*****************************************************************************
* 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: St001848
-----------------------------------------------------------------------------
Collection: Signed permutations
-----------------------------------------------------------------------------
Description: The atomic length of a signed permutation.
The atomic length of an element $w$ of a Weyl group is the sum of the heights of the inversions of $w$.
-----------------------------------------------------------------------------
References: [1] not yet indexed [[arXiv 2211.12359]]
-----------------------------------------------------------------------------
Code:
def atomic_length(pi):
"""
EXAMPLES::
sage: l = [atomic_length(SignedPermutations(n).long_element()) for n in range(1,8)]
sage: l
sage: fricas.guess(l)[0].sage().factor()
1/6*(4*n + 3)*(n + 2)*(n + 1)
"""
W = WeylGroup(pi.parent().coxeter_type())
w = W.from_reduced_word(pi.reduced_word())
return sum(a.height() for a in w.inversions(inversion_type="roots"))
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[-1] => 1
[1,2] => 0
[1,-2] => 1
[-1,2] => 6
[-1,-2] => 7
[2,1] => 1
[2,-1] => 3
[-2,1] => 4
[-2,-1] => 6
[1,2,3] => 0
[1,2,-3] => 1
[1,-2,3] => 6
[1,-2,-3] => 7
[-1,2,3] => 15
[-1,2,-3] => 16
[-1,-2,3] => 21
[-1,-2,-3] => 22
[1,3,2] => 1
[1,3,-2] => 3
[1,-3,2] => 4
[1,-3,-2] => 6
[-1,3,2] => 16
[-1,3,-2] => 18
[-1,-3,2] => 19
[-1,-3,-2] => 21
[2,1,3] => 1
[2,1,-3] => 2
[2,-1,3] => 10
[2,-1,-3] => 11
[-2,1,3] => 11
[-2,1,-3] => 12
[-2,-1,3] => 20
[-2,-1,-3] => 21
[2,3,1] => 3
[2,3,-1] => 6
[2,-3,1] => 6
[2,-3,-1] => 9
[-2,3,1] => 13
[-2,3,-1] => 16
[-2,-3,1] => 16
[-2,-3,-1] => 19
[3,1,2] => 3
[3,1,-2] => 5
[3,-1,2] => 12
[3,-1,-2] => 14
[-3,1,2] => 8
[-3,1,-2] => 10
[-3,-1,2] => 17
[-3,-1,-2] => 19
[3,2,1] => 4
[3,2,-1] => 7
[3,-2,1] => 10
[3,-2,-1] => 13
[-3,2,1] => 9
[-3,2,-1] => 12
[-3,-2,1] => 15
[-3,-2,-1] => 18
[1,2,3,4] => 0
[1,2,3,-4] => 1
[1,2,-3,4] => 6
[1,2,-3,-4] => 7
[1,-2,3,4] => 15
[1,-2,3,-4] => 16
[1,-2,-3,4] => 21
[1,-2,-3,-4] => 22
[-1,2,3,4] => 28
[-1,2,3,-4] => 29
[-1,2,-3,4] => 34
[-1,2,-3,-4] => 35
[-1,-2,3,4] => 43
[-1,-2,3,-4] => 44
[-1,-2,-3,4] => 49
[-1,-2,-3,-4] => 50
[1,2,4,3] => 1
[1,2,4,-3] => 3
[1,2,-4,3] => 4
[1,2,-4,-3] => 6
[1,-2,4,3] => 16
[1,-2,4,-3] => 18
[1,-2,-4,3] => 19
[1,-2,-4,-3] => 21
[-1,2,4,3] => 29
[-1,2,4,-3] => 31
[-1,2,-4,3] => 32
[-1,2,-4,-3] => 34
[-1,-2,4,3] => 44
[-1,-2,4,-3] => 46
[-1,-2,-4,3] => 47
[-1,-2,-4,-3] => 49
[1,3,2,4] => 1
[1,3,2,-4] => 2
[1,3,-2,4] => 10
[1,3,-2,-4] => 11
[1,-3,2,4] => 11
[1,-3,2,-4] => 12
[1,-3,-2,4] => 20
[1,-3,-2,-4] => 21
[-1,3,2,4] => 29
[-1,3,2,-4] => 30
[-1,3,-2,4] => 38
[-1,3,-2,-4] => 39
[-1,-3,2,4] => 39
[-1,-3,2,-4] => 40
[-1,-3,-2,4] => 48
[-1,-3,-2,-4] => 49
[1,3,4,2] => 3
[1,3,4,-2] => 6
[1,3,-4,2] => 6
[1,3,-4,-2] => 9
[1,-3,4,2] => 13
[1,-3,4,-2] => 16
[1,-3,-4,2] => 16
[1,-3,-4,-2] => 19
[-1,3,4,2] => 31
[-1,3,4,-2] => 34
[-1,3,-4,2] => 34
[-1,3,-4,-2] => 37
[-1,-3,4,2] => 41
[-1,-3,4,-2] => 44
[-1,-3,-4,2] => 44
