,2,5] => 5
[4,6,3,1,5,2] => 6
[4,6,3,2,1,5] => 4
[4,6,3,2,5,1] => 5
[4,6,3,5,1,2] => 5
[4,6,3,5,2,1] => 5
[4,6,5,1,2,3] => 4
[4,6,5,1,3,2] => 5
[4,6,5,2,1,3] => 5
[4,6,5,2,3,1] => 5
[4,6,5,3,1,2] => 4
[4,6,5,3,2,1] => 3
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 4
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 5
[5,1,2,6,3,4] => 4
[5,1,2,6,4,3] => 5
[5,1,3,2,4,6] => 5
[5,1,3,2,6,4] => 5
[5,1,3,4,2,6] => 4
[5,1,3,4,6,2] => 5
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 6
[5,1,4,2,3,6] => 4
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 5
[5,1,4,6,2,3] => 5
[5,1,4,6,3,2] => 5
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 5
[5,1,6,3,2,4] => 6
[5,1,6,3,4,2] => 6
[5,1,6,4,2,3] => 5
[5,1,6,4,3,2] => 4
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 5
[5,2,1,6,4,3] => 4
[5,2,3,1,4,6] => 4
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 4
[5,2,3,4,6,1] => 4
[5,2,3,6,1,4] => 6
[5,2,3,6,4,1] => 5
[5,2,4,1,3,6] => 5
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 5
[5,2,4,6,1,3] => 6
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 5
[5,2,6,1,4,3] => 5
[5,2,6,3,1,4] => 6
[5,2,6,3,4,1] => 6
[5,2,6,4,1,3] => 6
[5,2,6,4,3,1] => 5
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 5
[5,3,1,4,2,6] => 5
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 6
[5,3,1,6,4,2] => 6
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 4
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 5
[5,3,2,6,1,4] => 5
[5,3,2,6,4,1] => 5
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 4
[5,3,4,2,6,1] => 6
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 4
[5,3,6,1,2,4] => 5
[5,3,6,1,4,2] => 7
[5,3,6,2,1,4] => 5
[5,3,6,2,4,1] => 6
[5,3,6,4,1,2] => 5
[5,3,6,4,2,1] => 5
[5,4,1,2,3,6] => 2
[5,4,1,2,6,3] => 4
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 5
[5,4,1,6,2,3] => 4
[5,4,1,6,3,2] => 5
[5,4,2,1,3,6] => 3
[5,4,2,1,6,3] => 5
[5,4,2,3,1,6] => 4
[5,4,2,3,6,1] => 4
[5,4,2,6,1,3] => 5
[5,4,2,6,3,1] => 5
[5,4,3,1,2,6] => 2
[5,4,3,1,6,2] => 4
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 3
[5,4,3,6,1,2] => 4
[5,4,3,6,2,1] => 3
[5,4,6,1,2,3] => 4
[5,4,6,1,3,2] => 5
[5,4,6,2,1,3] => 5
[5,4,6,2,3,1] => 5
[5,4,6,3,1,2] => 4
[5,4,6,3,2,1] => 3
[5,6,1,2,3,4] => 3
[5,6,1,2,4,3] => 4
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 5
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 4
[5,6,2,1,3,4] => 4
[5,6,2,1,4,3] => 4
[5,6,2,3,1,4] => 5
[5,6,2,3,4,1] => 5
[5,6,2,4,1,3] => 5
