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-----------------------------------------------------------------------------
Statistic identifier: St001898
-----------------------------------------------------------------------------
Collection: Ordered set partitions
-----------------------------------------------------------------------------
Description: The number of occurrences of an 132 pattern in an ordered set partition.
An occurrence of a pattern $\pi\in\mathfrak S_k$ ordered set partition with blocks $B_1|\dots|B_\ell$ is a sequence of elements $e_1,\dots,e_k$ with $e_i\in B_{j_i}$ and $j_1 < \dots < j_k$ order-isomorphic to $\pi$.
-----------------------------------------------------------------------------
References: [1] (service unreachable) [[MathSciNet:3245891]]
-----------------------------------------------------------------------------
Code:
from sage.combinat.permutation import to_standard
def occurrences(p, pattern):
"""
Return elements in sequences of distinct blocks order isomorphic
to `pattern`.
"""
o = []
for i, b in enumerate(p):
q = p[i+1:]
for e in b:
o.extend(occurrences_aux(q, [e], pattern))
return o
def occurrences_aux(p, prefix, pattern):
"""
Return all occurrences of the form `(prefix, suffix)` order
isomorphic to `pattern`, where `suffix` are elements in sequences
of distinct blocks of `p`.
"""
# TODO: we could do better, probably
if len(pattern) == len(prefix):
yield prefix
else:
pattern_prefix = to_standard(pattern[:len(prefix)+1])
for i, b in enumerate(p):
q = p[i+1:]
for e in b:
new_prefix = prefix + [e]
if to_standard(new_prefix) == pattern_prefix:
yield from occurrences_aux(q, new_prefix, pattern)
def statistic(p):
return len(occurrences(p, [1,3,2]))
-----------------------------------------------------------------------------
Statistic values:
[{1}] => 0
[{1},{2}] => 0
[{2},{1}] => 0
[{1,2}] => 0
[{1},{2},{3}] => 0
[{1},{3},{2}] => 1
[{2},{1},{3}] => 0
[{3},{1},{2}] => 0
[{2},{3},{1}] => 0
[{3},{2},{1}] => 0
[{1},{2,3}] => 0
[{2},{1,3}] => 0
[{3},{1,2}] => 0
[{1,2},{3}] => 0
[{1,3},{2}] => 0
[{2,3},{1}] => 0
[{1,2,3}] => 0
[{1},{2},{3},{4}] => 0
[{1},{2},{4},{3}] => 2
[{1},{3},{2},{4}] => 1
[{1},{4},{2},{3}] => 2
[{1},{3},{4},{2}] => 2
[{1},{4},{3},{2}] => 3
[{2},{1},{3},{4}] => 0
[{2},{1},{4},{3}] => 2
[{3},{1},{2},{4}] => 0
[{4},{1},{2},{3}] => 0
[{3},{1},{4},{2}] => 1
[{4},{1},{3},{2}] => 1
[{2},{3},{1},{4}] => 0
[{2},{4},{1},{3}] => 1
[{3},{2},{1},{4}] => 0
[{4},{2},{1},{3}] => 0
[{3},{4},{1},{2}] => 0
[{4},{3},{1},{2}] => 0
[{2},{3},{4},{1}] => 0
[{2},{4},{3},{1}] => 1
[{3},{2},{4},{1}] => 0
[{4},{2},{3},{1}] => 0
[{3},{4},{2},{1}] => 0
[{4},{3},{2},{1}] => 0
[{1},{2},{3,4}] => 0
[{1},{3},{2,4}] => 1
[{1},{4},{2,3}] => 2
[{2},{1},{3,4}] => 0
[{3},{1},{2,4}] => 0
[{4},{1},{2,3}] => 0
[{2},{3},{1,4}] => 0
[{2},{4},{1,3}] => 1
[{3},{2},{1,4}] => 0
[{4},{2},{1,3}] => 0
[{3},{4},{1,2}] => 0
[{4},{3},{1,2}] => 0
[{1},{2,3},{4}] => 0
[{1},{2,4},{3}] => 1
[{1},{3,4},{2}] => 2
[{2},{1,3},{4}] => 0
[{2},{1,4},{3}] => 1
[{3},{1,2},{4}] => 0
[{4},{1,2},{3}] => 0
[{3},{1,4},{2}] => 0
[{4},{1,3},{2}] => 0
[{2},{3,4},{1}] => 0
[{3},{2,4},{1}] => 0
[{4},{2,3},{1}] => 0
[{1},{2,3,4}] => 0
[{2},{1,3,4}] => 0
[{3},{1,2,4}] => 0
[{4},{1,2,3}] => 0
[{1,2},{3},{4}] => 0
[{1,2},{4},{3}] => 2
[{1,3},{2},{4}] => 0
[{1,4},{2},{3}] => 0
[{1,3},{4},{2}] => 1
[{1,4},{3},{2}] => 1
[{2,3},{1},{4}] => 0
[{2,4},{1},{3}] => 0
[{3,4},{1},{2}] => 0
[{2,3},{4},{1}] => 0
[{2,4},{3},{1}] => 0
[{3,4},{2},{1}] => 0
[{1,2},{3,4}] => 0
[{1,3},{2,4}] => 0
[{1,4},{2,3}] => 0
[{2,3},{1,4}] => 0
[{2,4},{1,3}] => 0
[{3,4},{1,2}] => 0
[{1,2,3},{4}] => 0
[{1,2,4},{3}] => 0
[{1,3,4},{2}] => 0
[{2,3,4},{1}] => 0
[{1,2,3,4}] => 0
[{1},{2},{3},{4},{5}] => 0
[{1},{2},{3},{5},{4}] => 3
[{1},{2},{4},{3},{5}] => 2
[{1},{2},{5},{3},{4}] => 4
[{1},{2},{4},{5},{3}] => 4
[{1},{2},{5},{4},{3}] => 6
[{1},{3},{2},{4},{5}] => 1
[{1},{3},{2},{5},{4}] => 4
[{1},{4},{2},{3},{5}] => 2
[{1},{5},{2},{3},{4}] => 3
[{1},{4},{2},{5},{3}] => 4
[{1},{5},{2},{4},{3}] => 5
[{1},{3},{4},{2},{5}] => 2
[{1},{3},{5},{2},{4}] => 4
[{1},{4},{3},{2},{5}] => 3
[{1},{5},{3},{2},{4}] => 4
[{1},{4},{5},{2},{3}] => 4
[{1},{5},{4},{2},{3}] => 5
[{1},{3},{4},{5},{2}] => 3
[{1},{3},{5},{4},{2}] => 5
[{1},{4},{3},{5},{2}] => 4
[{1},{5},{3},{4},{2}] => 5
[{1},{4},{5},{3},{2}] => 5
[{1},{5},{4},{3},{2}] => 6