[-1,-3,-4,-2] => 47
[1,4,2,3] => 3
[1,4,2,-3] => 5
[1,4,-2,3] => 12
[1,4,-2,-3] => 14
[1,-4,2,3] => 8
[1,-4,2,-3] => 10
[1,-4,-2,3] => 17
[1,-4,-2,-3] => 19
[-1,4,2,3] => 31
[-1,4,2,-3] => 33
[-1,4,-2,3] => 40
[-1,4,-2,-3] => 42
[-1,-4,2,3] => 36
[-1,-4,2,-3] => 38
[-1,-4,-2,3] => 45
[-1,-4,-2,-3] => 47
[1,4,3,2] => 4
[1,4,3,-2] => 7
[1,4,-3,2] => 10
[1,4,-3,-2] => 13
[1,-4,3,2] => 9
[1,-4,3,-2] => 12
[1,-4,-3,2] => 15
[1,-4,-3,-2] => 18
[-1,4,3,2] => 32
[-1,4,3,-2] => 35
[-1,4,-3,2] => 38
[-1,4,-3,-2] => 41
[-1,-4,3,2] => 37
[-1,-4,3,-2] => 40
[-1,-4,-3,2] => 43
[-1,-4,-3,-2] => 46
[2,1,3,4] => 1
[2,1,3,-4] => 2
[2,1,-3,4] => 7
[2,1,-3,-4] => 8
[2,-1,3,4] => 21
[2,-1,3,-4] => 22
[2,-1,-3,4] => 27
[2,-1,-3,-4] => 28
[-2,1,3,4] => 22
[-2,1,3,-4] => 23
[-2,1,-3,4] => 28
[-2,1,-3,-4] => 29
[-2,-1,3,4] => 42
[-2,-1,3,-4] => 43
[-2,-1,-3,4] => 48
[-2,-1,-3,-4] => 49
[2,1,4,3] => 2
[2,1,4,-3] => 4
[2,1,-4,3] => 5
[2,1,-4,-3] => 7
[2,-1,4,3] => 22
[2,-1,4,-3] => 24
[2,-1,-4,3] => 25
[2,-1,-4,-3] => 27
[-2,1,4,3] => 23
[-2,1,4,-3] => 25
[-2,1,-4,3] => 26
[-2,1,-4,-3] => 28
[-2,-1,4,3] => 43
[-2,-1,4,-3] => 45
[-2,-1,-4,3] => 46
[-2,-1,-4,-3] => 48
[2,3,1,4] => 3
[2,3,1,-4] => 4
[2,3,-1,4] => 15
[2,3,-1,-4] => 16
[2,-3,1,4] => 13
[2,-3,1,-4] => 14
[2,-3,-1,4] => 25
[2,-3,-1,-4] => 26
[-2,3,1,4] => 24
[-2,3,1,-4] => 25
[-2,3,-1,4] => 36
[-2,3,-1,-4] => 37
[-2,-3,1,4] => 34
[-2,-3,1,-4] => 35
[-2,-3,-1,4] => 46
[-2,-3,-1,-4] => 47
[2,3,4,1] => 6
[2,3,4,-1] => 10
[2,3,-4,1] => 9
[2,3,-4,-1] => 13
[2,-3,4,1] => 16
[2,-3,4,-1] => 20
[2,-3,-4,1] => 19
[2,-3,-4,-1] => 23
[-2,3,4,1] => 27
[-2,3,4,-1] => 31
[-2,3,-4,1] => 30
[-2,3,-4,-1] => 34
[-2,-3,4,1] => 37
[-2,-3,4,-1] => 41
[-2,-3,-4,1] => 40
[-2,-3,-4,-1] => 44
[2,4,1,3] => 5
[2,4,1,-3] => 7
[2,4,-1,3] => 17
[2,4,-1,-3] => 19
[2,-4,1,3] => 10
[2,-4,1,-3] => 12
[2,-4,-1,3] => 22
[2,-4,-1,-3] => 24
[-2,4,1,3] => 26
[-2,4,1,-3] => 28
[-2,4,-1,3] => 38
[-2,4,-1,-3] => 40
[-2,-4,1,3] => 31
[-2,-4,1,-3] => 33
[-2,-4,-1,3] => 43
[-2,-4,-1,-3] => 45
[2,4,3,1] => 7
[2,4,3,-1] => 11
[2,4,-3,1] => 13
[2,4,-3,-1] => 17
[2,-4,3,1] => 12
[2,-4,3,-1] => 16
[2,-4,-3,1] => 18
[2,-4,-3,-1] => 22
[-2,4,3,1] => 28
[-2,4,3,-1] => 32
[-2,4,-3,1] => 34
[-2,4,-3,-1] => 38
[-2,-4,3,1] => 33
[-2,-4,3,-1] => 37
[-2,-4,-3,1] => 39
[-2,-4,-3,-1] => 43
[3,1,2,4] => 3
[3,1,2,-4] => 4
[3,1,-2,4] => 12
[3,1,-2,-4] => 13
[3,-1,2,4] => 23
[3,-1,2,-4] => 24
[3,-1,-2,4] => 32
[3,-1,-2,-4] => 33
[-3,1,2,4] => 17
[-3,1,2,-4] => 18
[-3,1,-2,4] => 26
[-3,1,-2,-4] => 27
[-3,-1,2,4] => 37
[-3,-1,2,-4] => 38
[-3,-1,-2,4] => 46
[-3,-1,-2,-4] => 47
[3,1,4,2] => 5
[3,1,4,-2] => 8
[3,1,-4,2] => 8
[3,1,-4,-2] => 11
[3,-1,4,2] => 25
[3,-1,4,-2] => 28
[3,-1,-4,2] => 28
[3,-1,-4,-2] => 31
[-3,1,4,2] => 19
[-3,1,4,-2] => 22
[-3,1,-4,2] => 22
[-3,1,-4,-2] => 25
[-3,-1,4,2] => 39
[-3,-1,4,-2] => 42
[-3,-1,-4,2] => 42
[-3,-1,-4,-2] => 45
[3,2,1,4] => 4
[3,2,1,-4] => 5
[3,2,-1,4] => 16
[3,2,-1,-4] => 17
[3,-2,1,4] => 19
[3,-2,1,-4] => 20
[3,-2,-1,4] => 31
[3,-2,-1,-4] => 32
[-3,2,1,4] => 18
[-3,2,1,-4] => 19
