Identifier
Values
[1,0] => [1] => ([],1) => 1
[1,0,1,0] => [1,2] => ([(0,1)],2) => 2
[1,1,0,0] => [2,1] => ([],2) => 1
[1,0,1,0,1,0] => [1,2,3] => ([(0,2),(2,1)],3) => 6
[1,0,1,1,0,0] => [1,3,2] => ([(0,1),(0,2)],3) => 3
[1,1,0,0,1,0] => [2,1,3] => ([(0,2),(1,2)],3) => 4
[1,1,0,1,0,0] => [2,3,1] => ([(1,2)],3) => 2
[1,1,1,0,0,0] => [3,2,1] => ([],3) => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 24
[1,0,1,0,1,1,0,0] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4) => 12
[1,0,1,1,0,0,1,0] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4) => 16
[1,0,1,1,0,1,0,0] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4) => 8
[1,0,1,1,1,0,0,0] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4) => 4
[1,1,0,0,1,0,1,0] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 18
[1,1,0,0,1,1,0,0] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4) => 9
[1,1,0,1,0,0,1,0] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 12
[1,1,0,1,0,1,0,0] => [2,3,4,1] => ([(1,2),(2,3)],4) => 6
[1,1,0,1,1,0,0,0] => [2,4,3,1] => ([(1,2),(1,3)],4) => 3
[1,1,1,0,0,0,1,0] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 8
[1,1,1,0,0,1,0,0] => [3,2,4,1] => ([(1,3),(2,3)],4) => 4
[1,1,1,0,1,0,0,0] => [4,2,3,1] => ([(2,3)],4) => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => ([],4) => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5) => 60
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 80
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5) => 20
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 90
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 45
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 60
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5) => 15
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 40
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 20
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5) => 10
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5) => 5
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 96
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5) => 48
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 64
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 32
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 16
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 72
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 36
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 48
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 24
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5) => 12
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 32
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5) => 16
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5) => 8
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5) => 4
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 54
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 27
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 36
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 18
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5) => 9
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 24
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 12
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 6
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => ([(2,3),(2,4)],5) => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 16
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 8
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 4
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => ([(3,4)],5) => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => ([],5) => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 360
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 480
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 120
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 540
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 270
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 360
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 90
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 240
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 120
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 60
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 30
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 576
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 288
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 384
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 192
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 96
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 432
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 216
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 288
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 144
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 72
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 192
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 96
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 48
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 24
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 324
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 162
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 216
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 108
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 54
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 144
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 72
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 36
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 18
>>> Load all 450 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 96
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 48
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 24
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 12
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 600
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 300
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 400
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 200
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 100
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 450
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 225
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 300
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 150
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 75
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 200
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 100
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 50
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 25
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 480
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 240
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 320
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 160
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 80
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 360
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 180
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 240
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 120
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => ([(1,4),(4,5),(5,2),(5,3)],6) => 60
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 160
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 80
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => ([(1,5),(4,3),(5,2),(5,4)],6) => 40
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => ([(1,5),(5,2),(5,3),(5,4)],6) => 20
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 270
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 135
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 180
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 90
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 45
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 120
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 60
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => 30
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => ([(1,4),(1,5),(5,2),(5,3)],6) => 15
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 80
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 40
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 20
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(5,2)],6) => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6) => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 384
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 192
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 256
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 128
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 288
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 144
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 192
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 96
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => ([(1,5),(2,5),(5,3),(5,4)],6) => 48
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 128
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 64
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 32
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 16
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 216
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 108
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 144
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 72
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 36
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 96
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 48
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 24
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => ([(2,3),(3,4),(3,5)],6) => 12
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 64
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 32
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => ([(2,3),(2,4),(3,5),(4,5)],6) => 16
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => ([(2,3),(2,4),(4,5)],6) => 8
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => ([(2,3),(2,4),(2,5)],6) => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 162
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 81
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 108
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 54
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 27
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 72
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 36
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 18
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6) => 9
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 48
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 24
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 12
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => ([(3,4),(3,5)],6) => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 32
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 16
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 8
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => ([(4,5)],6) => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => ([],6) => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 3780
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 1680
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 840
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 210
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 1134
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 378
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 672
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 336
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 168
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 42
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2800
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => 700
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 3150
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 1575
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => 525
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1400
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 700
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => 350
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 175
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 1680
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => 945
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 1260
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => 315
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 560
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 280
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => ([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 140
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 35
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 1344
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 1792
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 896
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 448
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 2016
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1008
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => ([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => 336
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 896
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 448
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 224
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 112
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 1512
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 504
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 84
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 448
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => 224
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => 112
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 28
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 1134
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 567
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 756
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => 378
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 189
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 504
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 252
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => 126
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 63
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 336
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => 168
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => 84
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 42
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 21
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 224
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 112
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 56
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 28
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 4320
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 2160
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 2880
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 1440
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => 720
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 3240
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 1620
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2160
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 1080
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => 540
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 1440
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 720
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => 360
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 180
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 3456
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 1728
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2304
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 1152
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 576
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2592
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 1296
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 1728
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 864
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 432
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 1152
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 576
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 288
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 144
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2400
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 150
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2160
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 960
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 480
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => ([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => 120
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 810
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 480
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => ([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 30
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 1152
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => 288
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 384
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => 192
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => ([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 648
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => 432
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 384
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => ([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 24
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 972
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 324
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 162
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => 216
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 108
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => 54
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 288
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 144
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => ([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 72
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => ([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => 36
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => ([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => 18
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 192
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => ([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 96
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 48
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 24
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => 12
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 3000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 1500
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 1000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 500
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 2250
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 1125
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 1500
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 750
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 375
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 2400
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 1200
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 1600
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 800
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 400
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 1800
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 900
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 1200
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 600
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => ([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 300
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 800
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 400
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => ([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 200
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => ([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 100
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 1350
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 675
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 900
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 450
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 225
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 600
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => ([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 300
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 150
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => ([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 75
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 1920
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 960
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 1280
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 640
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 960
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 1080
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 540
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 480
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 240
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => ([(2,5),(5,6),(6,3),(6,4)],7) => 60
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => ([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 320
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => ([(2,6),(6,3),(6,4),(6,5)],7) => 20
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 810
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 405
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 360
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => ([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 90
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 45
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 240
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => ([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 60
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => ([(2,5),(2,6),(6,3),(6,4)],7) => 15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 160
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => ([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 80
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => ([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 40
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => ([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 20
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => ([(2,4),(2,5),(2,6),(6,3)],7) => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6)],7) => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 1536
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 768
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 1024
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 512
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 256
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 1152
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 576
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 768
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 384
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => ([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 192
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 512
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 256
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 128
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 864
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 432
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 576
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 288
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => ([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 144
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 384
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 192
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 96
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => ([(2,6),(3,6),(6,4),(6,5)],7) => 48
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 256
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 128
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 64
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => ([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 32
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 648
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 324
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 432
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 216
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 108
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 288
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 192
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 96
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7) => 24
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => ([(3,4),(4,5),(4,6)],7) => 12
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 128
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 64
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => ([(3,4),(3,5),(4,6),(5,6)],7) => 16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => ([(3,4),(3,5),(5,6)],7) => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => ([(3,4),(3,5),(3,6)],7) => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 486
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 243
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 324
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 162
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 81
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 216
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 108
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 54
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 27
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 144
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 72
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 36
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7) => 18
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => ([(3,5),(3,6),(4,5),(4,6)],7) => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 96
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 48
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 24
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => ([(4,5),(4,6)],7) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 64
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 32
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 16
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => ([],7) => 1
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Description
The product of the sizes of the principal order filters in a poset.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..