[{2},{1},{3},{4},{5}] => 0
[{2},{1},{3},{5},{4}] => 3
[{2},{1},{4},{3},{5}] => 2
[{2},{1},{5},{3},{4}] => 4
[{2},{1},{4},{5},{3}] => 4
[{2},{1},{5},{4},{3}] => 6
[{3},{1},{2},{4},{5}] => 0
[{3},{1},{2},{5},{4}] => 3
[{4},{1},{2},{3},{5}] => 0
[{5},{1},{2},{3},{4}] => 0
[{4},{1},{2},{5},{3}] => 2
[{5},{1},{2},{4},{3}] => 2
[{3},{1},{4},{2},{5}] => 1
[{3},{1},{5},{2},{4}] => 3
[{4},{1},{3},{2},{5}] => 1
[{5},{1},{3},{2},{4}] => 1
[{4},{1},{5},{2},{3}] => 2
[{5},{1},{4},{2},{3}] => 2
[{3},{1},{4},{5},{2}] => 2
[{3},{1},{5},{4},{2}] => 4
[{4},{1},{3},{5},{2}] => 2
[{5},{1},{3},{4},{2}] => 2
[{4},{1},{5},{3},{2}] => 3
[{5},{1},{4},{3},{2}] => 3
[{2},{3},{1},{4},{5}] => 0
[{2},{3},{1},{5},{4}] => 3
[{2},{4},{1},{3},{5}] => 1
[{2},{5},{1},{3},{4}] => 2
[{2},{4},{1},{5},{3}] => 3
[{2},{5},{1},{4},{3}] => 4
[{3},{2},{1},{4},{5}] => 0
[{3},{2},{1},{5},{4}] => 3
[{4},{2},{1},{3},{5}] => 0
[{5},{2},{1},{3},{4}] => 0
[{4},{2},{1},{5},{3}] => 2
[{5},{2},{1},{4},{3}] => 2
[{3},{4},{1},{2},{5}] => 0
[{3},{5},{1},{2},{4}] => 1
[{4},{3},{1},{2},{5}] => 0
[{5},{3},{1},{2},{4}] => 0
[{4},{5},{1},{2},{3}] => 0
[{5},{4},{1},{2},{3}] => 0
[{3},{4},{1},{5},{2}] => 1
[{3},{5},{1},{4},{2}] => 2
[{4},{3},{1},{5},{2}] => 1
[{5},{3},{1},{4},{2}] => 1
[{4},{5},{1},{3},{2}] => 1
[{5},{4},{1},{3},{2}] => 1
[{2},{3},{4},{1},{5}] => 0
[{2},{3},{5},{1},{4}] => 2
[{2},{4},{3},{1},{5}] => 1
[{2},{5},{3},{1},{4}] => 2
[{2},{4},{5},{1},{3}] => 2
[{2},{5},{4},{1},{3}] => 3
[{3},{2},{4},{1},{5}] => 0
[{3},{2},{5},{1},{4}] => 2
[{4},{2},{3},{1},{5}] => 0
[{5},{2},{3},{1},{4}] => 0
[{4},{2},{5},{1},{3}] => 1
[{5},{2},{4},{1},{3}] => 1
[{3},{4},{2},{1},{5}] => 0
[{3},{5},{2},{1},{4}] => 1
[{4},{3},{2},{1},{5}] => 0
[{5},{3},{2},{1},{4}] => 0
[{4},{5},{2},{1},{3}] => 0
[{5},{4},{2},{1},{3}] => 0
[{3},{4},{5},{1},{2}] => 0
[{3},{5},{4},{1},{2}] => 1
[{4},{3},{5},{1},{2}] => 0
[{5},{3},{4},{1},{2}] => 0
[{4},{5},{3},{1},{2}] => 0
[{5},{4},{3},{1},{2}] => 0
[{2},{3},{4},{5},{1}] => 0
[{2},{3},{5},{4},{1}] => 2
[{2},{4},{3},{5},{1}] => 1
[{2},{5},{3},{4},{1}] => 2
[{2},{4},{5},{3},{1}] => 2
[{2},{5},{4},{3},{1}] => 3
[{3},{2},{4},{5},{1}] => 0
[{3},{2},{5},{4},{1}] => 2
[{4},{2},{3},{5},{1}] => 0
[{5},{2},{3},{4},{1}] => 0
[{4},{2},{5},{3},{1}] => 1
[{5},{2},{4},{3},{1}] => 1
[{3},{4},{2},{5},{1}] => 0
[{3},{5},{2},{4},{1}] => 1
[{4},{3},{2},{5},{1}] => 0
[{5},{3},{2},{4},{1}] => 0
[{4},{5},{2},{3},{1}] => 0
[{5},{4},{2},{3},{1}] => 0
[{3},{4},{5},{2},{1}] => 0
[{3},{5},{4},{2},{1}] => 1
[{4},{3},{5},{2},{1}] => 0
[{5},{3},{4},{2},{1}] => 0
[{4},{5},{3},{2},{1}] => 0
[{5},{4},{3},{2},{1}] => 0
[{1},{2},{3},{4,5}] => 0
[{1},{2},{4},{3,5}] => 2
[{1},{2},{5},{3,4}] => 4
[{1},{3},{2},{4,5}] => 1
[{1},{4},{2},{3,5}] => 2
[{1},{5},{2},{3,4}] => 3
[{1},{3},{4},{2,5}] => 2
[{1},{3},{5},{2,4}] => 4
[{1},{4},{3},{2,5}] => 3
[{1},{5},{3},{2,4}] => 4
[{1},{4},{5},{2,3}] => 4
[{1},{5},{4},{2,3}] => 5
[{2},{1},{3},{4,5}] => 0
[{2},{1},{4},{3,5}] => 2
[{2},{1},{5},{3,4}] => 4
[{3},{1},{2},{4,5}] => 0
[{4},{1},{2},{3,5}] => 0
[{5},{1},{2},{3,4}] => 0
[{3},{1},{4},{2,5}] => 1
[{3},{1},{5},{2,4}] => 3
[{4},{1},{3},{2,5}] => 1
[{5},{1},{3},{2,4}] => 1
[{4},{1},{5},{2,3}] => 2
[{5},{1},{4},{2,3}] => 2
[{2},{3},{1},{4,5}] => 0
[{2},{4},{1},{3,5}] => 1
[{2},{5},{1},{3,4}] => 2
[{3},{2},{1},{4,5}] => 0
[{4},{2},{1},{3,5}] => 0
[{5},{2},{1},{3,4}] => 0
[{3},{4},{1},{2,5}] => 0
[{3},{5},{1},{2,4}] => 1
[{4},{3},{1},{2,5}] => 0
[{5},{3},{1},{2,4}] => 0
[{4},{5},{1},{2,3}] => 0
[{5},{4},{1},{2,3}] => 0
[{2},{3},{4},{1,5}] => 0
[{2},{3},{5},{1,4}] => 2
[{2},{4},{3},{1,5}] => 1
[{2},{5},{3},{1,4}] => 2
[{2},{4},{5},{1,3}] => 2
[{2},{5},{4},{1,3}] => 3
[{3},{2},{4},{1,5}] => 0
[{3},{2},{5},{1,4}] => 2
[{4},{2},{3},{1,5}] => 0
[{5},{2},{3},{1,4}] => 0
[{4},{2},{5},{1,3}] => 1
[{5},{2},{4},{1,3}] => 1
[{3},{4},{2},{1,5}] => 0
[{3},{5},{2},{1,4}] => 1
[{4},{3},{2},{1,5}] => 0
[{5},{3},{2},{1,4}] => 0
[{4},{5},{2},{1,3}] => 0
[{5},{4},{2},{1,3}] => 0
[{3},{4},{5},{1,2}] => 0
[{3},{5},{4},{1,2}] => 1
[{4},{3},{5},{1,2}] => 0
[{5},{3},{4},{1,2}] => 0
[{4},{5},{3},{1,2}] => 0
[{5},{4},{3},{1,2}] => 0
[{1},{2},{3,4},{5}] => 0
[{1},{2},{3,5},{4}] => 2
[{1},{2},{4,5},{3}] => 4
[{1},{3},{2,4},{5}] => 1
[{1},{3},{2,5},{4}] => 3
[{1},{4},{2,3},{5}] => 2
[{1},{5},{2,3},{4}] => 3
[{1},{4},{2,5},{3}] => 3
[{1},{5},{2,4},{3}] => 4
[{1},{3},{4,5},{2}] => 3
[{1},{4},{3,5},{2}] => 4
