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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* 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. *
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-----------------------------------------------------------------------------
Statistic identifier: St001770
-----------------------------------------------------------------------------
Collection: Signed permutations
-----------------------------------------------------------------------------
Description: The number of facets of a certain subword complex associated with the signed permutation.
Let $Q=[1,\dots,n,1,\dots,n,\dots,1,\dots,n]$ be the word of length $n^2$, and let $\pi$ be a signed permutation. Then this statistic yields the number of facets of the subword complex $\Delta(Q, \pi)$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(pi):
n = len(list(pi))
S = SignedPermutations(n)
Q = S.w0.coxeter_sorting_word(S.coxeter_element())
return len(SubwordComplex(Q, pi).facets())
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[-1] => 1
[1,2] => 1
[1,-2] => 2
[-1,2] => 1
[-1,-2] => 1
[2,1] => 2
[2,-1] => 1
[-2,1] => 3
[-2,-1] => 1
[1,2,3] => 1
[1,2,-3] => 3
[1,-2,3] => 4
[1,-2,-3] => 6
[-1,2,3] => 1
[-1,2,-3] => 2
[-1,-2,3] => 1
[-1,-2,-3] => 1
[1,3,2] => 3
[1,3,-2] => 3
[1,-3,2] => 6
[1,-3,-2] => 4
[-1,3,2] => 2
[-1,3,-2] => 1
[-1,-3,2] => 3
[-1,-3,-2] => 1
[2,1,3] => 3
[2,1,-3] => 9
[2,-1,3] => 1
[2,-1,-3] => 2
[-2,1,3] => 5
[-2,1,-3] => 8
[-2,-1,3] => 1
[-2,-1,-3] => 1
[2,3,1] => 3
[2,3,-1] => 1
[2,-3,1] => 8
[2,-3,-1] => 2
[-2,3,1] => 8
[-2,3,-1] => 2
[-2,-3,1] => 10
[-2,-3,-1] => 2
[3,1,2] => 6
[3,1,-2] => 8
[3,-1,2] => 2
[3,-1,-2] => 1
[-3,1,2] => 10
[-3,1,-2] => 10
[-3,-1,2] => 3
[-3,-1,-2] => 1
[3,2,1] => 8
[3,2,-1] => 3
[3,-2,1] => 6
[3,-2,-1] => 1
[-3,2,1] => 15
[-3,2,-1] => 5
[-3,-2,1] => 7
[-3,-2,-1] => 1
[1,2,3,4] => 1
[1,2,3,-4] => 4
[1,2,-3,4] => 10
[1,2,-3,-4] => 20
[1,-2,3,4] => 6
[1,-2,3,-4] => 16
[1,-2,-3,4] => 15
[1,-2,-3,-4] => 20
[-1,2,3,4] => 1
[-1,2,3,-4] => 3
[-1,2,-3,4] => 4
[-1,2,-3,-4] => 6
[-1,-2,3,4] => 1
[-1,-2,3,-4] => 2
[-1,-2,-3,4] => 1
[-1,-2,-3,-4] => 1
[1,2,4,3] => 4
[1,2,4,-3] => 6
[1,2,-4,3] => 10
[1,2,-4,-3] => 10
[1,-2,4,3] => 16
[1,-2,4,-3] => 13
[1,-2,-4,3] => 29
[1,-2,-4,-3] => 16
[-1,2,4,3] => 3
[-1,2,4,-3] => 3
[-1,2,-4,3] => 6
[-1,2,-4,-3] => 4
[-1,-2,4,3] => 2
[-1,-2,4,-3] => 1
[-1,-2,-4,3] => 3
[-1,-2,-4,-3] => 1
[1,3,2,4] => 4
[1,3,2,-4] => 16
[1,3,-2,4] => 5
[1,3,-2,-4] => 13
[1,-3,2,4] => 15
[1,-3,2,-4] => 33
[1,-3,-2,4] => 11
[1,-3,-2,-4] => 14
[-1,3,2,4] => 3
[-1,3,2,-4] => 9
[-1,3,-2,4] => 1
[-1,3,-2,-4] => 2
[-1,-3,2,4] => 5
[-1,-3,2,-4] => 8
[-1,-3,-2,4] => 1
[-1,-3,-2,-4] => 1
[1,3,4,2] => 6
[1,3,4,-2] => 4
[1,3,-4,2] => 20
[1,3,-4,-2] => 10
[1,-3,4,2] => 33
[1,-3,4,-2] => 17
[1,-3,-4,2] => 50
[1,-3,-4,-2] => 20
[-1,3,4,2] => 3
[-1,3,4,-2] => 1
[-1,3,-4,2] => 8
[-1,3,-4,-2] => 2
[-1,-3,4,2] => 8
[-1,-3,4,-2] => 2
[-1,-3,-4,2] => 10
[-1,-3,-4,-2] => 2
[1,4,2,3] => 10
[1,4,2,-3] => 20
[1,4,-2,3] => 13
