*****************************************************************************
* 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: St001824
-----------------------------------------------------------------------------
Collection: Decorated permutations
-----------------------------------------------------------------------------
Description: The number of crossed alignments in a decorated permutation.
Let $w$ be a decorated permutation.
An alignment $(i \mapsto w(i), j \mapsto w(j))$ is crossed if there exists a third arc $(h \mapsto w(h))$ which forms a crossing with both arcs in the alignment.
-----------------------------------------------------------------------------
References: [1] Billey, S. C., Weaver, J. E. Criteria for smoothness of Positroid varieties via pattern avoidance, Johnson graphs, and spirographs [[arXiv:2207.06508]]
-----------------------------------------------------------------------------
Code:
def cyclic_interval(a, b, n):
if a <= b:
return list(range(a, b+1))
return list(range(a, n+1)) + list(range(1, b+1))
def alignments(x):
"""
sage: x = DecoratedPermutation([8,9,5,-4,7,6,1,3,2])
sage: (3, 5, 6, 6) in alignments(x)
True
sage: len(alignments(x))
13
sage: x = DecoratedPermutation([8,9,5,4,7,-6,1,3,2])
sage: (3, 5, 6, 6) in alignments(x)
False
"""
pi = x.to_signed_permutation().permutation()
n = len(pi)
al = []
for i, e in enumerate(pi, 1):
for j, f in enumerate(pi, 1):
if i == j:
continue
a, b = sorted([i, e])
c, d = sorted([j, f])
if a <= c <= b <= d or c <= a <= d <= b:
continue
if (e not in cyclic_interval(i, f-1, n)
or f not in cyclic_interval(e+1, j, n)):
continue
if j == f and x[j-1] < 0:
continue
if i == e and x[i-1] > 0:
continue
al.append((i, e, j, f))
return al
def statistic(x):
A = alignments(x)
pi = x.to_signed_permutation().permutation()
n = len(pi)
cal = []
for i, e, j, f in A:
a, b = sorted([i, e])
c, d = sorted([j, f])
for k, g in enumerate(pi, 1):
r, s = sorted([k, g])
if ((a <= r <= b <= s or r <= a <= s <= b) and
(c <= r <= d <= s or r <= c <= s <= d)):
cal.append((i, e, j, f, r, k))
break
return len(cal)
-----------------------------------------------------------------------------
Statistic values:
[+] => 0
[-] => 0
[+,+] => 0
[-,+] => 0
[+,-] => 0
[-,-] => 0
[2,1] => 0
[+,+,+] => 0
[-,+,+] => 0
[+,-,+] => 0
[+,+,-] => 0
[-,-,+] => 0
[-,+,-] => 0
[+,-,-] => 0
[-,-,-] => 0
[+,3,2] => 0
[-,3,2] => 0
[2,1,+] => 0
[2,1,-] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 0
[3,-,1] => 0
[+,+,+,+] => 0
[-,+,+,+] => 0
[+,-,+,+] => 0
[+,+,-,+] => 0
[+,+,+,-] => 0
[-,-,+,+] => 0
[-,+,-,+] => 0
[-,+,+,-] => 0
[+,-,-,+] => 0
[+,-,+,-] => 0
[+,+,-,-] => 0
[-,-,-,+] => 0
[-,-,+,-] => 0
[-,+,-,-] => 0
[+,-,-,-] => 0
[-,-,-,-] => 0
[+,+,4,3] => 0
[-,+,4,3] => 0
[+,-,4,3] => 0
[-,-,4,3] => 0
[+,3,2,+] => 0
[-,3,2,+] => 0
[+,3,2,-] => 0
[-,3,2,-] => 0
[+,3,4,2] => 0
[-,3,4,2] => 0
[+,4,2,3] => 0
[-,4,2,3] => 0
[+,4,+,2] => 0
[-,4,+,2] => 0
[+,4,-,2] => 0
[-,4,-,2] => 0
[2,1,+,+] => 0
[2,1,-,+] => 0
[2,1,+,-] => 0
[2,1,-,-] => 0
[2,1,4,3] => 0