[-3,2,-1,4] => 30
[-3,2,-1,-4] => 31
[-3,-2,1,4] => 33
[-3,-2,1,-4] => 34
[-3,-2,-1,4] => 45
[-3,-2,-1,-4] => 46
[3,2,4,1] => 7
[3,2,4,-1] => 11
[3,2,-4,1] => 10
[3,2,-4,-1] => 14
[3,-2,4,1] => 22
[3,-2,4,-1] => 26
[3,-2,-4,1] => 25
[3,-2,-4,-1] => 29
[-3,2,4,1] => 21
[-3,2,4,-1] => 25
[-3,2,-4,1] => 24
[-3,2,-4,-1] => 28
[-3,-2,4,1] => 36
[-3,-2,4,-1] => 40
[-3,-2,-4,1] => 39
[-3,-2,-4,-1] => 43
[3,4,1,2] => 8
[3,4,1,-2] => 11
[3,4,-1,2] => 20
[3,4,-1,-2] => 23
[3,-4,1,2] => 13
[3,-4,1,-2] => 16
[3,-4,-1,2] => 25
[3,-4,-1,-2] => 28
[-3,4,1,2] => 22
[-3,4,1,-2] => 25
[-3,4,-1,2] => 34
[-3,4,-1,-2] => 37
[-3,-4,1,2] => 27
[-3,-4,1,-2] => 30
[-3,-4,-1,2] => 39
[-3,-4,-1,-2] => 42
[3,4,2,1] => 9
[3,4,2,-1] => 13
[3,4,-2,1] => 18
[3,4,-2,-1] => 22
[3,-4,2,1] => 14
[3,-4,2,-1] => 18
[3,-4,-2,1] => 23
[3,-4,-2,-1] => 27
[-3,4,2,1] => 23
[-3,4,2,-1] => 27
[-3,4,-2,1] => 32
[-3,4,-2,-1] => 36
[-3,-4,2,1] => 28
[-3,-4,2,-1] => 32
[-3,-4,-2,1] => 37
[-3,-4,-2,-1] => 41
[4,1,2,3] => 6
[4,1,2,-3] => 8
[4,1,-2,3] => 15
[4,1,-2,-3] => 17
[4,-1,2,3] => 26
[4,-1,2,-3] => 28
[4,-1,-2,3] => 35
[4,-1,-2,-3] => 37
[-4,1,2,3] => 13
[-4,1,2,-3] => 15
[-4,1,-2,3] => 22
[-4,1,-2,-3] => 24
[-4,-1,2,3] => 33
[-4,-1,2,-3] => 35
[-4,-1,-2,3] => 42
[-4,-1,-2,-3] => 44
[4,1,3,2] => 7
[4,1,3,-2] => 10
[4,1,-3,2] => 13
[4,1,-3,-2] => 16
[4,-1,3,2] => 27
[4,-1,3,-2] => 30
[4,-1,-3,2] => 33
[4,-1,-3,-2] => 36
[-4,1,3,2] => 14
[-4,1,3,-2] => 17
[-4,1,-3,2] => 20
[-4,1,-3,-2] => 23
[-4,-1,3,2] => 34
[-4,-1,3,-2] => 37
[-4,-1,-3,2] => 40
[-4,-1,-3,-2] => 43
[4,2,1,3] => 7
[4,2,1,-3] => 9
[4,2,-1,3] => 19
[4,2,-1,-3] => 21
[4,-2,1,3] => 22
[4,-2,1,-3] => 24
[4,-2,-1,3] => 34
[4,-2,-1,-3] => 36
[-4,2,1,3] => 14
[-4,2,1,-3] => 16
[-4,2,-1,3] => 26
[-4,2,-1,-3] => 28
[-4,-2,1,3] => 29
[-4,-2,1,-3] => 31
[-4,-2,-1,3] => 41
[-4,-2,-1,-3] => 43
[4,2,3,1] => 9
[4,2,3,-1] => 13
[4,2,-3,1] => 15
[4,2,-3,-1] => 19
[4,-2,3,1] => 24
[4,-2,3,-1] => 28
[4,-2,-3,1] => 30
[4,-2,-3,-1] => 34
[-4,2,3,1] => 16
[-4,2,3,-1] => 20
[-4,2,-3,1] => 22
[-4,2,-3,-1] => 26
[-4,-2,3,1] => 31
[-4,-2,3,-1] => 35
[-4,-2,-3,1] => 37
[-4,-2,-3,-1] => 41
[4,3,1,2] => 9
[4,3,1,-2] => 12
[4,3,-1,2] => 21
[4,3,-1,-2] => 24
[4,-3,1,2] => 19
[4,-3,1,-2] => 22
[4,-3,-1,2] => 31
[4,-3,-1,-2] => 34
[-4,3,1,2] => 16
[-4,3,1,-2] => 19
[-4,3,-1,2] => 28
[-4,3,-1,-2] => 31
[-4,-3,1,2] => 26
[-4,-3,1,-2] => 29
[-4,-3,-1,2] => 38
[-4,-3,-1,-2] => 41
[4,3,2,1] => 10
[4,3,2,-1] => 14
[4,3,-2,1] => 19
[4,3,-2,-1] => 23
[4,-3,2,1] => 20
[4,-3,2,-1] => 24
[4,-3,-2,1] => 29
[4,-3,-2,-1] => 33
[-4,3,2,1] => 17
[-4,3,2,-1] => 21
[-4,3,-2,1] => 26
[-4,3,-2,-1] => 30
[-4,-3,2,1] => 27
[-4,-3,2,-1] => 31
[-4,-3,-2,1] => 36
[-4,-3,-2,-1] => 40
[1,2,3,4,5] => 0
[1,2,3,4,-5] => 1
[1,2,3,-4,5] => 6
[1,2,3,-4,-5] => 7
[1,2,-3,4,5] => 15
[1,2,-3,4,-5] => 16
[1,2,-3,-4,5] => 21
[1,2,-3,-4,-5] => 22
[1,-2,3,4,5] => 28
[1,-2,3,4,-5] => 29
[1,-2,3,-4,5] => 34
[1,-2,3,-4,-5] => 35
[1,-2,-3,4,5] => 43
[1,-2,-3,4,-5] => 44
[1,-2,-3,-4,5] => 49
[1,-2,-3,-4,-5] => 50
[-1,2,3,4,5] => 45
[-1,2,3,4,-5] => 46
[-1,2,3,-4,5] => 51