[1,4,-2,-3] => 10
[1,-4,2,3] => 20
[1,-4,2,-3] => 30
[1,-4,-2,3] => 23
[1,-4,-2,-3] => 12
[-1,4,2,3] => 6
[-1,4,2,-3] => 8
[-1,4,-2,3] => 2
[-1,4,-2,-3] => 1
[-1,-4,2,3] => 10
[-1,-4,2,-3] => 10
[-1,-4,-2,3] => 3
[-1,-4,-2,-3] => 1
[1,4,3,2] => 20
[1,4,3,-2] => 15
[1,4,-3,2] => 20
[1,4,-3,-2] => 7
[1,-4,3,2] => 45
[1,-4,3,-2] => 30
[1,-4,-3,2] => 27
[1,-4,-3,-2] => 8
[-1,4,3,2] => 8
[-1,4,3,-2] => 3
[-1,4,-3,2] => 6
[-1,4,-3,-2] => 1
[-1,-4,3,2] => 15
[-1,-4,3,-2] => 5
[-1,-4,-3,2] => 7
[-1,-4,-3,-2] => 1
[2,1,3,4] => 4
[2,1,3,-4] => 16
[2,1,-3,4] => 40
[2,1,-3,-4] => 80
[2,-1,3,4] => 1
[2,-1,3,-4] => 3
[2,-1,-3,4] => 4
[2,-1,-3,-4] => 6
[-2,1,3,4] => 7
[-2,1,3,-4] => 19
[-2,1,-3,4] => 19
[-2,1,-3,-4] => 26
[-2,-1,3,4] => 1
[-2,-1,3,-4] => 2
[-2,-1,-3,4] => 1
[-2,-1,-3,-4] => 1
[2,1,4,3] => 16
[2,1,4,-3] => 24
[2,1,-4,3] => 40
[2,1,-4,-3] => 40
[2,-1,4,3] => 3
[2,-1,4,-3] => 3
[2,-1,-4,3] => 6
[2,-1,-4,-3] => 4
[-2,1,4,3] => 19
[-2,1,4,-3] => 16
[-2,1,-4,3] => 35
[-2,1,-4,-3] => 20
[-2,-1,4,3] => 2
[-2,-1,4,-3] => 1
[-2,-1,-4,3] => 3
[-2,-1,-4,-3] => 1
[2,3,1,4] => 6
[2,3,1,-4] => 24
[2,3,-1,4] => 1
[2,3,-1,-4] => 3
[2,-3,1,4] => 39
[2,-3,1,-4] => 83
[2,-3,-1,4] => 4
[2,-3,-1,-4] => 6
[-2,3,1,4] => 19
[-2,3,1,-4] => 51
[-2,3,-1,4] => 2
[-2,3,-1,-4] => 4
[-2,-3,1,4] => 21
[-2,-3,1,-4] => 30
[-2,-3,-1,4] => 2
[-2,-3,-1,-4] => 2
[2,3,4,1] => 4
[2,3,4,-1] => 1
[2,3,-4,1] => 15
[2,3,-4,-1] => 3
[2,-3,4,1] => 33
[2,-3,4,-1] => 7
[2,-3,-4,1] => 60
[2,-3,-4,-1] => 10
[-2,3,4,1] => 16
[-2,3,4,-1] => 3
[-2,3,-4,1] => 39
[-2,3,-4,-1] => 6
[-2,-3,4,1] => 30
[-2,-3,4,-1] => 5
[-2,-3,-4,1] => 35
[-2,-3,-4,-1] => 5
[2,4,1,3] => 20
[2,4,1,-3] => 35
[2,4,-1,3] => 3
[2,4,-1,-3] => 3
[2,-4,1,3] => 45
[2,-4,1,-3] => 57
[2,-4,-1,3] => 6
[2,-4,-1,-3] => 4
[-2,4,1,3] => 35
[-2,4,1,-3] => 39
[-2,4,-1,3] => 4
[-2,4,-1,-3] => 2
[-2,-4,1,3] => 54
[-2,-4,1,-3] => 46
[-2,-4,-1,3] => 6
[-2,-4,-1,-3] => 2
[2,4,3,1] => 15
[2,4,3,-1] => 4
[2,4,-3,1] => 20
[2,4,-3,-1] => 3
[2,-4,3,1] => 36
[2,-4,3,-1] => 9
[2,-4,-3,1] => 31
[2,-4,-3,-1] => 4
[-2,4,3,1] => 39
[-2,4,3,-1] => 8
[-2,4,-3,1] => 26
[-2,4,-3,-1] => 3
[-2,-4,3,1] => 67
[-2,-4,3,-1] => 13
[-2,-4,-3,1] => 29
[-2,-4,-3,-1] => 3
[3,1,2,4] => 10
[3,1,2,-4] => 40
[3,1,-2,4] => 19
[3,1,-2,-4] => 49
[3,-1,2,4] => 3
[3,-1,2,-4] => 9
[3,-1,-2,4] => 1
[3,-1,-2,-4] => 2
[-3,1,2,4] => 21
[-3,1,2,-4] => 49
[-3,1,-2,4] => 26
[-3,1,-2,-4] => 34
[-3,-1,2,4] => 5
[-3,-1,2,-4] => 8
[-3,-1,-2,4] => 1
[-3,-1,-2,-4] => 1
[3,1,4,2] => 20
[3,1,4,-2] => 15
[3,1,-4,2] => 65
[3,1,-4,-2] => 37
[3,-1,4,2] => 3
[3,-1,4,-2] => 1
[3,-1,-4,2] => 8
[3,-1,-4,-2] => 2
[-3,1,4,2] => 49
[-3,1,4,-2] => 30
[-3,1,-4,2] => 79
[-3,1,-4,-2] => 36
[-3,-1,4,2] => 8
[-3,-1,4,-2] => 2
[-3,-1,-4,2] => 10
[-3,-1,-4,-2] => 2
[3,2,1,4] => 20
[3,2,1,-4] => 80
[3,2,-1,4] => 4
[3,2,-1,-4] => 12
[3,-2,1,4] => 16
[3,-2,1,-4] => 42
[3,-2,-1,4] => 1
[3,-2,-1,-4] => 2
[-3,2,1,4] => 56
[-3,2,1,-4] => 128
[-3,2,-1,4] => 9
[-3,2,-1,-4] => 14
[-3,-2,1,4] => 16
[-3,-2,1,-4] => 22
[-3,-2,-1,4] => 1
[-3,-2,-1,-4] => 1
[3,2,4,1] => 15