[2,3,1,+] => 0
[2,3,1,-] => 0
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,+,1] => 0
[2,4,-,1] => 0
[3,1,2,+] => 0
[3,1,2,-] => 0
[3,1,4,2] => 1
[3,+,1,+] => 0
[3,-,1,+] => 0
[3,+,1,-] => 0
[3,-,1,-] => 0
[3,+,4,1] => 0
[3,-,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 1
[4,1,2,3] => 0
[4,1,+,2] => 0
[4,1,-,2] => 0
[4,+,1,3] => 0
[4,-,1,3] => 0
[4,+,+,1] => 0
[4,-,+,1] => 0
[4,+,-,1] => 0
[4,-,-,1] => 0
[4,3,1,2] => 1
[4,3,2,1] => 0
[+,+,+,+,+] => 0
[-,+,+,+,+] => 0
[+,-,+,+,+] => 0
[+,+,-,+,+] => 0
[+,+,+,-,+] => 0
[+,+,+,+,-] => 0
[-,-,+,+,+] => 0
[-,+,-,+,+] => 0
[-,+,+,-,+] => 0
[-,+,+,+,-] => 0
[+,-,-,+,+] => 0
[+,-,+,-,+] => 0
[+,-,+,+,-] => 0
[+,+,-,-,+] => 0
[+,+,-,+,-] => 0
[+,+,+,-,-] => 0
[-,-,-,+,+] => 0
[-,-,+,-,+] => 0
[-,-,+,+,-] => 0
[-,+,-,-,+] => 0
[-,+,-,+,-] => 0
[-,+,+,-,-] => 0
[+,-,-,-,+] => 0
[+,-,-,+,-] => 0
[+,-,+,-,-] => 0
[+,+,-,-,-] => 0
[-,-,-,-,+] => 0
[-,-,-,+,-] => 0
[-,-,+,-,-] => 0
[-,+,-,-,-] => 0
[+,-,-,-,-] => 0
[-,-,-,-,-] => 0
[+,+,+,5,4] => 0
[-,+,+,5,4] => 0
[+,-,+,5,4] => 0
[+,+,-,5,4] => 0
[-,-,+,5,4] => 0
[-,+,-,5,4] => 0
[+,-,-,5,4] => 0
[-,-,-,5,4] => 0
[+,+,4,3,+] => 0
[-,+,4,3,+] => 0
[+,-,4,3,+] => 0
[+,+,4,3,-] => 0
[-,-,4,3,+] => 0
[-,+,4,3,-] => 0
[+,-,4,3,-] => 0
[-,-,4,3,-] => 0
[+,+,4,5,3] => 0
[-,+,4,5,3] => 0
[+,-,4,5,3] => 0
[-,-,4,5,3] => 0
[+,+,5,3,4] => 0
[-,+,5,3,4] => 0
[+,-,5,3,4] => 0
[-,-,5,3,4] => 0
[+,+,5,+,3] => 0
[-,+,5,+,3] => 0
[+,-,5,+,3] => 0
[+,+,5,-,3] => 0
[-,-,5,+,3] => 0
[-,+,5,-,3] => 0
[+,-,5,-,3] => 0
[-,-,5,-,3] => 0
[+,3,2,+,+] => 0
[-,3,2,+,+] => 0
[+,3,2,-,+] => 0
[+,3,2,+,-] => 0
[-,3,2,-,+] => 0
[-,3,2,+,-] => 0
[+,3,2,-,-] => 0
[-,3,2,-,-] => 0
[+,3,2,5,4] => 0
[-,3,2,5,4] => 0
[+,3,4,2,+] => 0
[-,3,4,2,+] => 0
[+,3,4,2,-] => 0
[-,3,4,2,-] => 0
[+,3,4,5,2] => 0
[-,3,4,5,2] => 0
[+,3,5,2,4] => 1
[-,3,5,2,4] => 1
[+,3,5,+,2] => 0
[-,3,5,+,2] => 0
[+,3,5,-,2] => 0
[-,3,5,-,2] => 0
[+,4,2,3,+] => 0
[-,4,2,3,+] => 0
[+,4,2,3,-] => 0
[-,4,2,3,-] => 0
[+,4,2,5,3] => 1
[-,4,2,5,3] => 1
[+,4,+,2,+] => 0
[-,4,+,2,+] => 0
[+,4,-,2,+] => 0
[+,4,+,2,-] => 0
[-,4,-,2,+] => 0
[-,4,+,2,-] => 0
[+,4,-,2,-] => 0
[-,4,-,2,-] => 0
[+,4,+,5,2] => 0
[-,4,+,5,2] => 0
[+,4,-,5,2] => 0
[-,4,-,5,2] => 0
[+,4,5,2,3] => 0
[-,4,5,2,3] => 0
[+,4,5,3,2] => 1
[-,4,5,3,2] => 1
[+,5,2,3,4] => 0
[-,5,2,3,4] => 0
[+,5,2,+,3] => 0
[-,5,2,+,3] => 0
[+,5,2,-,3] => 0
[-,5,2,-,3] => 0
[+,5,+,2,4] => 0
[-,5,+,2,4] => 0
[+,5,-,2,4] => 0
[-,5,-,2,4] => 0
[+,5,+,+,2] => 0
[-,5,+,+,2] => 0
[+,5,-,+,2] => 0
[+,5,+,-,2] => 0
[-,5,-,+,2] => 0
[-,5,+,-,2] => 0
[+,5,-,-,2] => 0
[-,5,-,-,2] => 0
[+,5,4,2,3] => 1
[-,5,4,2,3] => 1
[+,5,4,3,2] => 0
[-,5,4,3,2] => 0
[2,1,+,+,+] => 0
[2,1,-,+,+] => 0
[2,1,+,-,+] => 0
[2,1,+,+,-] => 0
[2,1,-,-,+] => 0
[2,1,-,+,-] => 0
[2,1,+,-,-] => 0
[2,1,-,-,-] => 0
[2,1,+,5,4] => 0
[2,1,-,5,4] => 0
[2,1,4,3,+] => 0
[2,1,4,3,-] => 0
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,+,3] => 0
[2,1,5,-,3] => 0
[2,3,1,+,+] => 0
[2,3,1,-,+] => 0
[2,3,1,+,-] => 0
[2,3,1,-,-] => 0