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 5
[5,6,3,1,4,2] => 5
[5,6,3,2,1,4] => 4
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 5
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 3
[5,6,4,1,3,2] => 4
[5,6,4,2,1,3] => 4
[5,6,4,2,3,1] => 5
[5,6,4,3,1,2] => 3
[5,6,4,3,2,1] => 2
[6,1,2,3,4,5] => 2
[6,1,2,3,5,4] => 3
[6,1,2,4,3,5] => 5
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 4
[6,1,2,5,4,3] => 3
[6,1,3,2,4,5] => 5
[6,1,3,2,5,4] => 5
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 4
[6,1,3,5,2,4] => 6
[6,1,3,5,4,2] => 5
[6,1,4,2,3,5] => 5
[6,1,4,2,5,3] => 6
[6,1,4,3,2,5] => 5
[6,1,4,3,5,2] => 5
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 4
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 5
[6,1,5,3,2,4] => 5
[6,1,5,3,4,2] => 6
[6,1,5,4,2,3] => 4
[6,1,5,4,3,2] => 3
[6,2,1,3,4,5] => 3
[6,2,1,3,5,4] => 4
[6,2,1,4,3,5] => 5
[6,2,1,4,5,3] => 5
[6,2,1,5,3,4] => 5
[6,2,1,5,4,3] => 4
[6,2,3,1,4,5] => 4
[6,2,3,1,5,4] => 5
[6,2,3,4,1,5] => 4
[6,2,3,4,5,1] => 4
[6,2,3,5,1,4] => 5
[6,2,3,5,4,1] => 5
[6,2,4,1,3,5] => 6
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 5
[6,2,4,3,5,1] => 6
[6,2,4,5,1,3] => 6
[6,2,4,5,3,1] => 5
[6,2,5,1,3,4] => 5
[6,2,5,1,4,3] => 5
[6,2,5,3,1,4] => 6
[6,2,5,3,4,1] => 5
[6,2,5,4,1,3] => 5
[6,2,5,4,3,1] => 4
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 5
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 5
[6,3,1,5,2,4] => 6
[6,3,1,5,4,2] => 5
[6,3,2,1,4,5] => 3
[6,3,2,1,5,4] => 4
[6,3,2,4,1,5] => 5
[6,3,2,4,5,1] => 5
[6,3,2,5,1,4] => 5
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 5
[6,3,4,1,5,2] => 6
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 5
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 5
[6,3,5,1,4,2] => 6
[6,3,5,2,1,4] => 5
[6,3,5,2,4,1] => 6
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 4
[6,4,1,2,3,5] => 4
[6,4,1,2,5,3] => 5
[6,4,1,3,2,5] => 5
[6,4,1,3,5,2] => 6
[6,4,1,5,2,3] => 5
[6,4,1,5,3,2] => 5
[6,4,2,1,3,5] => 5
[6,4,2,1,5,3] => 5
[6,4,2,3,1,5] => 6
[6,4,2,3,5,1] => 5
[6,4,2,5,1,3] => 6
[6,4,2,5,3,1] => 6
[6,4,3,1,2,5] => 4
[6,4,3,1,5,2] => 5
[6,4,3,2,1,5] => 3
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 4
[6,4,3,5,2,1] => 4
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 5
[6,4,5,2,1,3] => 5
[6,4,5,2,3,1] => 6
[6,4,5,3,1,2] => 5
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 2
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 5
[6,5,1,3,4,2] => 4
[6,5,1,4,2,3] => 4
[6,5,1,4,3,2] => 3
[6,5,2,1,3,4] => 3