[-1,2,3,-4,-5] => 52
[-1,2,-3,4,5] => 60
[-1,2,-3,4,-5] => 61
[-1,2,-3,-4,5] => 66
[-1,2,-3,-4,-5] => 67
[-1,-2,3,4,5] => 73
[-1,-2,3,4,-5] => 74
[-1,-2,3,-4,5] => 79
[-1,-2,3,-4,-5] => 80
[-1,-2,-3,4,5] => 88
[-1,-2,-3,4,-5] => 89
[-1,-2,-3,-4,5] => 94
[-1,-2,-3,-4,-5] => 95
[1,2,3,5,4] => 1
[1,2,3,5,-4] => 3
[1,2,3,-5,4] => 4
[1,2,3,-5,-4] => 6
[1,2,-3,5,4] => 16
[1,2,-3,5,-4] => 18
[1,2,-3,-5,4] => 19
[1,2,-3,-5,-4] => 21
[1,-2,3,5,4] => 29
[1,-2,3,5,-4] => 31
[1,-2,3,-5,4] => 32
[1,-2,3,-5,-4] => 34
[1,-2,-3,5,4] => 44
[1,-2,-3,5,-4] => 46
[1,-2,-3,-5,4] => 47
[1,-2,-3,-5,-4] => 49
[-1,2,3,5,4] => 46
[-1,2,3,5,-4] => 48
[-1,2,3,-5,4] => 49
[-1,2,3,-5,-4] => 51
[-1,2,-3,5,4] => 61
[-1,2,-3,5,-4] => 63
[-1,2,-3,-5,4] => 64
[-1,2,-3,-5,-4] => 66
[-1,-2,3,5,4] => 74
[-1,-2,3,5,-4] => 76
[-1,-2,3,-5,4] => 77
[-1,-2,3,-5,-4] => 79
[-1,-2,-3,5,4] => 89
[-1,-2,-3,5,-4] => 91
[-1,-2,-3,-5,4] => 92
[-1,-2,-3,-5,-4] => 94
[1,2,4,3,5] => 1
[1,2,4,3,-5] => 2
[1,2,4,-3,5] => 10
[1,2,4,-3,-5] => 11
[1,2,-4,3,5] => 11
[1,2,-4,3,-5] => 12
[1,2,-4,-3,5] => 20
[1,2,-4,-3,-5] => 21
[1,-2,4,3,5] => 29
[1,-2,4,3,-5] => 30
[1,-2,4,-3,5] => 38
[1,-2,4,-3,-5] => 39
[1,-2,-4,3,5] => 39
[1,-2,-4,3,-5] => 40
[1,-2,-4,-3,5] => 48
[1,-2,-4,-3,-5] => 49
[-1,2,4,3,5] => 46
[-1,2,4,3,-5] => 47
[-1,2,4,-3,5] => 55
[-1,2,4,-3,-5] => 56
[-1,2,-4,3,5] => 56
[-1,2,-4,3,-5] => 57
[-1,2,-4,-3,5] => 65
[-1,2,-4,-3,-5] => 66
[-1,-2,4,3,5] => 74
[-1,-2,4,3,-5] => 75
[-1,-2,4,-3,5] => 83
[-1,-2,4,-3,-5] => 84
[-1,-2,-4,3,5] => 84
[-1,-2,-4,3,-5] => 85
[-1,-2,-4,-3,5] => 93
[-1,-2,-4,-3,-5] => 94
[1,2,4,5,3] => 3
[1,2,4,5,-3] => 6
[1,2,4,-5,3] => 6
[1,2,4,-5,-3] => 9
[1,2,-4,5,3] => 13
[1,2,-4,5,-3] => 16
[1,2,-4,-5,3] => 16
[1,2,-4,-5,-3] => 19
[1,-2,4,5,3] => 31
[1,-2,4,5,-3] => 34
[1,-2,4,-5,3] => 34
[1,-2,4,-5,-3] => 37
[1,-2,-4,5,3] => 41
[1,-2,-4,5,-3] => 44
[1,-2,-4,-5,3] => 44
[1,-2,-4,-5,-3] => 47
[-1,2,4,5,3] => 48
[-1,2,4,5,-3] => 51
[-1,2,4,-5,3] => 51
[-1,2,4,-5,-3] => 54
[-1,2,-4,5,3] => 58
[-1,2,-4,5,-3] => 61
[-1,2,-4,-5,3] => 61
[-1,2,-4,-5,-3] => 64
[-1,-2,4,5,3] => 76
[-1,-2,4,5,-3] => 79
[-1,-2,4,-5,3] => 79
[-1,-2,4,-5,-3] => 82
[-1,-2,-4,5,3] => 86
[-1,-2,-4,5,-3] => 89
[-1,-2,-4,-5,3] => 89
[-1,-2,-4,-5,-3] => 92
[1,2,5,3,4] => 3
[1,2,5,3,-4] => 5
[1,2,5,-3,4] => 12
[1,2,5,-3,-4] => 14
[1,2,-5,3,4] => 8
[1,2,-5,3,-4] => 10
[1,2,-5,-3,4] => 17
[1,2,-5,-3,-4] => 19
[1,-2,5,3,4] => 31
[1,-2,5,3,-4] => 33
[1,-2,5,-3,4] => 40
[1,-2,5,-3,-4] => 42
[1,-2,-5,3,4] => 36
[1,-2,-5,3,-4] => 38
[1,-2,-5,-3,4] => 45
[1,-2,-5,-3,-4] => 47
[-1,2,5,3,4] => 48
[-1,2,5,3,-4] => 50
[-1,2,5,-3,4] => 57
[-1,2,5,-3,-4] => 59
[-1,2,-5,3,4] => 53
[-1,2,-5,3,-4] => 55
[-1,2,-5,-3,4] => 62
[-1,2,-5,-3,-4] => 64
[-1,-2,5,3,4] => 76
[-1,-2,5,3,-4] => 78
[-1,-2,5,-3,4] => 85
[-1,-2,5,-3,-4] => 87
[-1,-2,-5,3,4] => 81
[-1,-2,-5,3,-4] => 83
[-1,-2,-5,-3,4] => 90
[-1,-2,-5,-3,-4] => 92
[1,2,5,4,3] => 4
[1,2,5,4,-3] => 7
[1,2,5,-4,3] => 10
[1,2,5,-4,-3] => 13
[1,2,-5,4,3] => 9
[1,2,-5,4,-3] => 12
[1,2,-5,-4,3] => 15
[1,2,-5,-4,-3] => 18
[1,-2,5,4,3] => 32