[2,3,1,5,4] => 0
[2,3,4,1,+] => 0
[2,3,4,1,-] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 2
[2,3,5,+,1] => 0
[2,3,5,-,1] => 0
[2,4,1,3,+] => 1
[2,4,1,3,-] => 1
[2,4,1,5,3] => 2
[2,4,+,1,+] => 0
[2,4,-,1,+] => 0
[2,4,+,1,-] => 0
[2,4,-,1,-] => 0
[2,4,+,5,1] => 0
[2,4,-,5,1] => 0
[2,4,5,1,3] => 1
[2,4,5,3,1] => 2
[2,5,1,3,4] => 2
[2,5,1,+,3] => 1
[2,5,1,-,3] => 1
[2,5,+,1,4] => 1
[2,5,-,1,4] => 1
[2,5,+,+,1] => 0
[2,5,-,+,1] => 0
[2,5,+,-,1] => 0
[2,5,-,-,1] => 0
[2,5,4,1,3] => 2
[2,5,4,3,1] => 0
[3,1,2,+,+] => 0
[3,1,2,-,+] => 0
[3,1,2,+,-] => 0
[3,1,2,-,-] => 0
[3,1,2,5,4] => 0
[3,1,4,2,+] => 1
[3,1,4,2,-] => 1
[3,1,4,5,2] => 2
[3,1,5,2,4] => 2
[3,1,5,+,2] => 1
[3,1,5,-,2] => 1
[3,+,1,+,+] => 0
[3,-,1,+,+] => 0
[3,+,1,-,+] => 0
[3,+,1,+,-] => 0
[3,-,1,-,+] => 0
[3,-,1,+,-] => 0
[3,+,1,-,-] => 0
[3,-,1,-,-] => 0
[3,+,1,5,4] => 0
[3,-,1,5,4] => 0
[3,+,4,1,+] => 0
[3,-,4,1,+] => 0
[3,+,4,1,-] => 0
[3,-,4,1,-] => 0
[3,+,4,5,1] => 0
[3,-,4,5,1] => 0
[3,+,5,1,4] => 1
[3,-,5,1,4] => 1
[3,+,5,+,1] => 0
[3,-,5,+,1] => 0
[3,+,5,-,1] => 0
[3,-,5,-,1] => 0
[3,4,1,2,+] => 0
[3,4,1,2,-] => 0
[3,4,1,5,2] => 1
[3,4,2,1,+] => 1
[3,4,2,1,-] => 1
[3,4,2,5,1] => 2
[3,4,5,1,2] => 0
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,+,2] => 0
[3,5,1,-,2] => 0
[3,5,2,1,4] => 2
[3,5,2,+,1] => 1
[3,5,2,-,1] => 1
[3,5,4,1,2] => 1
[3,5,4,2,1] => 2
[4,1,2,3,+] => 0
[4,1,2,3,-] => 0
[4,1,2,5,3] => 2
[4,1,+,2,+] => 0
[4,1,-,2,+] => 0
[4,1,+,2,-] => 0
[4,1,-,2,-] => 0
[4,1,+,5,2] => 1
[4,1,-,5,2] => 1
[4,1,5,2,3] => 1
[4,1,5,3,2] => 2
[4,+,1,3,+] => 0
[4,-,1,3,+] => 0
[4,+,1,3,-] => 0
[4,-,1,3,-] => 0
[4,+,1,5,3] => 1
[4,-,1,5,3] => 1
[4,+,+,1,+] => 0
[4,-,+,1,+] => 0
[4,+,-,1,+] => 0
[4,+,+,1,-] => 0
[4,-,-,1,+] => 0
[4,-,+,1,-] => 0
[4,+,-,1,-] => 0
[4,-,-,1,-] => 0
[4,+,+,5,1] => 0
[4,-,+,5,1] => 0
[4,+,-,5,1] => 0
[4,-,-,5,1] => 0
[4,+,5,1,3] => 0
[4,-,5,1,3] => 0
[4,+,5,3,1] => 1
[4,-,5,3,1] => 1
[4,3,1,2,+] => 1
[4,3,1,2,-] => 1
[4,3,1,5,2] => 2
[4,3,2,1,+] => 0
[4,3,2,1,-] => 0
[4,3,2,5,1] => 0
[4,3,5,1,2] => 1
[4,3,5,2,1] => 2
[4,5,1,2,3] => 0
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 2
[4,5,+,1,2] => 0
[4,5,-,1,2] => 0
[4,5,+,2,1] => 1
[4,5,-,2,1] => 1
[5,1,2,3,4] => 0
[5,1,2,+,3] => 0
[5,1,2,-,3] => 0
[5,1,+,2,4] => 0
[5,1,-,2,4] => 0
[5,1,+,+,2] => 0
[5,1,-,+,2] => 0
[5,1,+,-,2] => 0
[5,1,-,-,2] => 0
[5,1,4,2,3] => 2
[5,1,4,3,2] => 0
[5,+,1,3,4] => 0
[5,-,1,3,4] => 0
[5,+,1,+,3] => 0
[5,-,1,+,3] => 0
[5,+,1,-,3] => 0
[5,-,1,-,3] => 0
[5,+,+,1,4] => 0
[5,-,+,1,4] => 0
[5,+,-,1,4] => 0
[5,-,-,1,4] => 0
[5,+,+,+,1] => 0
[5,-,+,+,1] => 0
[5,+,-,+,1] => 0
[5,+,+,-,1] => 0
[5,-,-,+,1] => 0
[5,-,+,-,1] => 0
[5,+,-,-,1] => 0
[5,-,-,-,1] => 0
[5,+,4,1,3] => 1
[5,-,4,1,3] => 1
[5,+,4,3,1] => 0
[5,-,4,3,1] => 0
[5,3,1,2,4] => 2
[5,3,1,+,2] => 1
[5,3,1,-,2] => 1
[5,3,2,1,4] => 0
[5,3,2,+,1] => 0
[5,3,2,-,1] => 0
[5,3,4,1,2] => 2
[5,3,4,2,1] => 0
[5,4,1,2,3] => 1
[5,4,1,3,2] => 2
[5,4,2,1,3] => 2
[5,4,2,3,1] => 0
[5,4,+,1,2] => 1
[5,4,-,1,2] => 1
[5,4,+,2,1] => 0
[5,4,-,2,1] => 0
[+,+,+,+,+,+] => 0
