- FindStat

Identifier

Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001813: Posets ⟶ ℤ

Values

[1,0] => [1] => [1] => ([],1) => 1

[1,0,1,0] => [1,2] => [2,1] => ([],2) => 1

[1,1,0,0] => [2,1] => [1,2] => ([(0,1)],2) => 2

[1,0,1,0,1,0] => [1,2,3] => [3,2,1] => ([],3) => 1

[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => ([(1,2)],3) => 2

[1,1,0,0,1,0] => [2,1,3] => [2,3,1] => ([(1,2)],3) => 2

[1,1,0,1,0,0] => [2,3,1] => [2,1,3] => ([(0,2),(1,2)],3) => 4

[1,1,1,0,0,0] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3) => 3

[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4,3,2,1] => ([],4) => 1

[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4) => 2

[1,0,1,1,0,0,1,0] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4) => 2

[1,0,1,1,0,1,0,0] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4

[1,0,1,1,1,0,0,0] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4) => 3

[1,1,0,0,1,0,1,0] => [2,1,3,4] => [3,4,2,1] => ([(2,3)],4) => 2

[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4

[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4) => 4

[1,1,0,1,0,1,0,0] => [2,3,4,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 8

[1,1,0,1,1,0,0,0] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4) => 6

[1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4) => 3

[1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 6

[1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4) => 9

[1,1,1,1,0,0,0,0] => [4,1,2,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4) => 4

[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5) => 1

[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,4,3,1,2] => ([(3,4)],5) => 2

[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [5,4,2,3,1] => ([(3,4)],5) => 2

[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 4

[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [5,4,1,3,2] => ([(2,3),(2,4)],5) => 3

[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [5,3,4,2,1] => ([(3,4)],5) => 2

[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 4

[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 4

[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 8

[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5) => 6

[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5) => 3

[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5) => 6

[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 9

[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5) => 4

[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [4,5,3,2,1] => ([(3,4)],5) => 2

[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 4

[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 4

[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 8

[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5) => 6

[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 4

[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 8

[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 8

[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 16

[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5) => 12

[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5) => 6

[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 12

[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 18

[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5) => 8

[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [3,5,4,2,1] => ([(2,3),(2,4)],5) => 3

[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5) => 6

[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [3,5,2,4,1] => ([(1,4),(2,3),(2,4)],5) => 6

[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [3,5,2,1,4] => ([(0,4),(1,4),(2,3),(2,4)],5) => 12

[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [3,5,1,4,2] => ([(0,3),(0,4),(1,2),(1,4)],5) => 9

[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5) => 9

[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [3,2,5,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 18

[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 27

[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 12

[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5) => 4

[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5) => 8

[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [2,5,1,4,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 12

[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 16

[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5) => 5

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => ([],6) => 1

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,5,4,3,1,2] => ([(4,5)],6) => 2

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [6,5,4,2,3,1] => ([(4,5)],6) => 2

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 4

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [6,5,4,1,3,2] => ([(3,4),(3,5)],6) => 3

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(4,5)],6) => 2

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 4

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 4

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 8

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [6,5,3,1,4,2] => ([(2,5),(3,4),(3,5)],6) => 6

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [6,5,2,4,3,1] => ([(3,4),(3,5)],6) => 3

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [6,5,2,4,1,3] => ([(2,5),(3,4),(3,5)],6) => 6

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [6,5,2,1,4,3] => ([(2,4),(2,5),(3,4),(3,5)],6) => 9

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6) => 4

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [6,4,5,3,2,1] => ([(4,5)],6) => 2

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 4

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 4

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 8

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [6,4,5,1,3,2] => ([(1,5),(2,3),(2,4)],6) => 6

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 8

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 8

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 16

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [6,4,3,1,5,2] => ([(1,5),(2,5),(3,4),(3,5)],6) => 12

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [6,4,2,5,3,1] => ([(2,5),(3,4),(3,5)],6) => 6

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [6,4,2,5,1,3] => ([(1,5),(2,4),(3,4),(3,5)],6) => 12

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [6,4,2,1,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [6,4,1,5,3,2] => ([(1,5),(2,3),(2,4),(2,5)],6) => 8

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [6,3,5,4,2,1] => ([(3,4),(3,5)],6) => 3

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [6,3,5,4,1,2] => ([(1,5),(2,3),(2,4)],6) => 6

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => ([(2,5),(3,4),(3,5)],6) => 6