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 4
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 5
[6,5,2,4,3,1] => 4
[6,5,3,1,2,4] => 4
[6,5,3,1,4,2] => 5
[6,5,3,2,1,4] => 3
[6,5,3,2,4,1] => 4
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 2
[6,5,4,1,3,2] => 3
[6,5,4,2,1,3] => 3
[6,5,4,2,3,1] => 4
[6,5,4,3,1,2] => 2
[6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 3
[1,2,3,4,6,5,7] => 3
[1,2,3,4,6,7,5] => 4
[1,2,3,4,7,5,6] => 4
[1,2,3,4,7,6,5] => 3
[1,2,3,5,4,6,7] => 3
[1,2,3,5,4,7,6] => 5
[1,2,3,5,6,4,7] => 4
[1,2,3,5,6,7,4] => 4
[1,2,3,5,7,4,6] => 6
[1,2,3,5,7,6,4] => 5
[1,2,3,6,4,5,7] => 4
[1,2,3,6,4,7,5] => 6
[1,2,3,6,5,4,7] => 3
[1,2,3,6,5,7,4] => 5
[1,2,3,6,7,4,5] => 4
[1,2,3,6,7,5,4] => 4
[1,2,3,7,4,5,6] => 4
[1,2,3,7,4,6,5] => 5
[1,2,3,7,5,4,6] => 5
[1,2,3,7,5,6,4] => 6
[1,2,3,7,6,4,5] => 4
[1,2,3,7,6,5,4] => 3
[1,2,4,3,5,6,7] => 3
[1,2,4,3,5,7,6] => 6
[1,2,4,3,6,5,7] => 5
[1,2,4,3,6,7,5] => 5
[1,2,4,3,7,5,6] => 5
[1,2,4,3,7,6,5] => 5
[1,2,4,5,3,6,7] => 4
[1,2,4,5,3,7,6] => 5
[1,2,4,5,6,3,7] => 4
[1,2,4,5,6,7,3] => 4
[1,2,4,5,7,3,6] => 6
[1,2,4,5,7,6,3] => 5
[1,2,4,6,3,5,7] => 6
[1,2,4,6,3,7,5] => 7
[1,2,4,6,5,3,7] => 5
[1,2,4,6,5,7,3] => 7
[1,2,4,6,7,3,5] => 6
[1,2,4,6,7,5,3] => 6
[1,2,4,7,3,5,6] => 6
[1,2,4,7,3,6,5] => 6
[1,2,4,7,5,3,6] => 7
[1,2,4,7,5,6,3] => 6
[1,2,4,7,6,3,5] => 6
[1,2,4,7,6,5,3] => 5
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 5
[1,2,5,3,6,4,7] => 6
[1,2,5,3,6,7,4] => 6
[1,2,5,3,7,4,6] => 7
[1,2,5,3,7,6,4] => 6
[1,2,5,4,3,6,7] => 3
[1,2,5,4,3,7,6] => 5
[1,2,5,4,6,3,7] => 5
[1,2,5,4,6,7,3] => 5
[1,2,5,4,7,3,6] => 6
[1,2,5,4,7,6,3] => 6
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 6
[1,2,5,6,4,3,7] => 4
[1,2,5,6,4,7,3] => 6
[1,2,5,6,7,3,4] => 4
[1,2,5,6,7,4,3] => 4
[1,2,5,7,3,4,6] => 6
[1,2,5,7,3,6,4] => 7
[1,2,5,7,4,3,6] => 6
[1,2,5,7,4,6,3] => 7
[1,2,5,7,6,3,4] => 5
[1,2,5,7,6,4,3] => 5
[1,2,6,3,4,5,7] => 4
[1,2,6,3,4,7,5] => 6
[1,2,6,3,5,4,7] => 5
[1,2,6,3,5,7,4] => 7
[1,2,6,3,7,4,5] => 6
[1,2,6,3,7,5,4] => 6
[1,2,6,4,3,5,7] => 5
[1,2,6,4,3,7,5] => 6
[1,2,6,4,5,3,7] => 6
[1,2,6,4,5,7,3] => 6
[1,2,6,4,7,3,5] => 7
[1,2,6,4,7,5,3] => 7
[1,2,6,5,3,4,7] => 4
[1,2,6,5,3,7,4] => 6
[1,2,6,5,4,3,7] => 3
[1,2,6,5,4,7,3] => 5
[1,2,6,5,7,3,4] => 6
[1,2,6,5,7,4,3] => 5
[1,2,6,7,3,4,5] => 4
[1,2,6,7,3,5,4] => 5
[1,2,6,7,4,3,5] => 6
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 5
[1,2,6,7,5,4,3] => 4
[1,2,7,3,4,5,6] => 4
[1,2,7,3,4,6,5] => 5
[1,2,7,3,5,4,6] => 7
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 6