[1,-2,5,4,-3] => 35
[1,-2,5,-4,3] => 38
[1,-2,5,-4,-3] => 41
[1,-2,-5,4,3] => 37
[1,-2,-5,4,-3] => 40
[1,-2,-5,-4,3] => 43
[1,-2,-5,-4,-3] => 46
[-1,2,5,4,3] => 49
[-1,2,5,4,-3] => 52
[-1,2,5,-4,3] => 55
[-1,2,5,-4,-3] => 58
[-1,2,-5,4,3] => 54
[-1,2,-5,4,-3] => 57
[-1,2,-5,-4,3] => 60
[-1,2,-5,-4,-3] => 63
[-1,-2,5,4,3] => 77
[-1,-2,5,4,-3] => 80
[-1,-2,5,-4,3] => 83
[-1,-2,5,-4,-3] => 86
[-1,-2,-5,4,3] => 82
[-1,-2,-5,4,-3] => 85
[-1,-2,-5,-4,3] => 88
[-1,-2,-5,-4,-3] => 91
[1,3,2,4,5] => 1
[1,3,2,4,-5] => 2
[1,3,2,-4,5] => 7
[1,3,2,-4,-5] => 8
[1,3,-2,4,5] => 21
[1,3,-2,4,-5] => 22
[1,3,-2,-4,5] => 27
[1,3,-2,-4,-5] => 28
[1,-3,2,4,5] => 22
[1,-3,2,4,-5] => 23
[1,-3,2,-4,5] => 28
[1,-3,2,-4,-5] => 29
[1,-3,-2,4,5] => 42
[1,-3,-2,4,-5] => 43
[1,-3,-2,-4,5] => 48
[1,-3,-2,-4,-5] => 49
[-1,3,2,4,5] => 46
[-1,3,2,4,-5] => 47
[-1,3,2,-4,5] => 52
[-1,3,2,-4,-5] => 53
[-1,3,-2,4,5] => 66
[-1,3,-2,4,-5] => 67
[-1,3,-2,-4,5] => 72
[-1,3,-2,-4,-5] => 73
[-1,-3,2,4,5] => 67
[-1,-3,2,4,-5] => 68
[-1,-3,2,-4,5] => 73
[-1,-3,2,-4,-5] => 74
[-1,-3,-2,4,5] => 87
[-1,-3,-2,4,-5] => 88
[-1,-3,-2,-4,5] => 93
[-1,-3,-2,-4,-5] => 94
[1,3,2,5,4] => 2
[1,3,2,5,-4] => 4
[1,3,2,-5,4] => 5
[1,3,2,-5,-4] => 7
[1,3,-2,5,4] => 22
[1,3,-2,5,-4] => 24
[1,3,-2,-5,4] => 25
[1,3,-2,-5,-4] => 27
[1,-3,2,5,4] => 23
[1,-3,2,5,-4] => 25
[1,-3,2,-5,4] => 26
[1,-3,2,-5,-4] => 28
[1,-3,-2,5,4] => 43
[1,-3,-2,5,-4] => 45
[1,-3,-2,-5,4] => 46
[1,-3,-2,-5,-4] => 48
[-1,3,2,5,4] => 47
[-1,3,2,5,-4] => 49
[-1,3,2,-5,4] => 50
[-1,3,2,-5,-4] => 52
[-1,3,-2,5,4] => 67
[-1,3,-2,5,-4] => 69
[-1,3,-2,-5,4] => 70
[-1,3,-2,-5,-4] => 72
[-1,-3,2,5,4] => 68
[-1,-3,2,5,-4] => 70
[-1,-3,2,-5,4] => 71
[-1,-3,2,-5,-4] => 73
[-1,-3,-2,5,4] => 88
[-1,-3,-2,5,-4] => 90
[-1,-3,-2,-5,4] => 91
[-1,-3,-2,-5,-4] => 93
[1,3,4,2,5] => 3
[1,3,4,2,-5] => 4
[1,3,4,-2,5] => 15
[1,3,4,-2,-5] => 16
[1,3,-4,2,5] => 13
[1,3,-4,2,-5] => 14
[1,3,-4,-2,5] => 25
[1,3,-4,-2,-5] => 26
[1,-3,4,2,5] => 24
[1,-3,4,2,-5] => 25
[1,-3,4,-2,5] => 36
[1,-3,4,-2,-5] => 37
[1,-3,-4,2,5] => 34
[1,-3,-4,2,-5] => 35
[1,-3,-4,-2,5] => 46
[1,-3,-4,-2,-5] => 47
[-1,3,4,2,5] => 48
[-1,3,4,2,-5] => 49
[-1,3,4,-2,5] => 60
[-1,3,4,-2,-5] => 61
[-1,3,-4,2,5] => 58
[-1,3,-4,2,-5] => 59
[-1,3,-4,-2,5] => 70
[-1,3,-4,-2,-5] => 71
[-1,-3,4,2,5] => 69
[-1,-3,4,2,-5] => 70
[-1,-3,4,-2,5] => 81
[-1,-3,4,-2,-5] => 82
[-1,-3,-4,2,5] => 79
[-1,-3,-4,2,-5] => 80
[-1,-3,-4,-2,5] => 91
[-1,-3,-4,-2,-5] => 92
[1,3,4,5,2] => 6
[1,3,4,5,-2] => 10
[1,3,4,-5,2] => 9
[1,3,4,-5,-2] => 13
[1,3,-4,5,2] => 16
[1,3,-4,5,-2] => 20
[1,3,-4,-5,2] => 19
[1,3,-4,-5,-2] => 23
[1,-3,4,5,2] => 27
[1,-3,4,5,-2] => 31
[1,-3,4,-5,2] => 30
[1,-3,4,-5,-2] => 34
[1,-3,-4,5,2] => 37
[1,-3,-4,5,-2] => 41
[1,-3,-4,-5,2] => 40
[1,-3,-4,-5,-2] => 44
[-1,3,4,5,2] => 51
[-1,3,4,5,-2] => 55
[-1,3,4,-5,2] => 54
[-1,3,4,-5,-2] => 58
[-1,3,-4,5,2] => 61
[-1,3,-4,5,-2] => 65
[-1,3,-4,-5,2] => 64
[-1,3,-4,-5,-2] => 68
[-1,-3,4,5,2] => 72
[-1,-3,4,5,-2] => 76
[-1,-3,4,-5,2] => 75
[-1,-3,4,-5,-2] => 79
[-1,-3,-4,5,2] => 82
[-1,-3,-4,5,-2] => 86
[-1,-3,-4,-5,2] => 85