[-,+,+,+,+,+] => 0
[+,-,+,+,+,+] => 0
[+,+,-,+,+,+] => 0
[+,+,+,-,+,+] => 0
[+,+,+,+,-,+] => 0
[+,+,+,+,+,-] => 0
[-,-,+,+,+,+] => 0
[-,+,-,+,+,+] => 0
[-,+,+,-,+,+] => 0
[-,+,+,+,-,+] => 0
[-,+,+,+,+,-] => 0
[+,-,-,+,+,+] => 0
[+,-,+,-,+,+] => 0
[+,-,+,+,-,+] => 0
[+,-,+,+,+,-] => 0
[+,+,-,-,+,+] => 0
[+,+,-,+,-,+] => 0
[+,+,-,+,+,-] => 0
[+,+,+,-,-,+] => 0
[+,+,+,-,+,-] => 0
[+,+,+,+,-,-] => 0
[-,-,-,+,+,+] => 0
[-,-,+,-,+,+] => 0
[-,-,+,+,-,+] => 0
[-,-,+,+,+,-] => 0
[-,+,-,-,+,+] => 0
[-,+,-,+,-,+] => 0
[-,+,-,+,+,-] => 0
[-,+,+,-,-,+] => 0
[-,+,+,-,+,-] => 0
[-,+,+,+,-,-] => 0
[+,-,-,-,+,+] => 0
[+,-,-,+,-,+] => 0
[+,-,-,+,+,-] => 0
[+,-,+,-,-,+] => 0
[+,-,+,-,+,-] => 0
[+,-,+,+,-,-] => 0
[+,+,-,-,-,+] => 0
[+,+,-,-,+,-] => 0
[+,+,-,+,-,-] => 0
[+,+,+,-,-,-] => 0
[-,-,-,-,+,+] => 0
[-,-,-,+,-,+] => 0
[-,-,-,+,+,-] => 0
[-,-,+,-,-,+] => 0
[-,-,+,-,+,-] => 0
[-,-,+,+,-,-] => 0
[-,+,-,-,-,+] => 0
[-,+,-,-,+,-] => 0
[-,+,-,+,-,-] => 0
[-,+,+,-,-,-] => 0
[+,-,-,-,-,+] => 0
[+,-,-,-,+,-] => 0
[+,-,-,+,-,-] => 0
[+,-,+,-,-,-] => 0
[+,+,-,-,-,-] => 0
[-,-,-,-,-,+] => 0
[-,-,-,-,+,-] => 0
[-,-,-,+,-,-] => 0
[-,-,+,-,-,-] => 0
[-,+,-,-,-,-] => 0
[+,-,-,-,-,-] => 0
[-,-,-,-,-,-] => 0
[+,+,+,+,6,5] => 0
[-,+,+,+,6,5] => 0
[+,-,+,+,6,5] => 0
[+,+,-,+,6,5] => 0
[+,+,+,-,6,5] => 0
[-,-,+,+,6,5] => 0
[-,+,-,+,6,5] => 0
[-,+,+,-,6,5] => 0
[+,-,-,+,6,5] => 0
[+,-,+,-,6,5] => 0
[+,+,-,-,6,5] => 0
[-,-,-,+,6,5] => 0
[-,-,+,-,6,5] => 0
[-,+,-,-,6,5] => 0
[+,-,-,-,6,5] => 0
[-,-,-,-,6,5] => 0
[+,+,+,5,4,+] => 0
[-,+,+,5,4,+] => 0
[+,-,+,5,4,+] => 0
[+,+,-,5,4,+] => 0
[+,+,+,5,4,-] => 0
[-,-,+,5,4,+] => 0
[-,+,-,5,4,+] => 0
[-,+,+,5,4,-] => 0
[+,-,-,5,4,+] => 0
[+,-,+,5,4,-] => 0
[+,+,-,5,4,-] => 0
[-,-,-,5,4,+] => 0
[-,-,+,5,4,-] => 0
[-,+,-,5,4,-] => 0
[+,-,-,5,4,-] => 0
[-,-,-,5,4,-] => 0
[+,+,+,5,6,4] => 0
[-,+,+,5,6,4] => 0
[+,-,+,5,6,4] => 0
[+,+,-,5,6,4] => 0
[-,-,+,5,6,4] => 0
[-,+,-,5,6,4] => 0
[+,-,-,5,6,4] => 0
[-,-,-,5,6,4] => 0
[+,+,+,6,4,5] => 0
[-,+,+,6,4,5] => 0
[+,-,+,6,4,5] => 0
[+,+,-,6,4,5] => 0
[-,-,+,6,4,5] => 0
[-,+,-,6,4,5] => 0
[+,-,-,6,4,5] => 0
[-,-,-,6,4,5] => 0
[+,+,+,6,+,4] => 0
[-,+,+,6,+,4] => 0
[+,-,+,6,+,4] => 0
[+,+,-,6,+,4] => 0
[+,+,+,6,-,4] => 0
[-,-,+,6,+,4] => 0
[-,+,-,6,+,4] => 0
[-,+,+,6,-,4] => 0
[+,-,-,6,+,4] => 0
[+,-,+,6,-,4] => 0
[+,+,-,6,-,4] => 0
[-,-,-,6,+,4] => 0
[-,-,+,6,-,4] => 0
[-,+,-,6,-,4] => 0
[+,-,-,6,-,4] => 0
[-,-,-,6,-,4] => 0
[+,+,4,3,+,+] => 0
[-,+,4,3,+,+] => 0
[+,-,4,3,+,+] => 0
[+,+,4,3,-,+] => 0
[+,+,4,3,+,-] => 0
[-,-,4,3,+,+] => 0
[-,+,4,3,-,+] => 0
[-,+,4,3,+,-] => 0
[+,-,4,3,-,+] => 0
[+,-,4,3,+,-] => 0
[+,+,4,3,-,-] => 0
[-,-,4,3,-,+] => 0
[-,-,4,3,+,-] => 0
[-,+,4,3,-,-] => 0
[+,-,4,3,-,-] => 0
[-,-,4,3,-,-] => 0
[+,+,4,3,6,5] => 0
[-,+,4,3,6,5] => 0
[+,-,4,3,6,5] => 0
[-,-,4,3,6,5] => 0
[+,+,4,5,3,+] => 0
[-,+,4,5,3,+] => 0
[+,-,4,5,3,+] => 0
[+,+,4,5,3,-] => 0
[-,-,4,5,3,+] => 0
[-,+,4,5,3,-] => 0
[+,-,4,5,3,-] => 0
[-,-,4,5,3,-] => 0
[+,+,4,5,6,3] => 0
[-,+,4,5,6,3] => 0
[+,-,4,5,6,3] => 0
[-,-,4,5,6,3] => 0