[3,2,4,-1] => 4
[3,2,-4,1] => 56
[3,2,-4,-1] => 12
[3,-2,4,1] => 13
[3,-2,4,-1] => 2
[3,-2,-4,1] => 31
[3,-2,-4,-1] => 4
[-3,2,4,1] => 49
[-3,2,4,-1] => 12
[-3,2,-4,1] => 97
[-3,2,-4,-1] => 18
[-3,-2,4,1] => 22
[-3,-2,4,-1] => 3
[-3,-2,-4,1] => 25
[-3,-2,-4,-1] => 3
[3,4,1,2] => 20
[3,4,1,-2] => 20
[3,4,-1,2] => 3
[3,4,-1,-2] => 1
[3,-4,1,2] => 60
[3,-4,1,-2] => 48
[3,-4,-1,2] => 8
[3,-4,-1,-2] => 2
[-3,4,1,2] => 79
[-3,4,1,-2] => 62
[-3,4,-1,2] => 14
[-3,4,-1,-2] => 3
[-3,-4,1,2] => 105
[-3,-4,1,-2] => 70
[-3,-4,-1,2] => 17
[-3,-4,-1,-2] => 3
[3,4,2,1] => 20
[3,4,2,-1] => 6
[3,4,-2,1] => 10
[3,4,-2,-1] => 1
[3,-4,2,1] => 64
[3,-4,2,-1] => 17
[3,-4,-2,1] => 23
[3,-4,-2,-1] => 2
[-3,4,2,1] => 97
[-3,4,2,-1] => 27
[-3,4,-2,1] => 34
[-3,4,-2,-1] => 3
[-3,-4,2,1] => 140
[-3,-4,2,-1] => 35
[-3,-4,-2,1] => 37
[-3,-4,-2,-1] => 3
[4,1,2,3] => 20
[4,1,2,-3] => 45
[4,1,-2,3] => 39
[4,1,-2,-3] => 36
[4,-1,2,3] => 6
[4,-1,2,-3] => 8
[4,-1,-2,3] => 2
[4,-1,-2,-3] => 1
[-4,1,2,3] => 35
[-4,1,2,-3] => 63
[-4,1,-2,3] => 63
[-4,1,-2,-3] => 42
[-4,-1,2,3] => 10
[-4,-1,2,-3] => 10
[-4,-1,-2,3] => 3
[-4,-1,-2,-3] => 1
[4,1,3,2] => 45
[4,1,3,-2] => 36
[4,1,-3,2] => 60
[4,1,-3,-2] => 25
[4,-1,3,2] => 8
[4,-1,3,-2] => 3
[4,-1,-3,2] => 6
[4,-1,-3,-2] => 1
[-4,1,3,2] => 84
[-4,1,3,-2] => 63
[-4,1,-3,2] => 77
[-4,1,-3,-2] => 28
[-4,-1,3,2] => 15
[-4,-1,3,-2] => 5
[-4,-1,-3,2] => 7
[-4,-1,-3,-2] => 1
[4,2,1,3] => 45
[4,2,1,-3] => 96
[4,2,-1,3] => 9
[4,2,-1,-3] => 11
[4,-2,1,3] => 29
[4,-2,1,-3] => 31
[4,-2,-1,3] => 2
[4,-2,-1,-3] => 1
[-4,2,1,3] => 84
[-4,2,1,-3] => 140
[-4,2,-1,3] => 16
[-4,2,-1,-3] => 14
[-4,-2,1,3] => 44
[-4,-2,1,-3] => 36
[-4,-2,-1,3] => 3
[-4,-2,-1,-3] => 1
[4,2,3,1] => 36
[4,2,3,-1] => 10
[4,2,-3,1] => 64
[4,2,-3,-1] => 11
[4,-2,3,1] => 31
[4,-2,3,-1] => 5
[4,-2,-3,1] => 20
[4,-2,-3,-1] => 2
[-4,2,3,1] => 70
[-4,2,3,-1] => 19
[-4,2,-3,1] => 91
[-4,2,-3,-1] => 14
[-4,-2,3,1] => 52
[-4,-2,3,-1] => 8
[-4,-2,-3,1] => 22
[-4,-2,-3,-1] => 2
[4,3,1,2] => 60
[4,3,1,-2] => 64
[4,3,-1,2] => 11
[4,3,-1,-2] => 4
[4,-3,1,2] => 50
[4,-3,1,-2] => 31
[4,-3,-1,2] => 6
[4,-3,-1,-2] => 1
[-4,3,1,2] => 126
[-4,3,1,-2] => 121
[-4,3,-1,2] => 23
[-4,3,-1,-2] => 7
[-4,-3,1,2] => 61
[-4,-3,1,-2] => 34
[-4,-3,-1,2] => 7
[-4,-3,-1,-2] => 1
[4,3,2,1] => 64
[4,3,2,-1] => 20
[4,3,-2,1] => 36
[4,3,-2,-1] => 4
[4,-3,2,1] => 60
[4,-3,2,-1] => 14
[4,-3,-2,1] => 14
[4,-3,-2,-1] => 1
[-4,3,2,1] => 140
[-4,3,2,-1] => 42
[-4,3,-2,1] => 68
[-4,3,-2,-1] => 7
[-4,-3,2,1] => 78
[-4,-3,2,-1] => 17
[-4,-3,-2,1] => 15
[-4,-3,-2,-1] => 1
[1,2,3,4,5] => 1
[1,2,3,4,-5] => 5
[1,2,3,-4,5] => 20
[1,2,3,-4,-5] => 50
[1,2,-3,4,5] => 21
[1,2,-3,4,-5] => 70
[1,2,-3,-4,5] => 105
[1,2,-3,-4,-5] => 175
[1,-2,3,4,5] => 8
[1,-2,3,4,-5] => 30
[1,-2,3,-4,5] => 64
[1,-2,3,-4,-5] => 120
[1,-2,-3,4,5] => 28
[1,-2,-3,4,-5] => 70
[1,-2,-3,-4,5] => 56
[1,-2,-3,-4,-5] => 70
[-1,2,3,4,5] => 1
[-1,2,3,4,-5] => 4
[-1,2,3,-4,5] => 10
[-1,2,3,-4,-5] => 20
[-1,2,-3,4,5] => 6
[-1,2,-3,4,-5] => 16
[-1,2,-3,-4,5] => 15
[-1,2,-3,-4,-5] => 20
[-1,-2,3,4,5] => 1
[-1,-2,3,4,-5] => 3