[-1,-3,-4,-5,-2] => 89
[1,3,5,2,4] => 5
[1,3,5,2,-4] => 7
[1,3,5,-2,4] => 17
[1,3,5,-2,-4] => 19
[1,3,-5,2,4] => 10
[1,3,-5,2,-4] => 12
[1,3,-5,-2,4] => 22
[1,3,-5,-2,-4] => 24
[1,-3,5,2,4] => 26
[1,-3,5,2,-4] => 28
[1,-3,5,-2,4] => 38
[1,-3,5,-2,-4] => 40
[1,-3,-5,2,4] => 31
[1,-3,-5,2,-4] => 33
[1,-3,-5,-2,4] => 43
[1,-3,-5,-2,-4] => 45
[-1,3,5,2,4] => 50
[-1,3,5,2,-4] => 52
[-1,3,5,-2,4] => 62
[-1,3,5,-2,-4] => 64
[-1,3,-5,2,4] => 55
[-1,3,-5,2,-4] => 57
[-1,3,-5,-2,4] => 67
[-1,3,-5,-2,-4] => 69
[-1,-3,5,2,4] => 71
[-1,-3,5,2,-4] => 73
[-1,-3,5,-2,4] => 83
[-1,-3,5,-2,-4] => 85
[-1,-3,-5,2,4] => 76
[-1,-3,-5,2,-4] => 78
[-1,-3,-5,-2,4] => 88
[-1,-3,-5,-2,-4] => 90
[1,3,5,4,2] => 7
[1,3,5,4,-2] => 11
[1,3,5,-4,2] => 13
[1,3,5,-4,-2] => 17
[1,3,-5,4,2] => 12
[1,3,-5,4,-2] => 16
[1,3,-5,-4,2] => 18
[1,3,-5,-4,-2] => 22
[1,-3,5,4,2] => 28
[1,-3,5,4,-2] => 32
[1,-3,5,-4,2] => 34
[1,-3,5,-4,-2] => 38
[1,-3,-5,4,2] => 33
[1,-3,-5,4,-2] => 37
[1,-3,-5,-4,2] => 39
[1,-3,-5,-4,-2] => 43
[-1,3,5,4,2] => 52
[-1,3,5,4,-2] => 56
[-1,3,5,-4,2] => 58
[-1,3,5,-4,-2] => 62
[-1,3,-5,4,2] => 57
[-1,3,-5,4,-2] => 61
[-1,3,-5,-4,2] => 63
[-1,3,-5,-4,-2] => 67
[-1,-3,5,4,2] => 73
[-1,-3,5,4,-2] => 77
[-1,-3,5,-4,2] => 79
[-1,-3,5,-4,-2] => 83
[-1,-3,-5,4,2] => 78
[-1,-3,-5,4,-2] => 82
[-1,-3,-5,-4,2] => 84
[-1,-3,-5,-4,-2] => 88
[1,4,2,3,5] => 3
[1,4,2,3,-5] => 4
[1,4,2,-3,5] => 12
[1,4,2,-3,-5] => 13
[1,4,-2,3,5] => 23
[1,4,-2,3,-5] => 24
[1,4,-2,-3,5] => 32
[1,4,-2,-3,-5] => 33
[1,-4,2,3,5] => 17
[1,-4,2,3,-5] => 18
[1,-4,2,-3,5] => 26
[1,-4,2,-3,-5] => 27
[1,-4,-2,3,5] => 37
[1,-4,-2,3,-5] => 38
[1,-4,-2,-3,5] => 46
[1,-4,-2,-3,-5] => 47
[-1,4,2,3,5] => 48
[-1,4,2,3,-5] => 49
[-1,4,2,-3,5] => 57
[-1,4,2,-3,-5] => 58
[-1,4,-2,3,5] => 68
[-1,4,-2,3,-5] => 69
[-1,4,-2,-3,5] => 77
[-1,4,-2,-3,-5] => 78
[-1,-4,2,3,5] => 62
[-1,-4,2,3,-5] => 63
[-1,-4,2,-3,5] => 71
[-1,-4,2,-3,-5] => 72
[-1,-4,-2,3,5] => 82
[-1,-4,-2,3,-5] => 83
[-1,-4,-2,-3,5] => 91
[-1,-4,-2,-3,-5] => 92
[1,4,2,5,3] => 5
[1,4,2,5,-3] => 8
[1,4,2,-5,3] => 8
[1,4,2,-5,-3] => 11
[1,4,-2,5,3] => 25
[1,4,-2,5,-3] => 28
[1,4,-2,-5,3] => 28
[1,4,-2,-5,-3] => 31
[1,-4,2,5,3] => 19
[1,-4,2,5,-3] => 22
[1,-4,2,-5,3] => 22
[1,-4,2,-5,-3] => 25
[1,-4,-2,5,3] => 39
[1,-4,-2,5,-3] => 42
[1,-4,-2,-5,3] => 42
[1,-4,-2,-5,-3] => 45
[-1,4,2,5,3] => 50
[-1,4,2,5,-3] => 53
[-1,4,2,-5,3] => 53
[-1,4,2,-5,-3] => 56
[-1,4,-2,5,3] => 70
[-1,4,-2,5,-3] => 73
[-1,4,-2,-5,3] => 73
[-1,4,-2,-5,-3] => 76
[-1,-4,2,5,3] => 64
[-1,-4,2,5,-3] => 67
[-1,-4,2,-5,3] => 67
[-1,-4,2,-5,-3] => 70
[-1,-4,-2,5,3] => 84
[-1,-4,-2,5,-3] => 87
[-1,-4,-2,-5,3] => 87
[-1,-4,-2,-5,-3] => 90
[1,4,3,2,5] => 4
[1,4,3,2,-5] => 5
[1,4,3,-2,5] => 16
[1,4,3,-2,-5] => 17
[1,4,-3,2,5] => 19
[1,4,-3,2,-5] => 20
[1,4,-3,-2,5] => 31
[1,4,-3,-2,-5] => 32
[1,-4,3,2,5] => 18
[1,-4,3,2,-5] => 19
[1,-4,3,-2,5] => 30
[1,-4,3,-2,-5] => 31
[1,-4,-3,2,5] => 33
[1,-4,-3,2,-5] => 34
[1,-4,-3,-2,5] => 45
[1,-4,-3,-2,-5] => 46
[-1,4,3,2,5] => 49
[-1,4,3,2,-5] => 50
[-1,4,3,-2,5] => 61
[-1,4,3,-2,-5] => 62
[-1,4,-3,2,5] => 64