[{1},{5},{3,4},{2}] => 5
[{2},{1},{3,4},{5}] => 0
[{2},{1},{3,5},{4}] => 2
[{2},{1},{4,5},{3}] => 4
[{3},{1},{2,4},{5}] => 0
[{3},{1},{2,5},{4}] => 2
[{4},{1},{2,3},{5}] => 0
[{5},{1},{2,3},{4}] => 0
[{4},{1},{2,5},{3}] => 1
[{5},{1},{2,4},{3}] => 1
[{3},{1},{4,5},{2}] => 2
[{4},{1},{3,5},{2}] => 2
[{5},{1},{3,4},{2}] => 2
[{2},{3},{1,4},{5}] => 0
[{2},{3},{1,5},{4}] => 2
[{2},{4},{1,3},{5}] => 1
[{2},{5},{1,3},{4}] => 2
[{2},{4},{1,5},{3}] => 2
[{2},{5},{1,4},{3}] => 3
[{3},{2},{1,4},{5}] => 0
[{3},{2},{1,5},{4}] => 2
[{4},{2},{1,3},{5}] => 0
[{5},{2},{1,3},{4}] => 0
[{4},{2},{1,5},{3}] => 1
[{5},{2},{1,4},{3}] => 1
[{3},{4},{1,2},{5}] => 0
[{3},{5},{1,2},{4}] => 1
[{4},{3},{1,2},{5}] => 0
[{5},{3},{1,2},{4}] => 0
[{4},{5},{1,2},{3}] => 0
[{5},{4},{1,2},{3}] => 0
[{3},{4},{1,5},{2}] => 0
[{3},{5},{1,4},{2}] => 1
[{4},{3},{1,5},{2}] => 0
[{5},{3},{1,4},{2}] => 0
[{4},{5},{1,3},{2}] => 0
[{5},{4},{1,3},{2}] => 0
[{2},{3},{4,5},{1}] => 0
[{2},{4},{3,5},{1}] => 1
[{2},{5},{3,4},{1}] => 2
[{3},{2},{4,5},{1}] => 0
[{4},{2},{3,5},{1}] => 0
[{5},{2},{3,4},{1}] => 0
[{3},{4},{2,5},{1}] => 0
[{3},{5},{2,4},{1}] => 1
[{4},{3},{2,5},{1}] => 0
[{5},{3},{2,4},{1}] => 0
[{4},{5},{2,3},{1}] => 0
[{5},{4},{2,3},{1}] => 0
[{1},{2},{3,4,5}] => 0
[{1},{3},{2,4,5}] => 1
[{1},{4},{2,3,5}] => 2
[{1},{5},{2,3,4}] => 3
[{2},{1},{3,4,5}] => 0
[{3},{1},{2,4,5}] => 0
[{4},{1},{2,3,5}] => 0
[{5},{1},{2,3,4}] => 0
[{2},{3},{1,4,5}] => 0
[{2},{4},{1,3,5}] => 1
[{2},{5},{1,3,4}] => 2
[{3},{2},{1,4,5}] => 0
[{4},{2},{1,3,5}] => 0
[{5},{2},{1,3,4}] => 0
[{3},{4},{1,2,5}] => 0
[{3},{5},{1,2,4}] => 1
[{4},{3},{1,2,5}] => 0
[{5},{3},{1,2,4}] => 0
[{4},{5},{1,2,3}] => 0
[{5},{4},{1,2,3}] => 0
[{1},{2,3},{4},{5}] => 0
[{1},{2,3},{5},{4}] => 3
[{1},{2,4},{3},{5}] => 1
[{1},{2,5},{3},{4}] => 2
[{1},{2,4},{5},{3}] => 3
[{1},{2,5},{4},{3}] => 4
[{1},{3,4},{2},{5}] => 2
[{1},{3,5},{2},{4}] => 3
[{1},{4,5},{2},{3}] => 4
[{1},{3,4},{5},{2}] => 3
[{1},{3,5},{4},{2}] => 4
[{1},{4,5},{3},{2}] => 5
[{2},{1,3},{4},{5}] => 0
[{2},{1,3},{5},{4}] => 3
[{2},{1,4},{3},{5}] => 1
[{2},{1,5},{3},{4}] => 2
[{2},{1,4},{5},{3}] => 3
[{2},{1,5},{4},{3}] => 4
[{3},{1,2},{4},{5}] => 0
[{3},{1,2},{5},{4}] => 3
[{4},{1,2},{3},{5}] => 0
[{5},{1,2},{3},{4}] => 0
[{4},{1,2},{5},{3}] => 2
[{5},{1,2},{4},{3}] => 2
[{3},{1,4},{2},{5}] => 0
[{3},{1,5},{2},{4}] => 1
[{4},{1,3},{2},{5}] => 0
[{5},{1,3},{2},{4}] => 0
[{4},{1,5},{2},{3}] => 0
[{5},{1,4},{2},{3}] => 0
[{3},{1,4},{5},{2}] => 1
[{3},{1,5},{4},{2}] => 2
[{4},{1,3},{5},{2}] => 1
[{5},{1,3},{4},{2}] => 1
[{4},{1,5},{3},{2}] => 1
[{5},{1,4},{3},{2}] => 1
[{2},{3,4},{1},{5}] => 0
[{2},{3,5},{1},{4}] => 1
[{2},{4,5},{1},{3}] => 2
[{3},{2,4},{1},{5}] => 0
[{3},{2,5},{1},{4}] => 1
[{4},{2,3},{1},{5}] => 0
[{5},{2,3},{1},{4}] => 0
[{4},{2,5},{1},{3}] => 0
[{5},{2,4},{1},{3}] => 0
[{3},{4,5},{1},{2}] => 0
[{4},{3,5},{1},{2}] => 0
[{5},{3,4},{1},{2}] => 0
[{2},{3,4},{5},{1}] => 0
[{2},{3,5},{4},{1}] => 1
[{2},{4,5},{3},{1}] => 2
[{3},{2,4},{5},{1}] => 0
[{3},{2,5},{4},{1}] => 1
[{4},{2,3},{5},{1}] => 0
[{5},{2,3},{4},{1}] => 0
[{4},{2,5},{3},{1}] => 0
[{5},{2,4},{3},{1}] => 0
[{3},{4,5},{2},{1}] => 0
[{4},{3,5},{2},{1}] => 0
[{5},{3,4},{2},{1}] => 0
[{1},{2,3},{4,5}] => 0
[{1},{2,4},{3,5}] => 1
[{1},{2,5},{3,4}] => 2
[{1},{3,4},{2,5}] => 2
[{1},{3,5},{2,4}] => 3
[{1},{4,5},{2,3}] => 4
[{2},{1,3},{4,5}] => 0
[{2},{1,4},{3,5}] => 1
[{2},{1,5},{3,4}] => 2
[{3},{1,2},{4,5}] => 0
[{4},{1,2},{3,5}] => 0
[{5},{1,2},{3,4}] => 0
[{3},{1,4},{2,5}] => 0
[{3},{1,5},{2,4}] => 1
[{4},{1,3},{2,5}] => 0
[{5},{1,3},{2,4}] => 0
[{4},{1,5},{2,3}] => 0
[{5},{1,4},{2,3}] => 0
[{2},{3,4},{1,5}] => 0
[{2},{3,5},{1,4}] => 1
[{2},{4,5},{1,3}] => 2
[{3},{2,4},{1,5}] => 0
[{3},{2,5},{1,4}] => 1
[{4},{2,3},{1,5}] => 0
[{5},{2,3},{1,4}] => 0
[{4},{2,5},{1,3}] => 0
[{5},{2,4},{1,3}] => 0
[{3},{4,5},{1,2}] => 0
[{4},{3,5},{1,2}] => 0
[{5},{3,4},{1,2}] => 0
[{1},{2,3,4},{5}] => 0
[{1},{2,3,5},{4}] => 1
[{1},{2,4,5},{3}] => 2
[{1},{3,4,5},{2}] => 3
[{2},{1,3,4},{5}] => 0
[{2},{1,3,5},{4}] => 1
[{2},{1,4,5},{3}] => 2
[{3},{1,2,4},{5}] => 0
[{3},{1,2,5},{4}] => 1
[{4},{1,2,3},{5}] => 0
[{5},{1,2,3},{4}] => 0
[{4},{1,2,5},{3}] => 0
[{5},{1,2,4},{3}] => 0
[{3},{1,4,5},{2}] => 0
[{4},{1,3,5},{2}] => 0
[{5},{1,3,4},{2}] => 0
[{2},{3,4,5},{1}] => 0
[{3},{2,4,5},{1}] => 0
[{4},{2,3,5},{1}] => 0
[{5},{2,3,4},{1}] => 0
[{1},{2,3,4,5}] => 0