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [6,3,5,2,1,4] => ([(1,5),(2,5),(3,4),(3,5)],6) => 12

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [6,3,5,1,4,2] => ([(1,4),(1,5),(2,3),(2,5)],6) => 9

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6) => 9

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [6,3,2,5,1,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [6,3,2,1,5,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 27

[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [6,3,1,5,4,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12

>>> Load all 480 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [6,2,5,4,3,1] => ([(2,3),(2,4),(2,5)],6) => 4

[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [6,2,5,4,1,3] => ([(1,5),(2,3),(2,4),(2,5)],6) => 8

[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [6,2,5,1,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12

[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [6,2,1,5,4,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 16

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6) => 5

[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => ([(4,5)],6) => 2

[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 4

[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 4

[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 8

[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [5,6,4,1,3,2] => ([(1,5),(2,3),(2,4)],6) => 6

[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 4

[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 8

[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 8

[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 16

[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [5,6,3,1,4,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => 12

[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [5,6,2,4,3,1] => ([(1,5),(2,3),(2,4)],6) => 6

[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [5,6,2,4,1,3] => ([(0,5),(1,3),(2,4),(2,5)],6) => 12

[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [5,6,2,1,4,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 18

[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [5,6,1,4,3,2] => ([(0,5),(1,2),(1,3),(1,4)],6) => 8

[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 4

[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 8

[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 8

[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 16

[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [5,4,6,1,3,2] => ([(0,5),(1,5),(2,3),(2,4)],6) => 12

[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 8

[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 16

[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 16

[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 32

[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [5,4,3,1,6,2] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 24

[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [5,4,2,6,3,1] => ([(1,5),(2,5),(3,4),(3,5)],6) => 12

[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [5,4,2,6,1,3] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 24

[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [5,4,2,1,6,3] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 36

[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [5,4,1,6,3,2] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 16

[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [5,3,6,4,2,1] => ([(2,5),(3,4),(3,5)],6) => 6

[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [5,3,6,4,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => 12

[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [5,3,6,2,4,1] => ([(1,5),(2,4),(3,4),(3,5)],6) => 12

[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [5,3,6,2,1,4] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 24

[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [5,3,6,1,4,2] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 18

[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [5,3,2,6,4,1] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18

[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [5,3,2,6,1,4] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 36

[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [5,3,2,1,6,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 54

[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24

[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [5,2,6,4,3,1] => ([(1,5),(2,3),(2,4),(2,5)],6) => 8

[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [5,2,6,4,1,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 16

[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [5,2,6,1,4,3] => ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24

[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 32

[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [5,1,6,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 10

[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => ([(3,4),(3,5)],6) => 3

[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [4,6,5,3,1,2] => ([(1,5),(2,3),(2,4)],6) => 6

[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [4,6,5,2,3,1] => ([(1,5),(2,3),(2,4)],6) => 6

[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [4,6,5,2,1,3] => ([(0,5),(1,5),(2,3),(2,4)],6) => 12

[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => ([(0,4),(0,5),(1,2),(1,3)],6) => 9

[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,6,3,5,2,1] => ([(2,5),(3,4),(3,5)],6) => 6

[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [4,6,3,5,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => 12

[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [4,6,3,2,5,1] => ([(1,5),(2,5),(3,4),(3,5)],6) => 12

[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [4,6,3,2,1,5] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 24

[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [4,6,3,1,5,2] => ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 18

[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [4,6,2,5,3,1] => ([(1,4),(1,5),(2,3),(2,5)],6) => 9

[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [4,6,2,5,1,3] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 18

[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [4,6,2,1,5,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 27

[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [4,6,1,5,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 12

[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => ([(2,4),(2,5),(3,4),(3,5)],6) => 9

[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [4,3,6,5,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 18

[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [4,3,6,2,5,1] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18

[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [4,3,6,2,1,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 36

[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [4,3,6,1,5,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 27

[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 27

[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [4,3,2,6,1,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 54

[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 81

[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 36

[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [4,2,6,5,3,1] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12

[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [4,2,6,5,1,3] => ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24

[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 36

[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 48

[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [4,1,6,5,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 15

[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => ([(2,3),(2,4),(2,5)],6) => 4

[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [3,6,5,4,1,2] => ([(0,5),(1,2),(1,3),(1,4)],6) => 8

[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [3,6,5,2,4,1] => ([(1,5),(2,3),(2,4),(2,5)],6) => 8

[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [3,6,5,2,1,4] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 16

[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [3,6,5,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 12