[-1,-2,3,-4,5] => 4
[-1,-2,3,-4,-5] => 6
[-1,-2,-3,4,5] => 1
[-1,-2,-3,4,-5] => 2
[-1,-2,-3,-4,5] => 1
[-1,-2,-3,-4,-5] => 1
[1,2,3,5,4] => 5
[1,2,3,5,-4] => 10
[1,2,3,-5,4] => 15
[1,2,3,-5,-4] => 20
[1,2,-3,5,4] => 70
[1,2,-3,5,-4] => 79
[1,2,-3,-5,4] => 149
[1,2,-3,-5,-4] => 115
[1,-2,3,5,4] => 30
[1,-2,3,5,-4] => 41
[1,-2,3,-5,4] => 71
[1,-2,3,-5,-4] => 65
[1,-2,-3,5,4] => 70
[1,-2,-3,5,-4] => 51
[1,-2,-3,-5,4] => 121
[1,-2,-3,-5,-4] => 60
[-1,2,3,5,4] => 4
[-1,2,3,5,-4] => 6
[-1,2,3,-5,4] => 10
[-1,2,3,-5,-4] => 10
[-1,2,-3,5,4] => 16
[-1,2,-3,5,-4] => 13
[-1,2,-3,-5,4] => 29
[-1,2,-3,-5,-4] => 16
[-1,-2,3,5,4] => 3
[-1,-2,3,5,-4] => 3
[-1,-2,3,-5,4] => 6
[-1,-2,3,-5,-4] => 4
[-1,-2,-3,5,4] => 2
[-1,-2,-3,5,-4] => 1
[-1,-2,-3,-5,4] => 3
[-1,-2,-3,-5,-4] => 1
[1,2,4,3,5] => 5
[1,2,4,3,-5] => 25
[1,2,4,-3,5] => 15
[1,2,4,-3,-5] => 48
[1,2,-4,3,5] => 35
[1,2,-4,3,-5] => 98
[1,2,-4,-3,5] => 61
[1,2,-4,-3,-5] => 95
[1,-2,4,3,5] => 30
[1,-2,4,3,-5] => 112
[1,-2,4,-3,5] => 26
[1,-2,4,-3,-5] => 64
[1,-2,-4,3,5] => 90
[1,-2,-4,3,-5] => 184
[1,-2,-4,-3,5] => 48
[1,-2,-4,-3,-5] => 58
[-1,2,4,3,5] => 4
[-1,2,4,3,-5] => 16
[-1,2,4,-3,5] => 5
[-1,2,4,-3,-5] => 13
[-1,2,-4,3,5] => 15
[-1,2,-4,3,-5] => 33
[-1,2,-4,-3,5] => 11
[-1,2,-4,-3,-5] => 14
[-1,-2,4,3,5] => 3
[-1,-2,4,3,-5] => 9
[-1,-2,4,-3,5] => 1
[-1,-2,4,-3,-5] => 2
[-1,-2,-4,3,5] => 5
[-1,-2,-4,3,-5] => 8
[-1,-2,-4,-3,5] => 1
[-1,-2,-4,-3,-5] => 1
[1,2,4,5,3] => 10
[1,2,4,5,-3] => 10
[1,2,4,-5,3] => 40
[1,2,4,-5,-3] => 30
[1,2,-4,5,3] => 98
[1,2,-4,5,-3] => 77
[1,2,-4,-5,3] => 175
[1,2,-4,-5,-3] => 105
[1,-2,4,5,3] => 41
[1,-2,4,5,-3] => 23
[1,-2,4,-5,3] => 129
[1,-2,4,-5,-3] => 55
[1,-2,-4,5,3] => 184
[1,-2,-4,5,-3] => 81
[1,-2,-4,-5,3] => 265
[1,-2,-4,-5,-3] => 92
[-1,2,4,5,3] => 6
[-1,2,4,5,-3] => 4
[-1,2,4,-5,3] => 20
[-1,2,4,-5,-3] => 10
[-1,2,-4,5,3] => 33
[-1,2,-4,5,-3] => 17
[-1,2,-4,-5,3] => 50
[-1,2,-4,-5,-3] => 20
[-1,-2,4,5,3] => 3
[-1,-2,4,5,-3] => 1
[-1,-2,4,-5,3] => 8
[-1,-2,4,-5,-3] => 2
[-1,-2,-4,5,3] => 8
[-1,-2,-4,5,-3] => 2
[-1,-2,-4,-5,3] => 10
[-1,-2,-4,-5,-3] => 2
[1,2,5,3,4] => 15
[1,2,5,3,-4] => 40
[1,2,5,-3,4] => 48
[1,2,5,-3,-4] => 50
[1,2,-5,3,4] => 35
[1,2,-5,3,-4] => 70
[1,2,-5,-3,4] => 98
[1,2,-5,-3,-4] => 70
[1,-2,5,3,4] => 71
[1,-2,5,3,-4] => 129
[1,-2,5,-3,4] => 64
[1,-2,5,-3,-4] => 45
[1,-2,-5,3,4] => 135
[1,-2,-5,3,-4] => 185
[1,-2,-5,-3,4] => 109
[1,-2,-5,-3,-4] => 52
[-1,2,5,3,4] => 10
[-1,2,5,3,-4] => 20
[-1,2,5,-3,4] => 13
[-1,2,5,-3,-4] => 10
[-1,2,-5,3,4] => 20
[-1,2,-5,3,-4] => 30
[-1,2,-5,-3,4] => 23
[-1,2,-5,-3,-4] => 12
[-1,-2,5,3,4] => 6
[-1,-2,5,3,-4] => 8
[-1,-2,5,-3,4] => 2
[-1,-2,5,-3,-4] => 1
[-1,-2,-5,3,4] => 10
[-1,-2,-5,3,-4] => 10
[-1,-2,-5,-3,4] => 3
[-1,-2,-5,-3,-4] => 1
[1,2,5,4,3] => 40
[1,2,5,4,-3] => 45
[1,2,5,-4,3] => 50
[1,2,5,-4,-3] => 27
[1,2,-5,4,3] => 105
[1,2,-5,4,-3] => 105
[1,2,-5,-4,3] => 77
[1,2,-5,-4,-3] => 35
[1,-2,5,4,3] => 129
[1,-2,5,4,-3] => 81
[1,-2,5,-4,3] => 120
[1,-2,5,-4,-3] => 36
[1,-2,-5,4,3] => 275
[1,-2,-5,4,-3] => 155
[1,-2,-5,-4,3] => 156