[1,2,7,3,6,5,4] => 5
[1,2,7,4,3,5,6] => 5
[1,2,7,4,3,6,5] => 6
[1,2,7,4,5,3,6] => 6
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 7
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 6
[1,2,7,5,3,6,4] => 7
[1,2,7,5,4,3,6] => 5
[1,2,7,5,4,6,3] => 6
[1,2,7,5,6,3,4] => 6
[1,2,7,5,6,4,3] => 6
[1,2,7,6,3,4,5] => 4
[1,2,7,6,3,5,4] => 5
[1,2,7,6,4,3,5] => 5
[1,2,7,6,4,5,3] => 6
[1,2,7,6,5,3,4] => 4
[1,2,7,6,5,4,3] => 3
[1,3,2,4,5,6,7] => 3
[1,3,2,4,5,7,6] => 6
[1,3,2,4,6,5,7] => 6
[1,3,2,4,6,7,5] => 7
[1,3,2,4,7,5,6] => 7
[1,3,2,4,7,6,5] => 6
[1,3,2,5,4,6,7] => 5
[1,3,2,5,4,7,6] => 7
[1,3,2,5,6,4,7] => 5
[1,3,2,5,6,7,4] => 5
[1,3,2,5,7,4,6] => 7
[1,3,2,5,7,6,4] => 6
[1,3,2,6,4,5,7] => 5
[1,3,2,6,4,7,5] => 7
[1,3,2,6,5,4,7] => 5
[1,3,2,6,5,7,4] => 7
[1,3,2,6,7,4,5] => 5
[1,3,2,6,7,5,4] => 6
[1,3,2,7,4,5,6] => 5
[1,3,2,7,4,6,5] => 6
[1,3,2,7,5,4,6] => 7
[1,3,2,7,5,6,4] => 7
[1,3,2,7,6,4,5] => 6
[1,3,2,7,6,5,4] => 5
[1,3,4,2,5,6,7] => 3
[1,3,4,2,5,7,6] => 6
[1,3,4,2,6,5,7] => 5
[1,3,4,2,6,7,5] => 5
[1,3,4,2,7,5,6] => 5
[1,3,4,2,7,6,5] => 5
[1,3,4,5,2,6,7] => 3
[1,3,4,5,2,7,6] => 5
[1,3,4,5,6,2,7] => 3
[1,3,4,5,6,7,2] => 3
[1,3,4,5,7,2,6] => 5
[1,3,4,5,7,6,2] => 4
[1,3,4,6,2,5,7] => 5
[1,3,4,6,2,7,5] => 6
[1,3,4,6,5,2,7] => 4
[1,3,4,6,5,7,2] => 6
[1,3,4,6,7,2,5] => 5
[1,3,4,6,7,5,2] => 5
[1,3,4,7,2,5,6] => 5
[1,3,4,7,2,6,5] => 6
[1,3,4,7,5,2,6] => 6
[1,3,4,7,5,6,2] => 5
[1,3,4,7,6,2,5] => 6
[1,3,4,7,6,5,2] => 4
[1,3,5,2,4,6,7] => 5
[1,3,5,2,4,7,6] => 7
[1,3,5,2,6,4,7] => 6
[1,3,5,2,6,7,4] => 6
[1,3,5,2,7,4,6] => 7
[1,3,5,2,7,6,4] => 7
[1,3,5,4,2,6,7] => 4
[1,3,5,4,2,7,6] => 6
[1,3,5,4,6,2,7] => 6
[1,3,5,4,6,7,2] => 6
[1,3,5,4,7,2,6] => 6
[1,3,5,4,7,6,2] => 6
[1,3,5,6,2,4,7] => 5
[1,3,5,6,2,7,4] => 7
[1,3,5,6,4,2,7] => 5
[1,3,5,6,4,7,2] => 6
[1,3,5,6,7,2,4] => 5
[1,3,5,6,7,4,2] => 5
[1,3,5,7,2,4,6] => 7
[1,3,5,7,2,6,4] => 7
[1,3,5,7,4,2,6] => 7
[1,3,5,7,4,6,2] => 7
[1,3,5,7,6,2,4] => 6
[1,3,5,7,6,4,2] => 6
[1,3,6,2,4,5,7] => 5
[1,3,6,2,4,7,5] => 7
[1,3,6,2,5,4,7] => 6
[1,3,6,2,5,7,4] => 7
[1,3,6,2,7,4,5] => 7
[1,3,6,2,7,5,4] => 6
[1,3,6,4,2,5,7] => 6
[1,3,6,4,2,7,5] => 7
[1,3,6,4,5,2,7] => 5
[1,3,6,4,5,7,2] => 6
[1,3,6,4,7,2,5] => 7
[1,3,6,4,7,5,2] => 7
[1,3,6,5,2,4,7] => 6
[1,3,6,5,2,7,4] => 6
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 6
[1,3,6,5,7,2,4] => 7
[1,3,6,5,7,4,2] => 6
[1,3,6,7,2,4,5] => 5
[1,3,6,7,2,5,4] => 6
[1,3,6,7,4,2,5] => 7
[1,3,6,7,4,5,2] => 6
[1,3,6,7,5,2,4] => 7
[1,3,6,7,5,4,2] => 5
[1,3,7,2,4,5,6] => 5
[1,3,7,2,4,6,5] => 6