[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [3,6,2,5,4,1] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12

[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [3,6,2,5,1,4] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24

[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [3,6,2,1,5,4] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 36

[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [3,6,1,5,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 16

[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 16

[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [3,2,6,5,1,4] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 32

[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [3,2,6,1,5,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 48

[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [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

[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [3,1,6,5,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 20

[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6) => 5

[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 10

[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [2,6,5,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 15

[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [2,6,1,5,4,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 20

[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 25

[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 6

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => ([],7) => 1

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 2

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 2

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 4

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [7,6,5,4,1,3,2] => ([(4,5),(4,6)],7) => 3

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 2

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 4

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 4

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 8

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [7,6,5,3,1,4,2] => ([(3,6),(4,5),(4,6)],7) => 6

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [7,6,5,2,4,3,1] => ([(4,5),(4,6)],7) => 3

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [7,6,5,2,4,1,3] => ([(3,6),(4,5),(4,6)],7) => 6

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [7,6,5,2,1,4,3] => ([(3,5),(3,6),(4,5),(4,6)],7) => 9

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [7,6,5,1,4,3,2] => ([(3,4),(3,5),(3,6)],7) => 4

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 2

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 4

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 4

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [7,6,4,5,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 8

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [7,6,4,5,1,3,2] => ([(2,6),(3,4),(3,5)],7) => 6

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 4

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [7,6,4,3,5,1,2] => ([(2,6),(3,6),(4,5)],7) => 8

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [7,6,4,3,2,5,1] => ([(3,6),(4,6),(5,6)],7) => 8

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 16

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [7,6,4,3,1,5,2] => ([(2,6),(3,6),(4,5),(4,6)],7) => 12

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [7,6,4,2,5,3,1] => ([(3,6),(4,5),(4,6)],7) => 6

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [7,6,4,2,5,1,3] => ([(2,6),(3,5),(4,5),(4,6)],7) => 12

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [7,6,4,2,1,5,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18

[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [7,6,4,1,5,3,2] => ([(2,6),(3,4),(3,5),(3,6)],7) => 8

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [7,6,3,5,4,2,1] => ([(4,5),(4,6)],7) => 3

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [7,6,3,5,4,1,2] => ([(2,6),(3,4),(3,5)],7) => 6

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [7,6,3,5,2,4,1] => ([(3,6),(4,5),(4,6)],7) => 6

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [7,6,3,5,2,1,4] => ([(2,6),(3,6),(4,5),(4,6)],7) => 12

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [7,6,3,2,5,4,1] => ([(3,5),(3,6),(4,5),(4,6)],7) => 9

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [7,6,3,2,5,1,4] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [7,6,3,2,1,5,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 27

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [7,6,2,5,4,3,1] => ([(3,4),(3,5),(3,6)],7) => 4

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [7,6,2,5,4,1,3] => ([(2,6),(3,4),(3,5),(3,6)],7) => 8

[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [7,6,1,5,4,3,2] => ([(2,3),(2,4),(2,5),(2,6)],7) => 5

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 2

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 4

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => ([(3,6),(4,5)],7) => 4

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [7,5,6,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 8

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [7,5,6,4,1,3,2] => ([(2,6),(3,4),(3,5)],7) => 6

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 4

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [7,5,6,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 8

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 16

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [7,5,6,2,4,3,1] => ([(2,6),(3,4),(3,5)],7) => 6

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [7,5,6,2,1,4,3] => ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18

[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [7,5,6,1,4,3,2] => ([(1,6),(2,3),(2,4),(2,5)],7) => 8

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [7,5,4,6,3,2,1] => ([(4,6),(5,6)],7) => 4

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [7,5,4,6,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 8

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [7,5,4,6,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 8

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 16

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [7,5,4,6,1,3,2] => ([(1,6),(2,6),(3,4),(3,5)],7) => 12

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 8

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 16

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 16

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [7,5,4,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 32

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [7,5,4,3,1,6,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [7,5,4,2,6,3,1] => ([(2,6),(3,6),(4,5),(4,6)],7) => 12

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [7,5,4,2,6,1,3] => ([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [7,5,4,2,1,6,3] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36

[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [7,5,4,1,6,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 16

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [7,5,3,6,4,2,1] => ([(3,6),(4,5),(4,6)],7) => 6

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [7,5,3,6,2,4,1] => ([(2,6),(3,5),(4,5),(4,6)],7) => 12