[1,-2,-5,-4,-3] => 40
[-1,2,5,4,3] => 20
[-1,2,5,4,-3] => 15
[-1,2,5,-4,3] => 20
[-1,2,5,-4,-3] => 7
[-1,2,-5,4,3] => 45
[-1,2,-5,4,-3] => 30
[-1,2,-5,-4,3] => 27
[-1,2,-5,-4,-3] => 8
[-1,-2,5,4,3] => 8
[-1,-2,5,4,-3] => 3
[-1,-2,5,-4,3] => 6
[-1,-2,5,-4,-3] => 1
[-1,-2,-5,4,3] => 15
[-1,-2,-5,4,-3] => 5
[-1,-2,-5,-4,3] => 7
[-1,-2,-5,-4,-3] => 1
[1,3,2,4,5] => 5
[1,3,2,4,-5] => 25
[1,3,2,-4,5] => 100
[1,3,2,-4,-5] => 250
[1,3,-2,4,5] => 7
[1,3,-2,4,-5] => 26
[1,3,-2,-4,5] => 54
[1,3,-2,-4,-5] => 100
[1,-3,2,4,5] => 28
[1,-3,2,4,-5] => 96
[1,-3,2,-4,5] => 159
[1,-3,2,-4,-5] => 275
[1,-3,-2,4,5] => 22
[1,-3,-2,4,-5] => 54
[1,-3,-2,-4,5] => 41
[1,-3,-2,-4,-5] => 50
[-1,3,2,4,5] => 4
[-1,3,2,4,-5] => 16
[-1,3,2,-4,5] => 40
[-1,3,2,-4,-5] => 80
[-1,3,-2,4,5] => 1
[-1,3,-2,4,-5] => 3
[-1,3,-2,-4,5] => 4
[-1,3,-2,-4,-5] => 6
[-1,-3,2,4,5] => 7
[-1,-3,2,4,-5] => 19
[-1,-3,2,-4,5] => 19
[-1,-3,2,-4,-5] => 26
[-1,-3,-2,4,5] => 1
[-1,-3,-2,4,-5] => 2
[-1,-3,-2,-4,5] => 1
[-1,-3,-2,-4,-5] => 1
[1,3,2,5,4] => 25
[1,3,2,5,-4] => 50
[1,3,2,-5,4] => 75
[1,3,2,-5,-4] => 100
[1,3,-2,5,4] => 26
[1,3,-2,5,-4] => 35
[1,3,-2,-5,4] => 61
[1,3,-2,-5,-4] => 55
[1,-3,2,5,4] => 96
[1,-3,2,5,-4] => 114
[1,-3,2,-5,4] => 210
[1,-3,2,-5,-4] => 170
[1,-3,-2,5,4] => 54
[1,-3,-2,5,-4] => 38
[1,-3,-2,-5,4] => 92
[1,-3,-2,-5,-4] => 44
[-1,3,2,5,4] => 16
[-1,3,2,5,-4] => 24
[-1,3,2,-5,4] => 40
[-1,3,2,-5,-4] => 40
[-1,3,-2,5,4] => 3
[-1,3,-2,5,-4] => 3
[-1,3,-2,-5,4] => 6
[-1,3,-2,-5,-4] => 4
[-1,-3,2,5,4] => 19
[-1,-3,2,5,-4] => 16
[-1,-3,2,-5,4] => 35
[-1,-3,2,-5,-4] => 20
[-1,-3,-2,5,4] => 2
[-1,-3,-2,5,-4] => 1
[-1,-3,-2,-5,4] => 3
[-1,-3,-2,-5,-4] => 1
[1,3,4,2,5] => 10
[1,3,4,2,-5] => 50
[1,3,4,-2,5] => 6
[1,3,4,-2,-5] => 22
[1,3,-4,2,5] => 119
[1,3,-4,2,-5] => 322
[1,3,-4,-2,5] => 44
[1,3,-4,-2,-5] => 80
[1,-3,4,2,5] => 96
[1,-3,4,2,-5] => 324
[1,-3,4,-2,5] => 37
[1,-3,4,-2,-5] => 89
[1,-3,-4,2,5] => 196
[1,-3,-4,2,-5] => 364
[1,-3,-4,-2,5] => 63
[1,-3,-4,-2,-5] => 74
[-1,3,4,2,5] => 6
[-1,3,4,2,-5] => 24
[-1,3,4,-2,5] => 1
[-1,3,4,-2,-5] => 3
[-1,3,-4,2,5] => 39
[-1,3,-4,2,-5] => 83
[-1,3,-4,-2,5] => 4
[-1,3,-4,-2,-5] => 6
[-1,-3,4,2,5] => 19
[-1,-3,4,2,-5] => 51
[-1,-3,4,-2,5] => 2
[-1,-3,4,-2,-5] => 4
[-1,-3,-4,2,5] => 21
[-1,-3,-4,2,-5] => 30
[-1,-3,-4,-2,5] => 2
[-1,-3,-4,-2,-5] => 2
[1,3,4,5,2] => 10
[1,3,4,5,-2] => 5
[1,3,4,-5,2] => 45
[1,3,4,-5,-2] => 18
[1,3,-4,5,2] => 147
[1,3,-4,5,-2] => 63
[1,3,-4,-5,2] => 315
[1,3,-4,-5,-2] => 105
[1,-3,4,5,2] => 114
[1,-3,4,5,-2] => 45
[1,-3,4,-5,2] => 329
[1,-3,4,-5,-2] => 105
[1,-3,-4,5,2] => 364
[1,-3,-4,5,-2] => 126
[1,-3,-4,-5,2] => 490
[1,-3,-4,-5,-2] => 140
[-1,3,4,5,2] => 4
[-1,3,4,5,-2] => 1
[-1,3,4,-5,2] => 15
[-1,3,4,-5,-2] => 3
[-1,3,-4,5,2] => 33
[-1,3,-4,5,-2] => 7
[-1,3,-4,-5,2] => 60
[-1,3,-4,-5,-2] => 10
[-1,-3,4,5,2] => 16
[-1,-3,4,5,-2] => 3
[-1,-3,4,-5,2] => 39
[-1,-3,4,-5,-2] => 6
[-1,-3,-4,5,2] => 30
[-1,-3,-4,5,-2] => 5
[-1,-3,-4,-5,2] => 35
[-1,-3,-4,-5,-2] => 5
[1,3,5,2,4] => 40
[1,3,5,2,-4] => 95
[1,3,5,-2,4] => 22
[1,3,5,-2,-4] => 29
[1,3,-5,2,4] => 105