[+,+,4,6,3,5] => 1
[-,+,4,6,3,5] => 1
[+,-,4,6,3,5] => 1
[-,-,4,6,3,5] => 1
[+,+,4,6,+,3] => 0
[-,+,4,6,+,3] => 0
[+,-,4,6,+,3] => 0
[+,+,4,6,-,3] => 0
[-,-,4,6,+,3] => 0
[-,+,4,6,-,3] => 0
[+,-,4,6,-,3] => 0
[-,-,4,6,-,3] => 0
[+,+,5,3,4,+] => 0
[-,+,5,3,4,+] => 0
[+,-,5,3,4,+] => 0
[+,+,5,3,4,-] => 0
[-,-,5,3,4,+] => 0
[-,+,5,3,4,-] => 0
[+,-,5,3,4,-] => 0
[-,-,5,3,4,-] => 0
[+,+,5,3,6,4] => 1
[-,+,5,3,6,4] => 1
[+,-,5,3,6,4] => 1
[-,-,5,3,6,4] => 1
[+,+,5,+,3,+] => 0
[-,+,5,+,3,+] => 0
[+,-,5,+,3,+] => 0
[+,+,5,-,3,+] => 0
[+,+,5,+,3,-] => 0
[-,-,5,+,3,+] => 0
[-,+,5,-,3,+] => 0
[-,+,5,+,3,-] => 0
[+,-,5,-,3,+] => 0
[+,-,5,+,3,-] => 0
[+,+,5,-,3,-] => 0
[-,-,5,-,3,+] => 0
[-,-,5,+,3,-] => 0
[-,+,5,-,3,-] => 0
[+,-,5,-,3,-] => 0
[-,-,5,-,3,-] => 0
[+,+,5,+,6,3] => 0
[-,+,5,+,6,3] => 0
[+,-,5,+,6,3] => 0
[+,+,5,-,6,3] => 0
[-,-,5,+,6,3] => 0
[-,+,5,-,6,3] => 0
[+,-,5,-,6,3] => 0
[-,-,5,-,6,3] => 0
[+,+,5,6,3,4] => 0
[-,+,5,6,3,4] => 0
[+,-,5,6,3,4] => 0
[-,-,5,6,3,4] => 0
[+,+,5,6,4,3] => 1
[-,+,5,6,4,3] => 1
[+,-,5,6,4,3] => 1
[-,-,5,6,4,3] => 1
[+,+,6,3,4,5] => 0
[-,+,6,3,4,5] => 0
[+,-,6,3,4,5] => 0
[-,-,6,3,4,5] => 0
[+,+,6,3,+,4] => 0
[-,+,6,3,+,4] => 0
[+,-,6,3,+,4] => 0
[+,+,6,3,-,4] => 0
[-,-,6,3,+,4] => 0
[-,+,6,3,-,4] => 0
[+,-,6,3,-,4] => 0
[-,-,6,3,-,4] => 0
[+,+,6,+,3,5] => 0
[-,+,6,+,3,5] => 0
[+,-,6,+,3,5] => 0
[+,+,6,-,3,5] => 0
[-,-,6,+,3,5] => 0
[-,+,6,-,3,5] => 0
[+,-,6,-,3,5] => 0
[-,-,6,-,3,5] => 0
[+,+,6,+,+,3] => 0
[-,+,6,+,+,3] => 0
[+,-,6,+,+,3] => 0
[+,+,6,-,+,3] => 0
[+,+,6,+,-,3] => 0
[-,-,6,+,+,3] => 0
[-,+,6,-,+,3] => 0
[-,+,6,+,-,3] => 0
[+,-,6,-,+,3] => 0
[+,-,6,+,-,3] => 0
[+,+,6,-,-,3] => 0
[-,-,6,-,+,3] => 0
[-,-,6,+,-,3] => 0
[-,+,6,-,-,3] => 0
[+,-,6,-,-,3] => 0
[-,-,6,-,-,3] => 0
[+,+,6,5,3,4] => 1
[-,+,6,5,3,4] => 1
[+,-,6,5,3,4] => 1
[-,-,6,5,3,4] => 1
[+,+,6,5,4,3] => 0
[-,+,6,5,4,3] => 0
[+,-,6,5,4,3] => 0
[-,-,6,5,4,3] => 0
[+,3,2,+,+,+] => 0
[-,3,2,+,+,+] => 0
[+,3,2,-,+,+] => 0
[+,3,2,+,-,+] => 0
[+,3,2,+,+,-] => 0
[-,3,2,-,+,+] => 0
[-,3,2,+,-,+] => 0
[-,3,2,+,+,-] => 0
[+,3,2,-,-,+] => 0
[+,3,2,-,+,-] => 0
[+,3,2,+,-,-] => 0
[-,3,2,-,-,+] => 0
[-,3,2,-,+,-] => 0
[-,3,2,+,-,-] => 0
[+,3,2,-,-,-] => 0
[-,3,2,-,-,-] => 0
[+,3,2,+,6,5] => 0
[-,3,2,+,6,5] => 0
[+,3,2,-,6,5] => 0
[-,3,2,-,6,5] => 0
[+,3,2,5,4,+] => 0
[-,3,2,5,4,+] => 0
[+,3,2,5,4,-] => 0
[-,3,2,5,4,-] => 0
[+,3,2,5,6,4] => 0
[-,3,2,5,6,4] => 0
[+,3,2,6,4,5] => 0
[-,3,2,6,4,5] => 0
[+,3,2,6,+,4] => 0
[-,3,2,6,+,4] => 0
[+,3,2,6,-,4] => 0
[-,3,2,6,-,4] => 0
[+,3,4,2,+,+] => 0
[-,3,4,2,+,+] => 0
[+,3,4,2,-,+] => 0
[+,3,4,2,+,-] => 0
[-,3,4,2,-,+] => 0
[-,3,4,2,+,-] => 0
[+,3,4,2,-,-] => 0
[-,3,4,2,-,-] => 0
[+,3,4,2,6,5] => 0
[-,3,4,2,6,5] => 0
[+,3,4,5,2,+] => 0
[-,3,4,5,2,+] => 0
[+,3,4,5,2,-] => 0
[-,3,4,5,2,-] => 0
[+,3,4,5,6,2] => 0
[-,3,4,5,6,2] => 0
[+,3,4,6,2,5] => 2
[-,3,4,6,2,5] => 2
[+,3,4,6,+,2] => 0
[-,3,4,6,+,2] => 0
[+,3,4,6,-,2] => 0
[-,3,4,6,-,2] => 0
[+,3,5,2,4,+] => 1
[-,3,5,2,4,+] => 1
[+,3,5,2,4,-] => 1
[-,3,5,2,4,-] => 1
[+,3,5,2,6,4] => 2
[-,3,5,2,6,4] => 2