[-1,4,-3,2,-5] => 65
[-1,4,-3,-2,5] => 76
[-1,4,-3,-2,-5] => 77
[-1,-4,3,2,5] => 63
[-1,-4,3,2,-5] => 64
[-1,-4,3,-2,5] => 75
[-1,-4,3,-2,-5] => 76
[-1,-4,-3,2,5] => 78
[-1,-4,-3,2,-5] => 79
[-1,-4,-3,-2,5] => 90
[-1,-4,-3,-2,-5] => 91
[1,4,3,5,2] => 7
[1,4,3,5,-2] => 11
[1,4,3,-5,2] => 10
[1,4,3,-5,-2] => 14
[1,4,-3,5,2] => 22
[1,4,-3,5,-2] => 26
[1,4,-3,-5,2] => 25
[1,4,-3,-5,-2] => 29
[1,-4,3,5,2] => 21
[1,-4,3,5,-2] => 25
[1,-4,3,-5,2] => 24
[1,-4,3,-5,-2] => 28
[1,-4,-3,5,2] => 36
[1,-4,-3,5,-2] => 40
[1,-4,-3,-5,2] => 39
[1,-4,-3,-5,-2] => 43
[-1,4,3,5,2] => 52
[-1,4,3,5,-2] => 56
[-1,4,3,-5,2] => 55
[-1,4,3,-5,-2] => 59
[-1,4,-3,5,2] => 67
[-1,4,-3,5,-2] => 71
[-1,4,-3,-5,2] => 70
[-1,4,-3,-5,-2] => 74
[-1,-4,3,5,2] => 66
[-1,-4,3,5,-2] => 70
[-1,-4,3,-5,2] => 69
[-1,-4,3,-5,-2] => 73
[-1,-4,-3,5,2] => 81
[-1,-4,-3,5,-2] => 85
[-1,-4,-3,-5,2] => 84
[-1,-4,-3,-5,-2] => 88
[1,4,5,2,3] => 8
[1,4,5,2,-3] => 11
[1,4,5,-2,3] => 20
[1,4,5,-2,-3] => 23
[1,4,-5,2,3] => 13
[1,4,-5,2,-3] => 16
[1,4,-5,-2,3] => 25
[1,4,-5,-2,-3] => 28
[1,-4,5,2,3] => 22
[1,-4,5,2,-3] => 25
[1,-4,5,-2,3] => 34
[1,-4,5,-2,-3] => 37
[1,-4,-5,2,3] => 27
[1,-4,-5,2,-3] => 30
[1,-4,-5,-2,3] => 39
[1,-4,-5,-2,-3] => 42
[-1,4,5,2,3] => 53
[-1,4,5,2,-3] => 56
[-1,4,5,-2,3] => 65
[-1,4,5,-2,-3] => 68
[-1,4,-5,2,3] => 58
[-1,4,-5,2,-3] => 61
[-1,4,-5,-2,3] => 70
[-1,4,-5,-2,-3] => 73
[-1,-4,5,2,3] => 67
[-1,-4,5,2,-3] => 70
[-1,-4,5,-2,3] => 79
[-1,-4,5,-2,-3] => 82
[-1,-4,-5,2,3] => 72
[-1,-4,-5,2,-3] => 75
[-1,-4,-5,-2,3] => 84
[-1,-4,-5,-2,-3] => 87
[1,4,5,3,2] => 9
[1,4,5,3,-2] => 13
[1,4,5,-3,2] => 18
[1,4,5,-3,-2] => 22
[1,4,-5,3,2] => 14
[1,4,-5,3,-2] => 18
[1,4,-5,-3,2] => 23
[1,4,-5,-3,-2] => 27
[1,-4,5,3,2] => 23
[1,-4,5,3,-2] => 27
[1,-4,5,-3,2] => 32
[1,-4,5,-3,-2] => 36
[1,-4,-5,3,2] => 28
[1,-4,-5,3,-2] => 32
[1,-4,-5,-3,2] => 37
[1,-4,-5,-3,-2] => 41
[-1,4,5,3,2] => 54
[-1,4,5,3,-2] => 58
[-1,4,5,-3,2] => 63
[-1,4,5,-3,-2] => 67
[-1,4,-5,3,2] => 59
[-1,4,-5,3,-2] => 63
[-1,4,-5,-3,2] => 68
[-1,4,-5,-3,-2] => 72
[-1,-4,5,3,2] => 68
[-1,-4,5,3,-2] => 72
[-1,-4,5,-3,2] => 77
[-1,-4,5,-3,-2] => 81
[-1,-4,-5,3,2] => 73
[-1,-4,-5,3,-2] => 77
[-1,-4,-5,-3,2] => 82
[-1,-4,-5,-3,-2] => 86
[1,5,2,3,4] => 6
[1,5,2,3,-4] => 8
[1,5,2,-3,4] => 15
[1,5,2,-3,-4] => 17
[1,5,-2,3,4] => 26
[1,5,-2,3,-4] => 28
[1,5,-2,-3,4] => 35
[1,5,-2,-3,-4] => 37
[1,-5,2,3,4] => 13
[1,-5,2,3,-4] => 15
[1,-5,2,-3,4] => 22
[1,-5,2,-3,-4] => 24
[1,-5,-2,3,4] => 33
[1,-5,-2,3,-4] => 35
[1,-5,-2,-3,4] => 42
[1,-5,-2,-3,-4] => 44
[-1,5,2,3,4] => 51
[-1,5,2,3,-4] => 53
[-1,5,2,-3,4] => 60
[-1,5,2,-3,-4] => 62
[-1,5,-2,3,4] => 71
[-1,5,-2,3,-4] => 73
[-1,5,-2,-3,4] => 80
[-1,5,-2,-3,-4] => 82
[-1,-5,2,3,4] => 58
[-1,-5,2,3,-4] => 60
[-1,-5,2,-3,4] => 67
[-1,-5,2,-3,-4] => 69
[-1,-5,-2,3,4] => 78
[-1,-5,-2,3,-4] => 80
[-1,-5,-2,-3,4] => 87
[-1,-5,-2,-3,-4] => 89
[1,5,2,4,3] => 7
[1,5,2,4,-3] => 10
[1,5,2,-4,3] => 13
[1,5,2,-4,-3] => 16
[1,5,-2,4,3] => 27
[1,5,-2,4,-3] => 30
[1,5,-2,-4,3] => 33
[1,5,-2,-4,-3] => 36
[1,-5,2,4,3] => 14
[1,-5,2,4,-3] => 17