[1,3,-5,2,-4] => 182
[1,3,-5,-2,4] => 51
[1,3,-5,-2,-4] => 45
[1,-3,5,2,4] => 210
[1,-3,5,2,-4] => 329
[1,-3,5,-2,4] => 89
[1,-3,5,-2,-4] => 60
[1,-3,-5,2,4] => 369
[1,-3,-5,2,-4] => 445
[1,-3,-5,-2,4] => 149
[1,-3,-5,-2,-4] => 68
[-1,3,5,2,4] => 20
[-1,3,5,2,-4] => 35
[-1,3,5,-2,4] => 3
[-1,3,5,-2,-4] => 3
[-1,3,-5,2,4] => 45
[-1,3,-5,2,-4] => 57
[-1,3,-5,-2,4] => 6
[-1,3,-5,-2,-4] => 4
[-1,-3,5,2,4] => 35
[-1,-3,5,2,-4] => 39
[-1,-3,5,-2,4] => 4
[-1,-3,5,-2,-4] => 2
[-1,-3,-5,2,4] => 54
[-1,-3,-5,2,-4] => 46
[-1,-3,-5,-2,4] => 6
[-1,-3,-5,-2,-4] => 2
[1,3,5,4,2] => 45
[1,3,5,4,-2] => 24
[1,3,5,-4,2] => 75
[1,3,5,-4,-2] => 23
[1,3,-5,4,2] => 126
[1,3,-5,4,-2] => 63
[1,3,-5,-4,2] => 133
[1,3,-5,-4,-2] => 35
[1,-3,5,4,2] => 329
[1,-3,5,4,-2] => 142
[1,-3,5,-4,2] => 275
[1,-3,5,-4,-2] => 66
[1,-3,-5,4,2] => 641
[1,-3,-5,4,-2] => 260
[1,-3,-5,-4,2] => 341
[1,-3,-5,-4,-2] => 72
[-1,3,5,4,2] => 15
[-1,3,5,4,-2] => 4
[-1,3,5,-4,2] => 20
[-1,3,5,-4,-2] => 3
[-1,3,-5,4,2] => 36
[-1,3,-5,4,-2] => 9
[-1,3,-5,-4,2] => 31
[-1,3,-5,-4,-2] => 4
[-1,-3,5,4,2] => 39
[-1,-3,5,4,-2] => 8
[-1,-3,5,-4,2] => 26
[-1,-3,5,-4,-2] => 3
[-1,-3,-5,4,2] => 67
[-1,-3,-5,4,-2] => 13
[-1,-3,-5,-4,2] => 29
[-1,-3,-5,-4,-2] => 3
[1,4,2,3,5] => 15
[1,4,2,3,-5] => 75
[1,4,2,-3,5] => 69
[1,4,2,-3,-5] => 218
[1,4,-2,3,5] => 26
[1,4,-2,3,-5] => 96
[1,4,-2,-3,5] => 21
[1,4,-2,-3,-5] => 51
[1,-4,2,3,5] => 56
[1,-4,2,3,-5] => 168
[1,-4,2,-3,5] => 166
[1,-4,2,-3,-5] => 270
[1,-4,-2,3,5] => 75
[1,-4,-2,3,-5] => 151
[1,-4,-2,-3,5] => 37
[1,-4,-2,-3,-5] => 44
[-1,4,2,3,5] => 10
[-1,4,2,3,-5] => 40
[-1,4,2,-3,5] => 19
[-1,4,2,-3,-5] => 49
[-1,4,-2,3,5] => 3
[-1,4,-2,3,-5] => 9
[-1,4,-2,-3,5] => 1
[-1,4,-2,-3,-5] => 2
[-1,-4,2,3,5] => 21
[-1,-4,2,3,-5] => 49
[-1,-4,2,-3,5] => 26
[-1,-4,2,-3,-5] => 34
[-1,-4,-2,3,5] => 5
[-1,-4,-2,3,-5] => 8
[-1,-4,-2,-3,5] => 1
[-1,-4,-2,-3,-5] => 1
[1,4,2,5,3] => 40
[1,4,2,5,-3] => 45
[1,4,2,-5,3] => 155
[1,4,2,-5,-3] => 132
[1,4,-2,5,3] => 35
[1,4,-2,5,-3] => 19
[1,4,-2,-5,3] => 109
[1,4,-2,-5,-3] => 45
[1,-4,2,5,3] => 168
[1,-4,2,5,-3] => 156
[1,-4,2,-5,3] => 324
[1,-4,2,-5,-3] => 220
[1,-4,-2,5,3] => 151
[1,-4,-2,5,-3] => 64
[1,-4,-2,-5,3] => 215
[1,-4,-2,-5,-3] => 72
[-1,4,2,5,3] => 20
[-1,4,2,5,-3] => 15
[-1,4,2,-5,3] => 65
[-1,4,2,-5,-3] => 37
[-1,4,-2,5,3] => 3
[-1,4,-2,5,-3] => 1
[-1,4,-2,-5,3] => 8
[-1,4,-2,-5,-3] => 2
[-1,-4,2,5,3] => 49
[-1,-4,2,5,-3] => 30
[-1,-4,2,-5,3] => 79
[-1,-4,2,-5,-3] => 36
[-1,-4,-2,5,3] => 8
[-1,-4,-2,5,-3] => 2
[-1,-4,-2,-5,3] => 10
[-1,-4,-2,-5,-3] => 2
[1,4,3,2,5] => 40
[1,4,3,2,-5] => 200
[1,4,3,-2,5] => 29
[1,4,3,-2,-5] => 106
[1,4,-3,2,5] => 70
[1,4,-3,2,-5] => 228
[1,4,-3,-2,5] => 16
[1,4,-3,-2,-5] => 38
[1,-4,3,2,5] => 196
[1,-4,3,2,-5] => 576
[1,-4,3,-2,5] => 114
[1,-4,3,-2,-5] => 218
[1,-4,-3,2,5] => 121
[1,-4,-3,2,-5] => 213
[1,-4,-3,-2,5] => 26
[1,-4,-3,-2,-5] => 30
[-1,4,3,2,5] => 20
[-1,4,3,2,-5] => 80
[-1,4,3,-2,5] => 4
[-1,4,3,-2,-5] => 12
[-1,4,-3,2,5] => 16
[-1,4,-3,2,-5] => 42
[-1,4,-3,-2,5] => 1
[-1,4,-3,-2,-5] => 2
[-1,-4,3,2,5] => 56