[1,3,7,2,5,4,6] => 7
[1,3,7,2,5,6,4] => 7
[1,3,7,2,6,4,5] => 7
[1,3,7,2,6,5,4] => 6
[1,3,7,4,2,5,6] => 6
[1,3,7,4,2,6,5] => 7
[1,3,7,4,5,2,6] => 7
[1,3,7,4,5,6,2] => 5
[1,3,7,4,6,2,5] => 7
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 7
[1,3,7,5,2,6,4] => 8
[1,3,7,5,4,2,6] => 6
[1,3,7,5,4,6,2] => 6
[1,3,7,5,6,2,4] => 7
[1,3,7,5,6,4,2] => 7
[1,3,7,6,2,4,5] => 6
[1,3,7,6,2,5,4] => 6
[1,3,7,6,4,2,5] => 6
[1,3,7,6,4,5,2] => 5
[1,3,7,6,5,2,4] => 6
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 3
[1,4,2,3,5,7,6] => 6
[1,4,2,3,6,5,7] => 5
[1,4,2,3,6,7,5] => 5
[1,4,2,3,7,5,6] => 5
[1,4,2,3,7,6,5] => 5
[1,4,2,5,3,6,7] => 5
[1,4,2,5,3,7,6] => 7
[1,4,2,5,6,3,7] => 5
[1,4,2,5,6,7,3] => 5
[1,4,2,5,7,3,6] => 7
[1,4,2,5,7,6,3] => 6
[1,4,2,6,3,5,7] => 6
[1,4,2,6,3,7,5] => 7
[1,4,2,6,5,3,7] => 6
[1,4,2,6,5,7,3] => 7
[1,4,2,6,7,3,5] => 7
[1,4,2,6,7,5,3] => 7
[1,4,2,7,3,5,6] => 6
[1,4,2,7,3,6,5] => 7
[1,4,2,7,5,3,6] => 7
[1,4,2,7,5,6,3] => 7
[1,4,2,7,6,3,5] => 6
[1,4,2,7,6,5,3] => 6
[1,4,3,2,5,6,7] => 3
[1,4,3,2,5,7,6] => 6
[1,4,3,2,6,5,7] => 5
[1,4,3,2,6,7,5] => 5
[1,4,3,2,7,5,6] => 5
[1,4,3,2,7,6,5] => 6
[1,4,3,5,2,6,7] => 5
[1,4,3,5,2,7,6] => 6
[1,4,3,5,6,2,7] => 5
[1,4,3,5,6,7,2] => 5
[1,4,3,5,7,2,6] => 7
[1,4,3,5,7,6,2] => 6
[1,4,3,6,2,5,7] => 6
[1,4,3,6,2,7,5] => 7
[1,4,3,6,5,2,7] => 6
[1,4,3,6,5,7,2] => 7
[1,4,3,6,7,2,5] => 6
[1,4,3,6,7,5,2] => 7
[1,4,3,7,2,5,6] => 6
[1,4,3,7,2,6,5] => 6
[1,4,3,7,5,2,6] => 7
[1,4,3,7,5,6,2] => 7
[1,4,3,7,6,2,5] => 6
[1,4,3,7,6,5,2] => 6
[1,4,5,2,3,6,7] => 3
[1,4,5,2,3,7,6] => 5
[1,4,5,2,6,3,7] => 5
[1,4,5,2,6,7,3] => 5
[1,4,5,2,7,3,6] => 6
[1,4,5,2,7,6,3] => 6
[1,4,5,3,2,6,7] => 4
[1,4,5,3,2,7,6] => 6
[1,4,5,3,6,2,7] => 5
[1,4,5,3,6,7,2] => 5
[1,4,5,3,7,2,6] => 7
[1,4,5,3,7,6,2] => 6
[1,4,5,6,2,3,7] => 3
[1,4,5,6,2,7,3] => 5
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 5
[1,4,5,6,7,2,3] => 3
[1,4,5,6,7,3,2] => 4
[1,4,5,7,2,3,6] => 5
[1,4,5,7,2,6,3] => 6
[1,4,5,7,3,2,6] => 6
[1,4,5,7,3,6,2] => 6
[1,4,5,7,6,2,3] => 4
[1,4,5,7,6,3,2] => 5
[1,4,6,2,3,5,7] => 5
[1,4,6,2,3,7,5] => 6
[1,4,6,2,5,3,7] => 6
[1,4,6,2,5,7,3] => 7
[1,4,6,2,7,3,5] => 7
[1,4,6,2,7,5,3] => 7
[1,4,6,3,2,5,7] => 6
[1,4,6,3,2,7,5] => 7
[1,4,6,3,5,2,7] => 6
[1,4,6,3,5,7,2] => 7
[1,4,6,3,7,2,5] => 7
[1,4,6,3,7,5,2] => 7
[1,4,6,5,2,3,7] => 4
[1,4,6,5,2,7,3] => 6
[1,4,6,5,3,2,7] => 5
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Created: Mar 25, 2019 at 14:37 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Mar 09, 2023 at 13:53 by Tilman Möller