[+,3,5,+,2,+] => 0
[-,3,5,+,2,+] => 0
[+,3,5,-,2,+] => 0
[+,3,5,+,2,-] => 0
[-,3,5,-,2,+] => 0
[-,3,5,+,2,-] => 0
[+,3,5,-,2,-] => 0
[-,3,5,-,2,-] => 0
[+,3,5,+,6,2] => 0
[-,3,5,+,6,2] => 0
[+,3,5,-,6,2] => 0
[-,3,5,-,6,2] => 0
[+,3,5,6,2,4] => 1
[-,3,5,6,2,4] => 1
[+,3,5,6,4,2] => 2
[-,3,5,6,4,2] => 2
[+,3,6,2,4,5] => 2
[-,3,6,2,4,5] => 2
[+,3,6,2,+,4] => 1
[-,3,6,2,+,4] => 1
[+,3,6,2,-,4] => 1
[-,3,6,2,-,4] => 1
[+,3,6,+,2,5] => 1
[-,3,6,+,2,5] => 1
[+,3,6,-,2,5] => 1
[-,3,6,-,2,5] => 1
[+,3,6,+,+,2] => 0
[-,3,6,+,+,2] => 0
[+,3,6,-,+,2] => 0
[+,3,6,+,-,2] => 0
[-,3,6,-,+,2] => 0
[-,3,6,+,-,2] => 0
[+,3,6,-,-,2] => 0
[-,3,6,-,-,2] => 0
[+,3,6,5,2,4] => 2
[-,3,6,5,2,4] => 2
[+,3,6,5,4,2] => 0
[-,3,6,5,4,2] => 0
[+,4,2,3,+,+] => 0
[-,4,2,3,+,+] => 0
[+,4,2,3,-,+] => 0
[+,4,2,3,+,-] => 0
[-,4,2,3,-,+] => 0
[-,4,2,3,+,-] => 0
[+,4,2,3,-,-] => 0
[-,4,2,3,-,-] => 0
[+,4,2,3,6,5] => 0
[-,4,2,3,6,5] => 0
[+,4,2,5,3,+] => 1
[-,4,2,5,3,+] => 1
[+,4,2,5,3,-] => 1
[-,4,2,5,3,-] => 1
[+,4,2,5,6,3] => 2
[-,4,2,5,6,3] => 2
[+,4,2,6,3,5] => 2
[-,4,2,6,3,5] => 2
[+,4,2,6,+,3] => 1
[-,4,2,6,+,3] => 1
[+,4,2,6,-,3] => 1
[-,4,2,6,-,3] => 1
[+,4,+,2,+,+] => 0
[-,4,+,2,+,+] => 0
[+,4,-,2,+,+] => 0
[+,4,+,2,-,+] => 0
[+,4,+,2,+,-] => 0
[-,4,-,2,+,+] => 0
[-,4,+,2,-,+] => 0
[-,4,+,2,+,-] => 0
[+,4,-,2,-,+] => 0
[+,4,-,2,+,-] => 0
[+,4,+,2,-,-] => 0
[-,4,-,2,-,+] => 0
[-,4,-,2,+,-] => 0
[-,4,+,2,-,-] => 0
[+,4,-,2,-,-] => 0
[-,4,-,2,-,-] => 0
[+,4,+,2,6,5] => 0
[-,4,+,2,6,5] => 0
[+,4,-,2,6,5] => 0
[-,4,-,2,6,5] => 0
[+,4,+,5,2,+] => 0
[-,4,+,5,2,+] => 0
[+,4,-,5,2,+] => 0
[+,4,+,5,2,-] => 0
[-,4,-,5,2,+] => 0
[-,4,+,5,2,-] => 0
[+,4,-,5,2,-] => 0
[-,4,-,5,2,-] => 0
[+,4,+,5,6,2] => 0
[-,4,+,5,6,2] => 0
[+,4,-,5,6,2] => 0
[-,4,-,5,6,2] => 0
[+,4,+,6,2,5] => 1
[-,4,+,6,2,5] => 1
[+,4,-,6,2,5] => 1
[-,4,-,6,2,5] => 1
[+,4,+,6,+,2] => 0
[-,4,+,6,+,2] => 0
[+,4,-,6,+,2] => 0
[+,4,+,6,-,2] => 0
[-,4,-,6,+,2] => 0
[-,4,+,6,-,2] => 0
[+,4,-,6,-,2] => 0
[-,4,-,6,-,2] => 0
[+,4,5,2,3,+] => 0
[-,4,5,2,3,+] => 0
[+,4,5,2,3,-] => 0
[-,4,5,2,3,-] => 0
[+,4,5,2,6,3] => 1
[-,4,5,2,6,3] => 1
[+,4,5,3,2,+] => 1
[-,4,5,3,2,+] => 1
[+,4,5,3,2,-] => 1
[-,4,5,3,2,-] => 1
[+,4,5,3,6,2] => 2
[-,4,5,3,6,2] => 2
[+,4,5,6,2,3] => 0
[-,4,5,6,2,3] => 0
[+,4,5,6,3,2] => 1
[-,4,5,6,3,2] => 1
[+,4,6,2,3,5] => 1
[-,4,6,2,3,5] => 1
[+,4,6,2,+,3] => 0
[-,4,6,2,+,3] => 0
[+,4,6,2,-,3] => 0
[-,4,6,2,-,3] => 0
[+,4,6,3,2,5] => 2
[-,4,6,3,2,5] => 2
[+,4,6,3,+,2] => 1
[-,4,6,3,+,2] => 1
[+,4,6,3,-,2] => 1
[-,4,6,3,-,2] => 1
[+,4,6,5,2,3] => 1
[-,4,6,5,2,3] => 1
[+,4,6,5,3,2] => 2
[-,4,6,5,3,2] => 2
[+,5,2,3,4,+] => 0
[-,5,2,3,4,+] => 0
[+,5,2,3,4,-] => 0
[-,5,2,3,4,-] => 0
[+,5,2,3,6,4] => 2
[-,5,2,3,6,4] => 2
[+,5,2,+,3,+] => 0
[-,5,2,+,3,+] => 0
[+,5,2,-,3,+] => 0
[+,5,2,+,3,-] => 0
[-,5,2,-,3,+] => 0
[-,5,2,+,3,-] => 0
[+,5,2,-,3,-] => 0
[-,5,2,-,3,-] => 0
[+,5,2,+,6,3] => 1
[-,5,2,+,6,3] => 1
[+,5,2,-,6,3] => 1
[-,5,2,-,6,3] => 1
[+,5,2,6,3,4] => 1
[-,5,2,6,3,4] => 1
[+,5,2,6,4,3] => 2
[-,5,2,6,4,3] => 2
[+,5,+,2,4,+] => 0