[1,-5,2,-4,3] => 20
[1,-5,2,-4,-3] => 23
[1,-5,-2,4,3] => 34
[1,-5,-2,4,-3] => 37
[1,-5,-2,-4,3] => 40
[1,-5,-2,-4,-3] => 43
[-1,5,2,4,3] => 52
[-1,5,2,4,-3] => 55
[-1,5,2,-4,3] => 58
[-1,5,2,-4,-3] => 61
[-1,5,-2,4,3] => 72
[-1,5,-2,4,-3] => 75
[-1,5,-2,-4,3] => 78
[-1,5,-2,-4,-3] => 81
[-1,-5,2,4,3] => 59
[-1,-5,2,4,-3] => 62
[-1,-5,2,-4,3] => 65
[-1,-5,2,-4,-3] => 68
[-1,-5,-2,4,3] => 79
[-1,-5,-2,4,-3] => 82
[-1,-5,-2,-4,3] => 85
[-1,-5,-2,-4,-3] => 88
[1,5,3,2,4] => 7
[1,5,3,2,-4] => 9
[1,5,3,-2,4] => 19
[1,5,3,-2,-4] => 21
[1,5,-3,2,4] => 22
[1,5,-3,2,-4] => 24
[1,5,-3,-2,4] => 34
[1,5,-3,-2,-4] => 36
[1,-5,3,2,4] => 14
[1,-5,3,2,-4] => 16
[1,-5,3,-2,4] => 26
[1,-5,3,-2,-4] => 28
[1,-5,-3,2,4] => 29
[1,-5,-3,2,-4] => 31
[1,-5,-3,-2,4] => 41
[1,-5,-3,-2,-4] => 43
[-1,5,3,2,4] => 52
[-1,5,3,2,-4] => 54
[-1,5,3,-2,4] => 64
[-1,5,3,-2,-4] => 66
[-1,5,-3,2,4] => 67
[-1,5,-3,2,-4] => 69
[-1,5,-3,-2,4] => 79
[-1,5,-3,-2,-4] => 81
[-1,-5,3,2,4] => 59
[-1,-5,3,2,-4] => 61
[-1,-5,3,-2,4] => 71
[-1,-5,3,-2,-4] => 73
[-1,-5,-3,2,4] => 74
[-1,-5,-3,2,-4] => 76
[-1,-5,-3,-2,4] => 86
[-1,-5,-3,-2,-4] => 88
[1,5,3,4,2] => 9
[1,5,3,4,-2] => 13
[1,5,3,-4,2] => 15
[1,5,3,-4,-2] => 19
[1,5,-3,4,2] => 24
[1,5,-3,4,-2] => 28
[1,5,-3,-4,2] => 30
[1,5,-3,-4,-2] => 34
[1,-5,3,4,2] => 16
[1,-5,3,4,-2] => 20
[1,-5,3,-4,2] => 22
[1,-5,3,-4,-2] => 26
[1,-5,-3,4,2] => 31
[1,-5,-3,4,-2] => 35
[1,-5,-3,-4,2] => 37
[1,-5,-3,-4,-2] => 41
[-1,5,3,4,2] => 54
[-1,5,3,4,-2] => 58
[-1,5,3,-4,2] => 60
[-1,5,3,-4,-2] => 64
[-1,5,-3,4,2] => 69
[-1,5,-3,4,-2] => 73
[-1,5,-3,-4,2] => 75
[-1,5,-3,-4,-2] => 79
[-1,-5,3,4,2] => 61
[-1,-5,3,4,-2] => 65
[-1,-5,3,-4,2] => 67
[-1,-5,3,-4,-2] => 71
[-1,-5,-3,4,2] => 76
[-1,-5,-3,4,-2] => 80
[-1,-5,-3,-4,2] => 82
[-1,-5,-3,-4,-2] => 86
[1,5,4,2,3] => 9
[1,5,4,2,-3] => 12
[1,5,4,-2,3] => 21
[1,5,4,-2,-3] => 24
[1,5,-4,2,3] => 19
[1,5,-4,2,-3] => 22
[1,5,-4,-2,3] => 31
[1,5,-4,-2,-3] => 34
[1,-5,4,2,3] => 16
[1,-5,4,2,-3] => 19
[1,-5,4,-2,3] => 28
[1,-5,4,-2,-3] => 31
[1,-5,-4,2,3] => 26
[1,-5,-4,2,-3] => 29
[1,-5,-4,-2,3] => 38
[1,-5,-4,-2,-3] => 41
[-1,5,4,2,3] => 54
[-1,5,4,2,-3] => 57
[-1,5,4,-2,3] => 66
[-1,5,4,-2,-3] => 69
[-1,5,-4,2,3] => 64
[-1,5,-4,2,-3] => 67
[-1,5,-4,-2,3] => 76
[-1,5,-4,-2,-3] => 79
[-1,-5,4,2,3] => 61
[-1,-5,4,2,-3] => 64
[-1,-5,4,-2,3] => 73
[-1,-5,4,-2,-3] => 76
[-1,-5,-4,2,3] => 71
[-1,-5,-4,2,-3] => 74
[-1,-5,-4,-2,3] => 83
[-1,-5,-4,-2,-3] => 86
[1,5,4,3,2] => 10
[1,5,4,3,-2] => 14
[1,5,4,-3,2] => 19
[1,5,4,-3,-2] => 23
[1,5,-4,3,2] => 20
[1,5,-4,3,-2] => 24
[1,5,-4,-3,2] => 29
[1,5,-4,-3,-2] => 33
[1,-5,4,3,2] => 17
[1,-5,4,3,-2] => 21
[1,-5,4,-3,2] => 26
[1,-5,4,-3,-2] => 30
[1,-5,-4,3,2] => 27
[1,-5,-4,3,-2] => 31
[1,-5,-4,-3,2] => 36
[1,-5,-4,-3,-2] => 40
[-1,5,4,3,2] => 55
[-1,5,4,3,-2] => 59
[-1,5,4,-3,2] => 64
[-1,5,4,-3,-2] => 68
[-1,5,-4,3,2] => 65
[-1,5,-4,3,-2] => 69
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Created: Nov 23, 2022 at 10:16 by Martin Rubey
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Last Updated: Nov 23, 2022 at 10:16 by Martin Rubey