[-1,-4,3,2,-5] => 128
[-1,-4,3,-2,5] => 9
[-1,-4,3,-2,-5] => 14
[-1,-4,-3,2,5] => 16
[-1,-4,-3,2,-5] => 22
[-1,-4,-3,-2,5] => 1
[-1,-4,-3,-2,-5] => 1
[1,4,3,5,2] => 45
[1,4,3,5,-2] => 24
[1,4,3,-5,2] => 201
[1,4,3,-5,-2] => 86
[1,4,-3,5,2] => 79
[1,4,-3,5,-2] => 26
[1,4,-3,-5,2] => 220
[1,4,-3,-5,-2] => 60
[1,-4,3,5,2] => 252
[1,-4,3,5,-2] => 124
[1,-4,3,-5,2] => 596
[1,-4,3,-5,-2] => 220
[1,-4,-3,5,2] => 213
[1,-4,-3,5,-2] => 62
[1,-4,-3,-5,2] => 275
[1,-4,-3,-5,-2] => 68
[-1,4,3,5,2] => 15
[-1,4,3,5,-2] => 4
[-1,4,3,-5,2] => 56
[-1,4,3,-5,-2] => 12
[-1,4,-3,5,2] => 13
[-1,4,-3,5,-2] => 2
[-1,4,-3,-5,2] => 31
[-1,4,-3,-5,-2] => 4
[-1,-4,3,5,2] => 49
[-1,-4,3,5,-2] => 12
[-1,-4,3,-5,2] => 97
[-1,-4,3,-5,-2] => 18
[-1,-4,-3,5,2] => 22
[-1,-4,-3,5,-2] => 3
[-1,-4,-3,-5,2] => 25
[-1,-4,-3,-5,-2] => 3
[1,4,5,2,3] => 50
[1,4,5,2,-3] => 75
[1,4,5,-2,3] => 29
[1,4,5,-2,-3] => 15
[1,4,-5,2,3] => 175
[1,4,-5,2,-3] => 210
[1,4,-5,-2,3] => 89
[1,4,-5,-2,-3] => 35
[1,-4,5,2,3] => 324
[1,-4,5,2,-3] => 386
[1,-4,5,-2,3] => 218
[1,-4,5,-2,-3] => 76
[1,-4,-5,2,3] => 490
[1,-4,-5,2,-3] => 490
[1,-4,-5,-2,3] => 294
[1,-4,-5,-2,-3] => 84
[-1,4,5,2,3] => 20
[-1,4,5,2,-3] => 20
[-1,4,5,-2,3] => 3
[-1,4,5,-2,-3] => 1
[-1,4,-5,2,3] => 60
[-1,4,-5,2,-3] => 48
[-1,4,-5,-2,3] => 8
[-1,4,-5,-2,-3] => 2
[-1,-4,5,2,3] => 79
[-1,-4,5,2,-3] => 62
[-1,-4,5,-2,3] => 14
[-1,-4,5,-2,-3] => 3
[-1,-4,-5,2,3] => 105
[-1,-4,-5,2,-3] => 70
[-1,-4,-5,-2,3] => 17
[-1,-4,-5,-2,-3] => 3
[1,4,5,3,2] => 75
[1,4,5,3,-2] => 45
[1,4,5,-3,2] => 50
[1,4,5,-3,-2] => 11
[1,4,-5,3,2] => 280
[1,4,-5,3,-2] => 149
[1,4,-5,-3,2] => 131
[1,4,-5,-3,-2] => 25
[1,-4,5,3,2] => 596
[1,-4,5,3,-2] => 334
[1,-4,5,-3,2] => 270
[1,-4,5,-3,-2] => 52
[1,-4,-5,3,2] => 980
[1,-4,-5,3,-2] => 490
[1,-4,-5,-3,2] => 322
[1,-4,-5,-3,-2] => 56
[-1,4,5,3,2] => 20
[-1,4,5,3,-2] => 6
[-1,4,5,-3,2] => 10
[-1,4,5,-3,-2] => 1
[-1,4,-5,3,2] => 64
[-1,4,-5,3,-2] => 17
[-1,4,-5,-3,2] => 23
[-1,4,-5,-3,-2] => 2
[-1,-4,5,3,2] => 97
[-1,-4,5,3,-2] => 27
[-1,-4,5,-3,2] => 34
[-1,-4,5,-3,-2] => 3
[-1,-4,-5,3,2] => 140
[-1,-4,-5,3,-2] => 35
[-1,-4,-5,-3,2] => 37
[-1,-4,-5,-3,-2] => 3
[1,5,2,3,4] => 35
[1,5,2,3,-4] => 105
[1,5,2,-3,4] => 168
[1,5,2,-3,-4] => 210
[1,5,-2,3,4] => 61
[1,5,-2,3,-4] => 109
[1,5,-2,-3,4] => 51
[1,5,-2,-3,-4] => 35
[1,-5,2,3,4] => 70
[1,-5,2,3,-4] => 168
[1,-5,2,-3,4] => 308
[1,-5,2,-3,-4] => 280
[1,-5,-2,3,4] => 115
[1,-5,-2,3,-4] => 155
[1,-5,-2,-3,4] => 86
[1,-5,-2,-3,-4] => 40
[-1,5,2,3,4] => 20
[-1,5,2,3,-4] => 45
[-1,5,2,-3,4] => 39
[-1,5,2,-3,-4] => 36
[-1,5,-2,3,4] => 6
[-1,5,-2,3,-4] => 8
[-1,5,-2,-3,4] => 2
[-1,5,-2,-3,-4] => 1
[-1,-5,2,3,4] => 35
[-1,-5,2,3,-4] => 63
[-1,-5,2,-3,4] => 63
[-1,-5,2,-3,-4] => 42
[-1,-5,-2,3,4] => 10
[-1,-5,-2,3,-4] => 10
[-1,-5,-2,-3,4] => 3
[-1,-5,-2,-3,-4] => 1
[1,5,2,4,3] => 105
[1,5,2,4,-3] => 126
[1,5,2,-4,3] => 175
[1,5,2,-4,-3] => 112
[1,5,-2,4,3] => 109
[1,5,-2,4,-3] => 66
[1,5,-2,-4,3] => 100
[1,5,-2,-4,-3] => 29
[1,-5,2,4,3] => 224
[1,-5,2,4,-3] => 252
[1,-5,2,-4,3] => 252
[1,-5,2,-4,-3] => 140
[1,-5,-2,4,3] => 230