[-,5,+,2,4,+] => 0
[+,5,-,2,4,+] => 0
[+,5,+,2,4,-] => 0
[-,5,-,2,4,+] => 0
[-,5,+,2,4,-] => 0
[+,5,-,2,4,-] => 0
[-,5,-,2,4,-] => 0
[+,5,+,2,6,4] => 1
[-,5,+,2,6,4] => 1
[+,5,-,2,6,4] => 1
[-,5,-,2,6,4] => 1
[+,5,+,+,2,+] => 0
[-,5,+,+,2,+] => 0
[+,5,-,+,2,+] => 0
[+,5,+,-,2,+] => 0
[+,5,+,+,2,-] => 0
[-,5,-,+,2,+] => 0
[-,5,+,-,2,+] => 0
[-,5,+,+,2,-] => 0
[+,5,-,-,2,+] => 0
[+,5,-,+,2,-] => 0
[+,5,+,-,2,-] => 0
[-,5,-,-,2,+] => 0
[-,5,-,+,2,-] => 0
[-,5,+,-,2,-] => 0
[+,5,-,-,2,-] => 0
[-,5,-,-,2,-] => 0
[+,5,+,+,6,2] => 0
[-,5,+,+,6,2] => 0
[+,5,-,+,6,2] => 0
[+,5,+,-,6,2] => 0
[-,5,-,+,6,2] => 0
[-,5,+,-,6,2] => 0
[+,5,-,-,6,2] => 0
[-,5,-,-,6,2] => 0
[+,5,+,6,2,4] => 0
[-,5,+,6,2,4] => 0
[+,5,-,6,2,4] => 0
[-,5,-,6,2,4] => 0
[+,5,+,6,4,2] => 1
[-,5,+,6,4,2] => 1
[+,5,-,6,4,2] => 1
[-,5,-,6,4,2] => 1
[+,5,4,2,3,+] => 1
[-,5,4,2,3,+] => 1
[+,5,4,2,3,-] => 1
[-,5,4,2,3,-] => 1
[+,5,4,2,6,3] => 2
[-,5,4,2,6,3] => 2
[+,5,4,3,2,+] => 0
[-,5,4,3,2,+] => 0
[+,5,4,3,2,-] => 0
[-,5,4,3,2,-] => 0
[+,5,4,3,6,2] => 0
[-,5,4,3,6,2] => 0
[+,5,4,6,2,3] => 1
[-,5,4,6,2,3] => 1
[+,5,4,6,3,2] => 2
[-,5,4,6,3,2] => 2
[+,5,6,2,3,4] => 0
[-,5,6,2,3,4] => 0
[+,5,6,2,4,3] => 1
[-,5,6,2,4,3] => 1
[+,5,6,3,2,4] => 1
[-,5,6,3,2,4] => 1
[+,5,6,3,4,2] => 2
[-,5,6,3,4,2] => 2
[+,5,6,+,2,3] => 0
[-,5,6,+,2,3] => 0
[+,5,6,-,2,3] => 0
[-,5,6,-,2,3] => 0
[+,5,6,+,3,2] => 1
[-,5,6,+,3,2] => 1
[+,5,6,-,3,2] => 1
[-,5,6,-,3,2] => 1
[+,6,2,3,4,5] => 0
[-,6,2,3,4,5] => 0
[+,6,2,3,+,4] => 0
[-,6,2,3,+,4] => 0
[+,6,2,3,-,4] => 0
[-,6,2,3,-,4] => 0
[+,6,2,+,3,5] => 0
[-,6,2,+,3,5] => 0
[+,6,2,-,3,5] => 0
[-,6,2,-,3,5] => 0
[+,6,2,+,+,3] => 0
[-,6,2,+,+,3] => 0
[+,6,2,-,+,3] => 0
[+,6,2,+,-,3] => 0
[-,6,2,-,+,3] => 0
[-,6,2,+,-,3] => 0
[+,6,2,-,-,3] => 0
[-,6,2,-,-,3] => 0
[+,6,2,5,3,4] => 2
[-,6,2,5,3,4] => 2
[+,6,2,5,4,3] => 0
[-,6,2,5,4,3] => 0
[+,6,+,2,4,5] => 0
[-,6,+,2,4,5] => 0
[+,6,-,2,4,5] => 0
[-,6,-,2,4,5] => 0
[+,6,+,2,+,4] => 0
[-,6,+,2,+,4] => 0
[+,6,-,2,+,4] => 0
[+,6,+,2,-,4] => 0
[-,6,-,2,+,4] => 0
[-,6,+,2,-,4] => 0
[+,6,-,2,-,4] => 0
[-,6,-,2,-,4] => 0
[+,6,+,+,2,5] => 0
[-,6,+,+,2,5] => 0
[+,6,-,+,2,5] => 0
[+,6,+,-,2,5] => 0
[-,6,-,+,2,5] => 0
[-,6,+,-,2,5] => 0
[+,6,-,-,2,5] => 0
[-,6,-,-,2,5] => 0
[+,6,+,+,+,2] => 0
[-,6,+,+,+,2] => 0
[+,6,-,+,+,2] => 0
[+,6,+,-,+,2] => 0
[+,6,+,+,-,2] => 0
[-,6,-,+,+,2] => 0
[-,6,+,-,+,2] => 0
[-,6,+,+,-,2] => 0
[+,6,-,-,+,2] => 0
[+,6,-,+,-,2] => 0
[+,6,+,-,-,2] => 0
[-,6,-,-,+,2] => 0
[-,6,-,+,-,2] => 0
[-,6,+,-,-,2] => 0
[+,6,-,-,-,2] => 0
[-,6,-,-,-,2] => 0
[+,6,+,5,2,4] => 1
[-,6,+,5,2,4] => 1
[+,6,-,5,2,4] => 1
[-,6,-,5,2,4] => 1
[+,6,+,5,4,2] => 0
[-,6,+,5,4,2] => 0
[+,6,-,5,4,2] => 0
[-,6,-,5,4,2] => 0
[+,6,4,2,3,5] => 2
[-,6,4,2,3,5] => 2
[+,6,4,2,+,3] => 1
[-,6,4,2,+,3] => 1
[+,6,4,2,-,3] => 1
[-,6,4,2,-,3] => 1
[+,6,4,3,2,5] => 0
[-,6,4,3,2,5] => 0
[+,6,4,3,+,2] => 0
[-,6,4,3,+,2] => 0
[+,6,4,3,-,2] => 0
[-,6,4,3,-,2] => 0
[+,6,4,5,2,3] => 2
[-,6,4,5,2,3] => 2
[+,6,4,5,3,2] => 0
[-,6,4,5,3,2] => 0
[+,6,5,2,3,4] => 1
[-,6,5,2,3,4] => 1
[+,6,5,2,4,3] => 2