[{2},{1,3,4,5}] => 0
[{3},{1,2,4,5}] => 0
[{4},{1,2,3,5}] => 0
[{5},{1,2,3,4}] => 0
[{1,2},{3},{4},{5}] => 0
[{1,2},{3},{5},{4}] => 3
[{1,2},{4},{3},{5}] => 2
[{1,2},{5},{3},{4}] => 4
[{1,2},{4},{5},{3}] => 4
[{1,2},{5},{4},{3}] => 6
[{1,3},{2},{4},{5}] => 0
[{1,3},{2},{5},{4}] => 3
[{1,4},{2},{3},{5}] => 0
[{1,5},{2},{3},{4}] => 0
[{1,4},{2},{5},{3}] => 2
[{1,5},{2},{4},{3}] => 2
[{1,3},{4},{2},{5}] => 1
[{1,3},{5},{2},{4}] => 3
[{1,4},{3},{2},{5}] => 1
[{1,5},{3},{2},{4}] => 1
[{1,4},{5},{2},{3}] => 2
[{1,5},{4},{2},{3}] => 2
[{1,3},{4},{5},{2}] => 2
[{1,3},{5},{4},{2}] => 4
[{1,4},{3},{5},{2}] => 2
[{1,5},{3},{4},{2}] => 2
[{1,4},{5},{3},{2}] => 3
[{1,5},{4},{3},{2}] => 3
[{2,3},{1},{4},{5}] => 0
[{2,3},{1},{5},{4}] => 3
[{2,4},{1},{3},{5}] => 0
[{2,5},{1},{3},{4}] => 0
[{2,4},{1},{5},{3}] => 2
[{2,5},{1},{4},{3}] => 2
[{3,4},{1},{2},{5}] => 0
[{3,5},{1},{2},{4}] => 0
[{4,5},{1},{2},{3}] => 0
[{3,4},{1},{5},{2}] => 1
[{3,5},{1},{4},{2}] => 1
[{4,5},{1},{3},{2}] => 1
[{2,3},{4},{1},{5}] => 0
[{2,3},{5},{1},{4}] => 2
[{2,4},{3},{1},{5}] => 0
[{2,5},{3},{1},{4}] => 0
[{2,4},{5},{1},{3}] => 1
[{2,5},{4},{1},{3}] => 1
[{3,4},{2},{1},{5}] => 0
[{3,5},{2},{1},{4}] => 0
[{4,5},{2},{1},{3}] => 0
[{3,4},{5},{1},{2}] => 0
[{3,5},{4},{1},{2}] => 0
[{4,5},{3},{1},{2}] => 0
[{2,3},{4},{5},{1}] => 0
[{2,3},{5},{4},{1}] => 2
[{2,4},{3},{5},{1}] => 0
[{2,5},{3},{4},{1}] => 0
[{2,4},{5},{3},{1}] => 1
[{2,5},{4},{3},{1}] => 1
[{3,4},{2},{5},{1}] => 0
[{3,5},{2},{4},{1}] => 0
[{4,5},{2},{3},{1}] => 0
[{3,4},{5},{2},{1}] => 0
[{3,5},{4},{2},{1}] => 0
[{4,5},{3},{2},{1}] => 0
[{1,2},{3},{4,5}] => 0
[{1,2},{4},{3,5}] => 2
[{1,2},{5},{3,4}] => 4
[{1,3},{2},{4,5}] => 0
[{1,4},{2},{3,5}] => 0
[{1,5},{2},{3,4}] => 0
[{1,3},{4},{2,5}] => 1
[{1,3},{5},{2,4}] => 3
[{1,4},{3},{2,5}] => 1
[{1,5},{3},{2,4}] => 1
[{1,4},{5},{2,3}] => 2
[{1,5},{4},{2,3}] => 2
[{2,3},{1},{4,5}] => 0
[{2,4},{1},{3,5}] => 0
[{2,5},{1},{3,4}] => 0
[{3,4},{1},{2,5}] => 0
[{3,5},{1},{2,4}] => 0
[{4,5},{1},{2,3}] => 0
[{2,3},{4},{1,5}] => 0
[{2,3},{5},{1,4}] => 2
[{2,4},{3},{1,5}] => 0
[{2,5},{3},{1,4}] => 0
[{2,4},{5},{1,3}] => 1
[{2,5},{4},{1,3}] => 1
[{3,4},{2},{1,5}] => 0
[{3,5},{2},{1,4}] => 0
[{4,5},{2},{1,3}] => 0
[{3,4},{5},{1,2}] => 0
[{3,5},{4},{1,2}] => 0
[{4,5},{3},{1,2}] => 0
[{1,2},{3,4},{5}] => 0
[{1,2},{3,5},{4}] => 2
[{1,2},{4,5},{3}] => 4
[{1,3},{2,4},{5}] => 0
[{1,3},{2,5},{4}] => 2
[{1,4},{2,3},{5}] => 0
[{1,5},{2,3},{4}] => 0
[{1,4},{2,5},{3}] => 1
[{1,5},{2,4},{3}] => 1
[{1,3},{4,5},{2}] => 2
[{1,4},{3,5},{2}] => 2
[{1,5},{3,4},{2}] => 2
[{2,3},{1,4},{5}] => 0
[{2,3},{1,5},{4}] => 2
[{2,4},{1,3},{5}] => 0
[{2,5},{1,3},{4}] => 0
[{2,4},{1,5},{3}] => 1
[{2,5},{1,4},{3}] => 1
[{3,4},{1,2},{5}] => 0
[{3,5},{1,2},{4}] => 0
[{4,5},{1,2},{3}] => 0
[{3,4},{1,5},{2}] => 0
[{3,5},{1,4},{2}] => 0
[{4,5},{1,3},{2}] => 0
[{2,3},{4,5},{1}] => 0
[{2,4},{3,5},{1}] => 0
[{2,5},{3,4},{1}] => 0
[{3,4},{2,5},{1}] => 0
[{3,5},{2,4},{1}] => 0
[{4,5},{2,3},{1}] => 0
[{1,2},{3,4,5}] => 0
[{1,3},{2,4,5}] => 0
[{1,4},{2,3,5}] => 0
[{1,5},{2,3,4}] => 0
[{2,3},{1,4,5}] => 0
[{2,4},{1,3,5}] => 0
[{2,5},{1,3,4}] => 0
[{3,4},{1,2,5}] => 0
[{3,5},{1,2,4}] => 0
[{4,5},{1,2,3}] => 0
[{1,2,3},{4},{5}] => 0
[{1,2,3},{5},{4}] => 3
[{1,2,4},{3},{5}] => 0
[{1,2,5},{3},{4}] => 0
[{1,2,4},{5},{3}] => 2
[{1,2,5},{4},{3}] => 2
[{1,3,4},{2},{5}] => 0
[{1,3,5},{2},{4}] => 0
[{1,4,5},{2},{3}] => 0
[{1,3,4},{5},{2}] => 1
[{1,3,5},{4},{2}] => 1
[{1,4,5},{3},{2}] => 1
[{2,3,4},{1},{5}] => 0
[{2,3,5},{1},{4}] => 0
[{2,4,5},{1},{3}] => 0
[{3,4,5},{1},{2}] => 0
[{2,3,4},{5},{1}] => 0
[{2,3,5},{4},{1}] => 0
[{2,4,5},{3},{1}] => 0
[{3,4,5},{2},{1}] => 0
[{1,2,3},{4,5}] => 0
[{1,2,4},{3,5}] => 0
[{1,2,5},{3,4}] => 0
[{1,3,4},{2,5}] => 0
[{1,3,5},{2,4}] => 0
[{1,4,5},{2,3}] => 0
[{2,3,4},{1,5}] => 0
[{2,3,5},{1,4}] => 0
[{2,4,5},{1,3}] => 0
[{3,4,5},{1,2}] => 0
[{1,2,3,4},{5}] => 0
[{1,2,3,5},{4}] => 0
[{1,2,4,5},{3}] => 0
[{1,3,4,5},{2}] => 0
[{2,3,4,5},{1}] => 0
[{1,2,3,4,5}] => 0
[{1},{2},{3},{4},{5},{6}] => 0
[{1},{2},{3},{4},{6},{5}] => 4
[{1},{2},{3},{5},{4},{6}] => 3
[{1},{2},{3},{6},{4},{5}] => 6
[{1},{2},{3},{5},{6},{4}] => 6
[{1},{2},{3},{6},{5},{4}] => 9
[{1},{2},{4},{3},{5},{6}] => 2
[{1},{2},{4},{3},{6},{5}] => 6
[{1},{2},{5},{3},{4},{6}] => 4
[{1},{2},{6},{3},{4},{5}] => 6
[{1},{2},{5},{3},{6},{4}] => 7
[{1},{2},{6},{3},{5},{4}] => 9