[1,-5,-2,4,-3] => 125
[1,-5,-2,-4,3] => 129
[1,-5,-2,-4,-3] => 32
[-1,5,2,4,3] => 45
[-1,5,2,4,-3] => 36
[-1,5,2,-4,3] => 60
[-1,5,2,-4,-3] => 25
[-1,5,-2,4,3] => 8
[-1,5,-2,4,-3] => 3
[-1,5,-2,-4,3] => 6
[-1,5,-2,-4,-3] => 1
[-1,-5,2,4,3] => 84
[-1,-5,2,4,-3] => 63
[-1,-5,2,-4,3] => 77
[-1,-5,2,-4,-3] => 28
[-1,-5,-2,4,3] => 15
[-1,-5,-2,4,-3] => 5
[-1,-5,-2,-4,3] => 7
[-1,-5,-2,-4,-3] => 1
[1,5,3,2,4] => 105
[1,5,3,2,-4] => 301
[1,5,3,-2,4] => 77
[1,5,3,-2,-4] => 124
[1,5,-3,2,4] => 149
[1,5,-3,2,-4] => 220
[1,5,-3,-2,4] => 38
[1,5,-3,-2,-4] => 25
[1,-5,3,2,4] => 224
[1,-5,3,2,-4] => 504
[1,-5,3,-2,4] => 156
[1,-5,3,-2,-4] => 180
[1,-5,-3,2,4] => 254
[1,-5,-3,2,-4] => 290
[1,-5,-3,-2,4] => 63
[1,-5,-3,-2,-4] => 28
[-1,5,3,2,4] => 45
[-1,5,3,2,-4] => 96
[-1,5,3,-2,4] => 9
[-1,5,3,-2,-4] => 11
[-1,5,-3,2,4] => 29
[-1,5,-3,2,-4] => 31
[-1,5,-3,-2,4] => 2
[-1,5,-3,-2,-4] => 1
[-1,-5,3,2,4] => 84
[-1,-5,3,2,-4] => 140
[-1,-5,3,-2,4] => 16
[-1,-5,3,-2,-4] => 14
[-1,-5,-3,2,4] => 44
[-1,-5,-3,2,-4] => 36
[-1,-5,-3,-2,4] => 3
[-1,-5,-3,-2,-4] => 1
[1,5,3,4,2] => 126
[1,5,3,4,-2] => 70
[1,5,3,-4,2] => 280
[1,5,3,-4,-2] => 98
[1,5,-3,4,2] => 220
[1,5,-3,4,-2] => 76
[1,5,-3,-4,2] => 175
[1,5,-3,-4,-2] => 37
[1,-5,3,4,2] => 280
[1,-5,3,4,-2] => 152
[1,-5,3,-4,2] => 448
[1,-5,3,-4,-2] => 140
[1,-5,-3,4,2] => 411
[1,-5,-3,4,-2] => 135
[1,-5,-3,-4,2] => 212
[1,-5,-3,-4,-2] => 40
[-1,5,3,4,2] => 36
[-1,5,3,4,-2] => 10
[-1,5,3,-4,2] => 64
[-1,5,3,-4,-2] => 11
[-1,5,-3,4,2] => 31
[-1,5,-3,4,-2] => 5
[-1,5,-3,-4,2] => 20
[-1,5,-3,-4,-2] => 2
[-1,-5,3,4,2] => 70
[-1,-5,3,4,-2] => 19
[-1,-5,3,-4,2] => 91
[-1,-5,3,-4,-2] => 14
[-1,-5,-3,4,2] => 52
[-1,-5,-3,4,-2] => 8
[-1,-5,-3,-4,2] => 22
[-1,-5,-3,-4,-2] => 2
[1,5,4,2,3] => 175
[1,5,4,2,-3] => 280
[1,5,4,-2,3] => 124
[1,5,4,-2,-3] => 70
[1,5,-4,2,3] => 175
[1,5,-4,2,-3] => 166
[1,5,-4,-2,3] => 80
[1,5,-4,-2,-3] => 22
[1,-5,4,2,3] => 420
[1,-5,4,2,-3] => 604
[1,-5,4,-2,3] => 294
[1,-5,4,-2,-3] => 140
[1,-5,-4,2,3] => 236
[1,-5,-4,2,-3] => 200
[1,-5,-4,-2,3] => 102
[1,-5,-4,-2,-3] => 24
[-1,5,4,2,3] => 60
[-1,5,4,2,-3] => 64
[-1,5,4,-2,3] => 11
[-1,5,4,-2,-3] => 4
[-1,5,-4,2,3] => 50
[-1,5,-4,2,-3] => 31
[-1,5,-4,-2,3] => 6
[-1,5,-4,-2,-3] => 1
[-1,-5,4,2,3] => 126
[-1,-5,4,2,-3] => 121
[-1,-5,4,-2,3] => 23
[-1,-5,4,-2,-3] => 7
[-1,-5,-4,2,3] => 61
[-1,-5,-4,2,-3] => 34
[-1,-5,-4,-2,3] => 7
[-1,-5,-4,-2,-3] => 1
[1,5,4,3,2] => 280
[1,5,4,3,-2] => 175
[1,5,4,-3,2] => 210
[1,5,4,-3,-2] => 51
[1,5,-4,3,2] => 315
[1,5,-4,3,-2] => 149
[1,5,-4,-3,2] => 95
[1,5,-4,-3,-2] => 15
[1,-5,4,3,2] => 700
[1,-5,4,3,-2] => 420
[1,-5,4,-3,2] => 446
[1,-5,4,-3,-2] => 100
[1,-5,-4,3,2] => 454
[1,-5,-4,3,-2] => 200
[1,-5,-4,-3,2] => 110
[1,-5,-4,-3,-2] => 16
[-1,5,4,3,2] => 64
[-1,5,4,3,-2] => 20
[-1,5,4,-3,2] => 36
[-1,5,4,-3,-2] => 4
[-1,5,-4,3,2] => 60
[-1,5,-4,3,-2] => 14
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Created: Feb 05, 2022 at 17:47 by Martin Rubey
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Last Updated: Feb 05, 2022 at 17:47 by Martin Rubey