[-,6,5,2,4,3] => 2
[+,6,5,3,2,4] => 2
[-,6,5,3,2,4] => 2
[+,6,5,3,4,2] => 0
[-,6,5,3,4,2] => 0
[+,6,5,+,2,3] => 1
[-,6,5,+,2,3] => 1
[+,6,5,-,2,3] => 1
[-,6,5,-,2,3] => 1
[+,6,5,+,3,2] => 0
[-,6,5,+,3,2] => 0
[+,6,5,-,3,2] => 0
[-,6,5,-,3,2] => 0
[2,1,+,+,+,+] => 0
[2,1,-,+,+,+] => 0
[2,1,+,-,+,+] => 0
[2,1,+,+,-,+] => 0
[2,1,+,+,+,-] => 0
[2,1,-,-,+,+] => 0
[2,1,-,+,-,+] => 0
[2,1,-,+,+,-] => 0
[2,1,+,-,-,+] => 0
[2,1,+,-,+,-] => 0
[2,1,+,+,-,-] => 0
[2,1,-,-,-,+] => 0
[2,1,-,-,+,-] => 0
[2,1,-,+,-,-] => 0
[2,1,+,-,-,-] => 0
[2,1,-,-,-,-] => 0
[2,1,+,+,6,5] => 0
[2,1,-,+,6,5] => 0
[2,1,+,-,6,5] => 0
[2,1,-,-,6,5] => 0
[2,1,+,5,4,+] => 0
[2,1,-,5,4,+] => 0
[2,1,+,5,4,-] => 0
[2,1,-,5,4,-] => 0
[2,1,+,5,6,4] => 0
[2,1,-,5,6,4] => 0
[2,1,+,6,4,5] => 0
[2,1,-,6,4,5] => 0
[2,1,+,6,+,4] => 0
[2,1,-,6,+,4] => 0
[2,1,+,6,-,4] => 0
[2,1,-,6,-,4] => 0
[2,1,4,3,+,+] => 0
[2,1,4,3,-,+] => 0
[2,1,4,3,+,-] => 0
[2,1,4,3,-,-] => 0
[2,1,4,3,6,5] => 0
[2,1,4,5,3,+] => 0
[2,1,4,5,3,-] => 0
[2,1,4,5,6,3] => 0
[2,1,4,6,3,5] => 1
[2,1,4,6,+,3] => 0
[2,1,4,6,-,3] => 0
[2,1,5,3,4,+] => 0
[2,1,5,3,4,-] => 0
[2,1,5,3,6,4] => 1
[2,1,5,+,3,+] => 0
[2,1,5,-,3,+] => 0
[2,1,5,+,3,-] => 0
[2,1,5,-,3,-] => 0
[2,1,5,+,6,3] => 0
[2,1,5,-,6,3] => 0
[2,1,5,6,3,4] => 0
[2,1,5,6,4,3] => 1
[2,1,6,3,4,5] => 0
[2,1,6,3,+,4] => 0
[2,1,6,3,-,4] => 0
[2,1,6,+,3,5] => 0
[2,1,6,-,3,5] => 0
[2,1,6,+,+,3] => 0
[2,1,6,-,+,3] => 0
[2,1,6,+,-,3] => 0
[2,1,6,-,-,3] => 0
[2,1,6,5,3,4] => 1
[2,1,6,5,4,3] => 0
[2,3,1,+,+,+] => 0
[2,3,1,-,+,+] => 0
[2,3,1,+,-,+] => 0
[2,3,1,+,+,-] => 0
[2,3,1,-,-,+] => 0
[2,3,1,-,+,-] => 0
[2,3,1,+,-,-] => 0
[2,3,1,-,-,-] => 0
[2,3,1,+,6,5] => 0
[2,3,1,-,6,5] => 0
[2,3,1,5,4,+] => 0
[2,3,1,5,4,-] => 0
[2,3,1,5,6,4] => 0
[2,3,1,6,4,5] => 0
[2,3,1,6,+,4] => 0
[2,3,1,6,-,4] => 0
[2,3,4,1,+,+] => 0
[2,3,4,1,-,+] => 0
[2,3,4,1,+,-] => 0
[2,3,4,1,-,-] => 0
[2,3,4,1,6,5] => 0
[2,3,4,5,1,+] => 0
[2,3,4,5,1,-] => 0
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 2
[2,3,4,6,+,1] => 0
[2,3,4,6,-,1] => 0
[2,3,5,1,4,+] => 2
[2,3,5,1,4,-] => 2
[2,3,5,1,6,4] => 3
[2,3,5,+,1,+] => 0
[2,3,5,-,1,+] => 0
[2,3,5,+,1,-] => 0
[2,3,5,-,1,-] => 0
[2,3,5,+,6,1] => 0
[2,3,5,-,6,1] => 0
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 2
[2,3,6,1,4,5] => 2
[2,3,6,1,+,4] => 2
[2,3,6,1,-,4] => 2
[2,3,6,+,1,5] => 2
[2,3,6,-,1,5] => 2
[2,3,6,+,+,1] => 0
[2,3,6,-,+,1] => 0
[2,3,6,+,-,1] => 0
[2,3,6,-,-,1] => 0
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 0
[2,4,1,3,+,+] => 1
[2,4,1,3,-,+] => 1
[2,4,1,3,+,-] => 1
[2,4,1,3,-,-] => 1
[2,4,1,3,6,5] => 1
[2,4,1,5,3,+] => 2
[2,4,1,5,3,-] => 2
[2,4,1,5,6,3] => 3
[2,4,1,6,3,5] => 3
[2,4,1,6,+,3] => 2
[2,4,1,6,-,3] => 2
[2,4,+,1,+,+] => 0
[2,4,-,1,+,+] => 0
[2,4,+,1,-,+] => 0
[2,4,+,1,+,-] => 0
[2,4,-,1,-,+] => 0
[2,4,-,1,+,-] => 0
[2,4,+,1,-,-] => 0
[2,4,-,1,-,-] => 0
[2,4,+,1,6,5] => 0
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Created: Jul 22, 2022 at 12:07 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Jul 22, 2022 at 12:07 by Martin Rubey