[{1},{2},{4},{5},{3},{6}] => 4
[{1},{2},{4},{6},{3},{5}] => 7
[{1},{2},{5},{4},{3},{6}] => 6
[{1},{2},{6},{4},{3},{5}] => 8
[{1},{2},{5},{6},{3},{4}] => 8
[{1},{2},{6},{5},{3},{4}] => 10
[{1},{2},{4},{5},{6},{3}] => 6
[{1},{2},{4},{6},{5},{3}] => 9
[{1},{2},{5},{4},{6},{3}] => 8
[{1},{2},{6},{4},{5},{3}] => 10
[{1},{2},{5},{6},{4},{3}] => 10
[{1},{2},{6},{5},{4},{3}] => 12
[{1},{3},{2},{4},{5},{6}] => 1
[{1},{3},{2},{4},{6},{5}] => 5
[{1},{3},{2},{5},{4},{6}] => 4
[{1},{3},{2},{6},{4},{5}] => 7
[{1},{3},{2},{5},{6},{4}] => 7
[{1},{3},{2},{6},{5},{4}] => 10
[{1},{4},{2},{3},{5},{6}] => 2
[{1},{4},{2},{3},{6},{5}] => 6
[{1},{5},{2},{3},{4},{6}] => 3
[{1},{6},{2},{3},{4},{5}] => 4
[{1},{5},{2},{3},{6},{4}] => 6
[{1},{6},{2},{3},{5},{4}] => 7
[{1},{4},{2},{5},{3},{6}] => 4
[{1},{4},{2},{6},{3},{5}] => 7
[{1},{5},{2},{4},{3},{6}] => 5
[{1},{6},{2},{4},{3},{5}] => 6
[{1},{5},{2},{6},{3},{4}] => 7
[{1},{6},{2},{5},{3},{4}] => 8
[{1},{4},{2},{5},{6},{3}] => 6
[{1},{4},{2},{6},{5},{3}] => 9
[{1},{5},{2},{4},{6},{3}] => 7
[{1},{6},{2},{4},{5},{3}] => 8
[{1},{5},{2},{6},{4},{3}] => 9
[{1},{6},{2},{5},{4},{3}] => 10
[{1},{3},{4},{2},{5},{6}] => 2
[{1},{3},{4},{2},{6},{5}] => 6
[{1},{3},{5},{2},{4},{6}] => 4
[{1},{3},{6},{2},{4},{5}] => 6
[{1},{3},{5},{2},{6},{4}] => 7
[{1},{3},{6},{2},{5},{4}] => 9
[{1},{4},{3},{2},{5},{6}] => 3
[{1},{4},{3},{2},{6},{5}] => 7
[{1},{5},{3},{2},{4},{6}] => 4
[{1},{6},{3},{2},{4},{5}] => 5
[{1},{5},{3},{2},{6},{4}] => 7
[{1},{6},{3},{2},{5},{4}] => 8
[{1},{4},{5},{2},{3},{6}] => 4
[{1},{4},{6},{2},{3},{5}] => 6
[{1},{5},{4},{2},{3},{6}] => 5
[{1},{6},{4},{2},{3},{5}] => 6
[{1},{5},{6},{2},{3},{4}] => 6
[{1},{6},{5},{2},{3},{4}] => 7
[{1},{4},{5},{2},{6},{3}] => 6
[{1},{4},{6},{2},{5},{3}] => 8
[{1},{5},{4},{2},{6},{3}] => 7
[{1},{6},{4},{2},{5},{3}] => 8
[{1},{5},{6},{2},{4},{3}] => 8
[{1},{6},{5},{2},{4},{3}] => 9
[{1},{3},{4},{5},{2},{6}] => 3
[{1},{3},{4},{6},{2},{5}] => 6
[{1},{3},{5},{4},{2},{6}] => 5
[{1},{3},{6},{4},{2},{5}] => 7
[{1},{3},{5},{6},{2},{4}] => 7
[{1},{3},{6},{5},{2},{4}] => 9
[{1},{4},{3},{5},{2},{6}] => 4
[{1},{4},{3},{6},{2},{5}] => 7
[{1},{5},{3},{4},{2},{6}] => 5
[{1},{6},{3},{4},{2},{5}] => 6
[{1},{5},{3},{6},{2},{4}] => 7
[{1},{6},{3},{5},{2},{4}] => 8
[{1},{4},{5},{3},{2},{6}] => 5
[{1},{4},{6},{3},{2},{5}] => 7
[{1},{5},{4},{3},{2},{6}] => 6
[{1},{6},{4},{3},{2},{5}] => 7
[{1},{5},{6},{3},{2},{4}] => 7
[{1},{6},{5},{3},{2},{4}] => 8
[{1},{4},{5},{6},{2},{3}] => 6
[{1},{4},{6},{5},{2},{3}] => 8
[{1},{5},{4},{6},{2},{3}] => 7
[{1},{6},{4},{5},{2},{3}] => 8
[{1},{5},{6},{4},{2},{3}] => 8
[{1},{6},{5},{4},{2},{3}] => 9
[{1},{3},{4},{5},{6},{2}] => 4
[{1},{3},{4},{6},{5},{2}] => 7
[{1},{3},{5},{4},{6},{2}] => 6
[{1},{3},{6},{4},{5},{2}] => 8
[{1},{3},{5},{6},{4},{2}] => 8
[{1},{3},{6},{5},{4},{2}] => 10
[{1},{4},{3},{5},{6},{2}] => 5
[{1},{4},{3},{6},{5},{2}] => 8
[{1},{5},{3},{4},{6},{2}] => 6
[{1},{6},{3},{4},{5},{2}] => 7
[{1},{5},{3},{6},{4},{2}] => 8
[{1},{6},{3},{5},{4},{2}] => 9
[{1},{4},{5},{3},{6},{2}] => 6
[{1},{4},{6},{3},{5},{2}] => 8
[{1},{5},{4},{3},{6},{2}] => 7
[{1},{6},{4},{3},{5},{2}] => 8
[{1},{5},{6},{3},{4},{2}] => 8
[{1},{6},{5},{3},{4},{2}] => 9
[{1},{4},{5},{6},{3},{2}] => 7
[{1},{4},{6},{5},{3},{2}] => 9
[{1},{5},{4},{6},{3},{2}] => 8
[{1},{6},{4},{5},{3},{2}] => 9
[{1},{5},{6},{4},{3},{2}] => 9
[{1},{6},{5},{4},{3},{2}] => 10
[{2},{1},{3},{4},{5},{6}] => 0
[{2},{1},{3},{4},{6},{5}] => 4
[{2},{1},{3},{5},{4},{6}] => 3
[{2},{1},{3},{6},{4},{5}] => 6
[{2},{1},{3},{5},{6},{4}] => 6
[{2},{1},{3},{6},{5},{4}] => 9
[{2},{1},{4},{3},{5},{6}] => 2
[{2},{1},{4},{3},{6},{5}] => 6
[{2},{1},{5},{3},{4},{6}] => 4
[{2},{1},{6},{3},{4},{5}] => 6
[{2},{1},{5},{3},{6},{4}] => 7
[{2},{1},{6},{3},{5},{4}] => 9
[{2},{1},{4},{5},{3},{6}] => 4
[{2},{1},{4},{6},{3},{5}] => 7
[{2},{1},{5},{4},{3},{6}] => 6
[{2},{1},{6},{4},{3},{5}] => 8
[{2},{1},{5},{6},{3},{4}] => 8
[{2},{1},{6},{5},{3},{4}] => 10
[{2},{1},{4},{5},{6},{3}] => 6
[{2},{1},{4},{6},{5},{3}] => 9
[{2},{1},{5},{4},{6},{3}] => 8
[{2},{1},{6},{4},{5},{3}] => 10
[{2},{1},{5},{6},{4},{3}] => 10
[{2},{1},{6},{5},{4},{3}] => 12
[{3},{1},{2},{4},{5},{6}] => 0
[{3},{1},{2},{4},{6},{5}] => 4
[{3},{1},{2},{5},{4},{6}] => 3
[{3},{1},{2},{6},{4},{5}] => 6
[{3},{1},{2},{5},{6},{4}] => 6
[{3},{1},{2},{6},{5},{4}] => 9
[{4},{1},{2},{3},{5},{6}] => 0
[{4},{1},{2},{3},{6},{5}] => 4
