Identifier
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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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 $w$.
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"))
Created
Nov 23, 2022 at 10:16 by Martin Rubey
Updated
Nov 23, 2022 at 10:16 by Martin Rubey
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