[{5},{1},{2},{3},{4},{6}] => 0
[{6},{1},{2},{3},{4},{5}] => 0
[{5},{1},{2},{3},{6},{4}] => 3
[{6},{1},{2},{3},{5},{4}] => 3
[{4},{1},{2},{5},{3},{6}] => 2
[{4},{1},{2},{6},{3},{5}] => 5
[{5},{1},{2},{4},{3},{6}] => 2
[{6},{1},{2},{4},{3},{5}] => 2
[{5},{1},{2},{6},{3},{4}] => 4
[{6},{1},{2},{5},{3},{4}] => 4
[{4},{1},{2},{5},{6},{3}] => 4
[{4},{1},{2},{6},{5},{3}] => 7
[{5},{1},{2},{4},{6},{3}] => 4
[{6},{1},{2},{4},{5},{3}] => 4
[{5},{1},{2},{6},{4},{3}] => 6
[{6},{1},{2},{5},{4},{3}] => 6
[{3},{1},{4},{2},{5},{6}] => 1
[{3},{1},{4},{2},{6},{5}] => 5
[{3},{1},{5},{2},{4},{6}] => 3
[{3},{1},{6},{2},{4},{5}] => 5
[{3},{1},{5},{2},{6},{4}] => 6
[{3},{1},{6},{2},{5},{4}] => 8
[{4},{1},{3},{2},{5},{6}] => 1
[{4},{1},{3},{2},{6},{5}] => 5
[{5},{1},{3},{2},{4},{6}] => 1
[{6},{1},{3},{2},{4},{5}] => 1
[{5},{1},{3},{2},{6},{4}] => 4
[{6},{1},{3},{2},{5},{4}] => 4
[{4},{1},{5},{2},{3},{6}] => 2
[{4},{1},{6},{2},{3},{5}] => 4
[{5},{1},{4},{2},{3},{6}] => 2
[{6},{1},{4},{2},{3},{5}] => 2
[{5},{1},{6},{2},{3},{4}] => 3
[{6},{1},{5},{2},{3},{4}] => 3
[{4},{1},{5},{2},{6},{3}] => 4
[{4},{1},{6},{2},{5},{3}] => 6
[{5},{1},{4},{2},{6},{3}] => 4
[{6},{1},{4},{2},{5},{3}] => 4
[{5},{1},{6},{2},{4},{3}] => 5
[{6},{1},{5},{2},{4},{3}] => 5
[{3},{1},{4},{5},{2},{6}] => 2
[{3},{1},{4},{6},{2},{5}] => 5
[{3},{1},{5},{4},{2},{6}] => 4
[{3},{1},{6},{4},{2},{5}] => 6
[{3},{1},{5},{6},{2},{4}] => 6
[{3},{1},{6},{5},{2},{4}] => 8
[{4},{1},{3},{5},{2},{6}] => 2
[{4},{1},{3},{6},{2},{5}] => 5
[{5},{1},{3},{4},{2},{6}] => 2
[{6},{1},{3},{4},{2},{5}] => 2
[{5},{1},{3},{6},{2},{4}] => 4
[{6},{1},{3},{5},{2},{4}] => 4
[{4},{1},{5},{3},{2},{6}] => 3
[{4},{1},{6},{3},{2},{5}] => 5
[{5},{1},{4},{3},{2},{6}] => 3
[{6},{1},{4},{3},{2},{5}] => 3
[{5},{1},{6},{3},{2},{4}] => 4
[{6},{1},{5},{3},{2},{4}] => 4
[{4},{1},{5},{6},{2},{3}] => 4
[{4},{1},{6},{5},{2},{3}] => 6
[{5},{1},{4},{6},{2},{3}] => 4
[{6},{1},{4},{5},{2},{3}] => 4
[{5},{1},{6},{4},{2},{3}] => 5
[{6},{1},{5},{4},{2},{3}] => 5
[{3},{1},{4},{5},{6},{2}] => 3
[{3},{1},{4},{6},{5},{2}] => 6
[{3},{1},{5},{4},{6},{2}] => 5
[{3},{1},{6},{4},{5},{2}] => 7
[{3},{1},{5},{6},{4},{2}] => 7
[{3},{1},{6},{5},{4},{2}] => 9
[{4},{1},{3},{5},{6},{2}] => 3
[{4},{1},{3},{6},{5},{2}] => 6
[{5},{1},{3},{4},{6},{2}] => 3
[{6},{1},{3},{4},{5},{2}] => 3
[{5},{1},{3},{6},{4},{2}] => 5
[{6},{1},{3},{5},{4},{2}] => 5
[{4},{1},{5},{3},{6},{2}] => 4
[{4},{1},{6},{3},{5},{2}] => 6
[{5},{1},{4},{3},{6},{2}] => 4
[{6},{1},{4},{3},{5},{2}] => 4
[{5},{1},{6},{3},{4},{2}] => 5
[{6},{1},{5},{3},{4},{2}] => 5
[{4},{1},{5},{6},{3},{2}] => 5
[{4},{1},{6},{5},{3},{2}] => 7
[{5},{1},{4},{6},{3},{2}] => 5
[{6},{1},{4},{5},{3},{2}] => 5
[{5},{1},{6},{4},{3},{2}] => 6
[{6},{1},{5},{4},{3},{2}] => 6
[{2},{3},{1},{4},{5},{6}] => 0
[{2},{3},{1},{4},{6},{5}] => 4
[{2},{3},{1},{5},{4},{6}] => 3
[{2},{3},{1},{6},{4},{5}] => 6
[{2},{3},{1},{5},{6},{4}] => 6
[{2},{3},{1},{6},{5},{4}] => 9
[{2},{4},{1},{3},{5},{6}] => 1
[{2},{4},{1},{3},{6},{5}] => 5
[{2},{5},{1},{3},{4},{6}] => 2
[{2},{6},{1},{3},{4},{5}] => 3
[{2},{5},{1},{3},{6},{4}] => 5
[{2},{6},{1},{3},{5},{4}] => 6
[{2},{4},{1},{5},{3},{6}] => 3
[{2},{4},{1},{6},{3},{5}] => 6
[{2},{5},{1},{4},{3},{6}] => 4
[{2},{6},{1},{4},{3},{5}] => 5
[{2},{5},{1},{6},{3},{4}] => 6
[{2},{6},{1},{5},{3},{4}] => 7
[{2},{4},{1},{5},{6},{3}] => 5
[{2},{4},{1},{6},{5},{3}] => 8
[{2},{5},{1},{4},{6},{3}] => 6
[{2},{6},{1},{4},{5},{3}] => 7
[{2},{5},{1},{6},{4},{3}] => 8
[{2},{6},{1},{5},{4},{3}] => 9
[{3},{2},{1},{4},{5},{6}] => 0
[{3},{2},{1},{4},{6},{5}] => 4
[{3},{2},{1},{5},{4},{6}] => 3
[{3},{2},{1},{6},{4},{5}] => 6
[{3},{2},{1},{5},{6},{4}] => 6
[{3},{2},{1},{6},{5},{4}] => 9
[{4},{2},{1},{3},{5},{6}] => 0
[{4},{2},{1},{3},{6},{5}] => 4
[{5},{2},{1},{3},{4},{6}] => 0
[{6},{2},{1},{3},{4},{5}] => 0
[{5},{2},{1},{3},{6},{4}] => 3
[{6},{2},{1},{3},{5},{4}] => 3
[{4},{2},{1},{5},{3},{6}] => 2
[{4},{2},{1},{6},{3},{5}] => 5
[{5},{2},{1},{4},{3},{6}] => 2
[{6},{2},{1},{4},{3},{5}] => 2
[{5},{2},{1},{6},{3},{4}] => 4
[{6},{2},{1},{5},{3},{4}] => 4
[{4},{2},{1},{5},{6},{3}] => 4
[{4},{2},{1},{6},{5},{3}] => 7
[{5},{2},{1},{4},{6},{3}] => 4
[{6},{2},{1},{4},{5},{3}] => 4
[{5},{2},{1},{6},{4},{3}] => 6
[{6},{2},{1},{5},{4},{3}] => 6
[{3},{4},{1},{2},{5},{6}] => 0
[{3},{4},{1},{2},{6},{5}] => 4
[{3},{5},{1},{2},{4},{6}] => 1
[{3},{6},{1},{2},{4},{5}] => 2
[{3},{5},{1},{2},{6},{4}] => 4
[{3},{6},{1},{2},{5},{4}] => 5
[{4},{3},{1},{2},{5},{6}] => 0
[{4},{3},{1},{2},{6},{5}] => 4
[{5},{3},{1},{2},{4},{6}] => 0
[{6},{3},{1},{2},{4},{5}] => 0
[{5},{3},{1},{2},{6},{4}] => 3
[{6},{3},{1},{2},{5},{4}] => 3
[{4},{5},{1},{2},{3},{6}] => 0
[{4},{6},{1},{2},{3},{5}] => 1
[{5},{4},{1},{2},{3},{6}] => 0
[{6},{4},{1},{2},{3},{5}] => 0
[{5},{6},{1},{2},{3},{4}] => 0
[{6},{5},{1},{2},{3},{4}] => 0
[{4},{5},{1},{2},{6},{3}] => 2
[{4},{6},{1},{2},{5},{3}] => 3
[{5},{4},{1},{2},{6},{3}] => 2
[{6},{4},{1},{2},{5},{3}] => 2
[{5},{6},{1},{2},{4},{3}] => 2
[{6},{5},{1},{2},{4},{3}] => 2
[{3},{4},{1},{5},{2},{6}] => 1
[{3},{4},{1},{6},{2},{5}] => 4
[{3},{5},{1},{4},{2},{6}] => 2
[{3},{6},{1},{4},{2},{5}] => 3
[{3},{5},{1},{6},{2},{4}] => 4
[{3},{6},{1},{5},{2},{4}] => 5
[{4},{3},{1},{5},{2},{6}] => 1
[{4},{3},{1},{6},{2},{5}] => 4
[{5},{3},{1},{4},{2},{6}] => 1
[{6},{3},{1},{4},{2},{5}] => 1
[{5},{3},{1},{6},{2},{4}] => 3
[{6},{3},{1},{5},{2},{4}] => 3
[{4},{5},{1},{3},{2},{6}] => 1
[{4},{6},{1},{3},{2},{5}] => 2
[{5},{4},{1},{3},{2},{6}] => 1
[{6},{4},{1},{3},{2},{5}] => 1
[{5},{6},{1},{3},{2},{4}] => 1
[{6},{5},{1},{3},{2},{4}] => 1
[{4},{5},{1},{6},{2},{3}] => 2
[{4},{6},{1},{5},{2},{3}] => 3
[{5},{4},{1},{6},{2},{3}] => 2
[{6},{4},{1},{5},{2},{3}] => 2
[{5},{6},{1},{4},{2},{3}] => 2
[{6},{5},{1},{4},{2},{3}] => 2
[{3},{4},{1},{5},{6},{2}] => 2
[{3},{4},{1},{6},{5},{2}] => 5
[{3},{5},{1},{4},{6},{2}] => 3
[{3},{6},{1},{4},{5},{2}] => 4
[{3},{5},{1},{6},{4},{2}] => 5
[{3},{6},{1},{5},{4},{2}] => 6
[{4},{3},{1},{5},{6},{2}] => 2
[{4},{3},{1},{6},{5},{2}] => 5
[{5},{3},{1},{4},{6},{2}] => 2
[{6},{3},{1},{4},{5},{2}] => 2
[{5},{3},{1},{6},{4},{2}] => 4
[{6},{3},{1},{5},{4},{2}] => 4
[{4},{5},{1},{3},{6},{2}] => 2
[{4},{6},{1},{3},{5},{2}] => 3
[{5},{4},{1},{3},{6},{2}] => 2
[{6},{4},{1},{3},{5},{2}] => 2
[{5},{6},{1},{3},{4},{2}] => 2
[{6},{5},{1},{3},{4},{2}] => 2
[{4},{5},{1},{6},{3},{2}] => 3
[{4},{6},{1},{5},{3},{2}] => 4
[{5},{4},{1},{6},{3},{2}] => 3
[{6},{4},{1},{5},{3},{2}] => 3
[{5},{6},{1},{4},{3},{2}] => 3
[{6},{5},{1},{4},{3},{2}] => 3
[{2},{3},{4},{1},{5},{6}] => 0
[{2},{3},{4},{1},{6},{5}] => 4
[{2},{3},{5},{1},{4},{6}] => 2
[{2},{3},{6},{1},{4},{5}] => 4
[{2},{3},{5},{1},{6},{4}] => 5
[{2},{3},{6},{1},{5},{4}] => 7
[{2},{4},{3},{1},{5},{6}] => 1
[{2},{4},{3},{1},{6},{5}] => 5
[{2},{5},{3},{1},{4},{6}] => 2
[{2},{6},{3},{1},{4},{5}] => 3
[{2},{5},{3},{1},{6},{4}] => 5
[{2},{6},{3},{1},{5},{4}] => 6
[{2},{4},{5},{1},{3},{6}] => 2
[{2},{4},{6},{1},{3},{5}] => 4
[{2},{5},{4},{1},{3},{6}] => 3
[{2},{6},{4},{1},{3},{5}] => 4
[{2},{5},{6},{1},{3},{4}] => 4
[{2},{6},{5},{1},{3},{4}] => 5
[{2},{4},{5},{1},{6},{3}] => 4
[{2},{4},{6},{1},{5},{3}] => 6
[{2},{5},{4},{1},{6},{3}] => 5
[{2},{6},{4},{1},{5},{3}] => 6
[{2},{5},{6},{1},{4},{3}] => 6
[{2},{6},{5},{1},{4},{3}] => 7
[{3},{2},{4},{1},{5},{6}] => 0
[{3},{2},{4},{1},{6},{5}] => 4
[{3},{2},{5},{1},{4},{6}] => 2
[{3},{2},{6},{1},{4},{5}] => 4
[{3},{2},{5},{1},{6},{4}] => 5
[{3},{2},{6},{1},{5},{4}] => 7
[{4},{2},{3},{1},{5},{6}] => 0
[{4},{2},{3},{1},{6},{5}] => 4
[{5},{2},{3},{1},{4},{6}] => 0
[{6},{2},{3},{1},{4},{5}] => 0
[{5},{2},{3},{1},{6},{4}] => 3
[{6},{2},{3},{1},{5},{4}] => 3
[{4},{2},{5},{1},{3},{6}] => 1
[{4},{2},{6},{1},{3},{5}] => 3
[{5},{2},{4},{1},{3},{6}] => 1
[{6},{2},{4},{1},{3},{5}] => 1
[{5},{2},{6},{1},{3},{4}] => 2
[{6},{2},{5},{1},{3},{4}] => 2
[{4},{2},{5},{1},{6},{3}] => 3
[{4},{2},{6},{1},{5},{3}] => 5
[{5},{2},{4},{1},{6},{3}] => 3
[{6},{2},{4},{1},{5},{3}] => 3
[{5},{2},{6},{1},{4},{3}] => 4
[{6},{2},{5},{1},{4},{3}] => 4
[{3},{4},{2},{1},{5},{6}] => 0
[{3},{4},{2},{1},{6},{5}] => 4
[{3},{5},{2},{1},{4},{6}] => 1
[{3},{6},{2},{1},{4},{5}] => 2
[{3},{5},{2},{1},{6},{4}] => 4
[{3},{6},{2},{1},{5},{4}] => 5
[{4},{3},{2},{1},{5},{6}] => 0
[{4},{3},{2},{1},{6},{5}] => 4
[{5},{3},{2},{1},{4},{6}] => 0
[{6},{3},{2},{1},{4},{5}] => 0
[{5},{3},{2},{1},{6},{4}] => 3
[{6},{3},{2},{1},{5},{4}] => 3
[{4},{5},{2},{1},{3},{6}] => 0
[{4},{6},{2},{1},{3},{5}] => 1
[{5},{4},{2},{1},{3},{6}] => 0
[{6},{4},{2},{1},{3},{5}] => 0
[{5},{6},{2},{1},{3},{4}] => 0
[{6},{5},{2},{1},{3},{4}] => 0
[{4},{5},{2},{1},{6},{3}] => 2
[{4},{6},{2},{1},{5},{3}] => 3
[{5},{4},{2},{1},{6},{3}] => 2
[{6},{4},{2},{1},{5},{3}] => 2
[{5},{6},{2},{1},{4},{3}] => 2
[{6},{5},{2},{1},{4},{3}] => 2
[{3},{4},{5},{1},{2},{6}] => 0
[{3},{4},{6},{1},{2},{5}] => 2
[{3},{5},{4},{1},{2},{6}] => 1
[{3},{6},{4},{1},{2},{5}] => 2
[{3},{5},{6},{1},{2},{4}] => 2
[{3},{6},{5},{1},{2},{4}] => 3
[{4},{3},{5},{1},{2},{6}] => 0
[{4},{3},{6},{1},{2},{5}] => 2
[{5},{3},{4},{1},{2},{6}] => 0
[{6},{3},{4},{1},{2},{5}] => 0
[{5},{3},{6},{1},{2},{4}] => 1
[{6},{3},{5},{1},{2},{4}] => 1
[{4},{5},{3},{1},{2},{6}] => 0
[{4},{6},{3},{1},{2},{5}] => 1
[{5},{4},{3},{1},{2},{6}] => 0
[{6},{4},{3},{1},{2},{5}] => 0
[{5},{6},{3},{1},{2},{4}] => 0
[{6},{5},{3},{1},{2},{4}] => 0
[{4},{5},{6},{1},{2},{3}] => 0
[{4},{6},{5},{1},{2},{3}] => 1
[{5},{4},{6},{1},{2},{3}] => 0
[{6},{4},{5},{1},{2},{3}] => 0
[{5},{6},{4},{1},{2},{3}] => 0
[{6},{5},{4},{1},{2},{3}] => 0
[{3},{4},{5},{1},{6},{2}] => 1
[{3},{4},{6},{1},{5},{2}] => 3
[{3},{5},{4},{1},{6},{2}] => 2
[{3},{6},{4},{1},{5},{2}] => 3
[{3},{5},{6},{1},{4},{2}] => 3
[{3},{6},{5},{1},{4},{2}] => 4
[{4},{3},{5},{1},{6},{2}] => 1
[{4},{3},{6},{1},{5},{2}] => 3
[{5},{3},{4},{1},{6},{2}] => 1
[{6},{3},{4},{1},{5},{2}] => 1
[{5},{3},{6},{1},{4},{2}] => 2
[{6},{3},{5},{1},{4},{2}] => 2
[{4},{5},{3},{1},{6},{2}] => 1
[{4},{6},{3},{1},{5},{2}] => 2
[{5},{4},{3},{1},{6},{2}] => 1
[{6},{4},{3},{1},{5},{2}] => 1
[{5},{6},{3},{1},{4},{2}] => 1
[{6},{5},{3},{1},{4},{2}] => 1
[{4},{5},{6},{1},{3},{2}] => 1
[{4},{6},{5},{1},{3},{2}] => 2
[{5},{4},{6},{1},{3},{2}] => 1
[{6},{4},{5},{1},{3},{2}] => 1
[{5},{6},{4},{1},{3},{2}] => 1
[{6},{5},{4},{1},{3},{2}] => 1
[{2},{3},{4},{5},{1},{6}] => 0
[{2},{3},{4},{6},{1},{5}] => 3
[{2},{3},{5},{4},{1},{6}] => 2
[{2},{3},{6},{4},{1},{5}] => 4
[{2},{3},{5},{6},{1},{4}] => 4
[{2},{3},{6},{5},{1},{4}] => 6
[{2},{4},{3},{5},{1},{6}] => 1
[{2},{4},{3},{6},{1},{5}] => 4
[{2},{5},{3},{4},{1},{6}] => 2
[{2},{6},{3},{4},{1},{5}] => 3
[{2},{5},{3},{6},{1},{4}] => 4
[{2},{6},{3},{5},{1},{4}] => 5
[{2},{4},{5},{3},{1},{6}] => 2
[{2},{4},{6},{3},{1},{5}] => 4
[{2},{5},{4},{3},{1},{6}] => 3
[{2},{6},{4},{3},{1},{5}] => 4
[{2},{5},{6},{3},{1},{4}] => 4
[{2},{6},{5},{3},{1},{4}] => 5
[{2},{4},{5},{6},{1},{3}] => 3
[{2},{4},{6},{5},{1},{3}] => 5
[{2},{5},{4},{6},{1},{3}] => 4
[{2},{6},{4},{5},{1},{3}] => 5
[{2},{5},{6},{4},{1},{3}] => 5
[{2},{6},{5},{4},{1},{3}] => 6
[{3},{2},{4},{5},{1},{6}] => 0
[{3},{2},{4},{6},{1},{5}] => 3
[{3},{2},{5},{4},{1},{6}] => 2
[{3},{2},{6},{4},{1},{5}] => 4
[{3},{2},{5},{6},{1},{4}] => 4
[{3},{2},{6},{5},{1},{4}] => 6
[{4},{2},{3},{5},{1},{6}] => 0
[{4},{2},{3},{6},{1},{5}] => 3
[{5},{2},{3},{4},{1},{6}] => 0
[{6},{2},{3},{4},{1},{5}] => 0
[{5},{2},{3},{6},{1},{4}] => 2
[{6},{2},{3},{5},{1},{4}] => 2
[{4},{2},{5},{3},{1},{6}] => 1
[{4},{2},{6},{3},{1},{5}] => 3
[{5},{2},{4},{3},{1},{6}] => 1
[{6},{2},{4},{3},{1},{5}] => 1
[{5},{2},{6},{3},{1},{4}] => 2
[{6},{2},{5},{3},{1},{4}] => 2
[{4},{2},{5},{6},{1},{3}] => 2
[{4},{2},{6},{5},{1},{3}] => 4
[{5},{2},{4},{6},{1},{3}] => 2
[{6},{2},{4},{5},{1},{3}] => 2
[{5},{2},{6},{4},{1},{3}] => 3
[{6},{2},{5},{4},{1},{3}] => 3
[{3},{4},{2},{5},{1},{6}] => 0
[{3},{4},{2},{6},{1},{5}] => 3
[{3},{5},{2},{4},{1},{6}] => 1
[{3},{6},{2},{4},{1},{5}] => 2
[{3},{5},{2},{6},{1},{4}] => 3
[{3},{6},{2},{5},{1},{4}] => 4
[{4},{3},{2},{5},{1},{6}] => 0
[{4},{3},{2},{6},{1},{5}] => 3
[{5},{3},{2},{4},{1},{6}] => 0
[{6},{3},{2},{4},{1},{5}] => 0
[{5},{3},{2},{6},{1},{4}] => 2
[{6},{3},{2},{5},{1},{4}] => 2
[{4},{5},{2},{3},{1},{6}] => 0
[{4},{6},{2},{3},{1},{5}] => 1
[{5},{4},{2},{3},{1},{6}] => 0
[{6},{4},{2},{3},{1},{5}] => 0
[{5},{6},{2},{3},{1},{4}] => 0
[{6},{5},{2},{3},{1},{4}] => 0
[{4},{5},{2},{6},{1},{3}] => 1
[{4},{6},{2},{5},{1},{3}] => 2
[{5},{4},{2},{6},{1},{3}] => 1
[{6},{4},{2},{5},{1},{3}] => 1
[{5},{6},{2},{4},{1},{3}] => 1
[{6},{5},{2},{4},{1},{3}] => 1
[{3},{4},{5},{2},{1},{6}] => 0
[{3},{4},{6},{2},{1},{5}] => 2
[{3},{5},{4},{2},{1},{6}] => 1
[{3},{6},{4},{2},{1},{5}] => 2
[{3},{5},{6},{2},{1},{4}] => 2
[{3},{6},{5},{2},{1},{4}] => 3
[{4},{3},{5},{2},{1},{6}] => 0
[{4},{3},{6},{2},{1},{5}] => 2
[{5},{3},{4},{2},{1},{6}] => 0
[{6},{3},{4},{2},{1},{5}] => 0
[{5},{3},{6},{2},{1},{4}] => 1
[{6},{3},{5},{2},{1},{4}] => 1
[{4},{5},{3},{2},{1},{6}] => 0
[{4},{6},{3},{2},{1},{5}] => 1
[{5},{4},{3},{2},{1},{6}] => 0
-----------------------------------------------------------------------------
Created: May 25, 2023 at 11:08 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: May 25, 2023 at 11:08 by Martin Rubey