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [7,5,3,6,2,1,4] => ([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [7,5,3,2,6,4,1] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [7,5,3,2,6,1,4] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 36

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [7,5,3,2,1,6,4] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 54

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [7,5,2,6,4,3,1] => ([(2,6),(3,4),(3,5),(3,6)],7) => 8

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [7,5,2,6,1,4,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24

[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [7,5,2,1,6,4,3] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 32

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [7,5,1,6,4,3,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [7,4,6,5,3,2,1] => ([(4,5),(4,6)],7) => 3

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [7,4,6,5,3,1,2] => ([(2,6),(3,4),(3,5)],7) => 6

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [7,4,6,5,2,3,1] => ([(2,6),(3,4),(3,5)],7) => 6

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [7,4,6,5,2,1,3] => ([(1,6),(2,6),(3,4),(3,5)],7) => 12

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [7,4,6,3,5,2,1] => ([(3,6),(4,5),(4,6)],7) => 6

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [7,4,6,3,2,5,1] => ([(2,6),(3,6),(4,5),(4,6)],7) => 12

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [7,4,6,3,2,1,5] => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [7,4,6,2,1,5,3] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 27

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [7,4,3,6,5,2,1] => ([(3,5),(3,6),(4,5),(4,6)],7) => 9

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [7,4,3,6,5,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [7,4,3,6,2,5,1] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [7,4,3,6,2,1,5] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [7,4,3,6,1,5,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 27

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [7,4,3,2,6,5,1] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 27

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [7,4,3,2,6,1,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 54

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [7,4,3,2,1,6,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 81

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [7,4,3,1,6,5,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 36

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [7,4,2,6,5,1,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [7,3,6,5,4,2,1] => ([(3,4),(3,5),(3,6)],7) => 4

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [7,3,6,5,4,1,2] => ([(1,6),(2,3),(2,4),(2,5)],7) => 8

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [7,3,6,5,2,4,1] => ([(2,6),(3,4),(3,5),(3,6)],7) => 8

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [7,3,6,5,2,1,4] => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 16

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [7,3,6,2,1,5,4] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 36

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [7,3,2,6,5,1,4] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 32

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [7,2,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6)],7) => 5

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [7,2,6,5,4,1,3] => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [7,1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 6

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 2

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [6,7,5,4,3,1,2] => ([(3,6),(4,5)],7) => 4

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 4

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [6,7,5,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 8

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [6,7,5,4,1,3,2] => ([(2,6),(3,4),(3,5)],7) => 6

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [6,7,5,3,4,2,1] => ([(3,6),(4,5)],7) => 4

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [6,7,5,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 8

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [6,7,5,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 16

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [6,7,5,2,4,3,1] => ([(2,6),(3,4),(3,5)],7) => 6

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [6,7,5,2,1,4,3] => ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [6,7,5,1,4,3,2] => ([(1,6),(2,3),(2,4),(2,5)],7) => 8

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [6,7,4,5,3,2,1] => ([(3,6),(4,5)],7) => 4

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [6,7,4,5,2,1,3] => ([(0,6),(1,6),(2,5),(3,4)],7) => 16

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [6,7,4,3,5,2,1] => ([(2,6),(3,6),(4,5)],7) => 8

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [6,7,4,3,5,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 16

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [6,7,4,3,2,5,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 16

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [6,7,4,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 32

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [6,7,4,3,1,5,2] => ([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 24

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [6,7,4,2,5,1,3] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 24

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [6,7,4,2,1,5,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 36

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [6,7,3,5,4,2,1] => ([(2,6),(3,4),(3,5)],7) => 6

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [6,7,3,5,2,1,4] => ([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 24

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [6,7,3,2,5,4,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [6,7,3,2,5,1,4] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 36

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [6,7,3,2,1,5,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 54

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [6,7,2,5,4,3,1] => ([(1,6),(2,3),(2,4),(2,5)],7) => 8

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [6,7,1,5,4,3,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 10

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 4

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 8

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [6,5,7,4,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 8

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 16

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [6,5,7,4,1,3,2] => ([(1,6),(2,6),(3,4),(3,5)],7) => 12

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [6,5,7,3,4,2,1] => ([(2,6),(3,6),(4,5)],7) => 8

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 16

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 16

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [6,5,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 32

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [6,5,7,3,1,4,2] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 24

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [6,5,7,2,4,3,1] => ([(1,6),(2,6),(3,4),(3,5)],7) => 12

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [6,5,7,2,4,1,3] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 24

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [6,5,7,2,1,4,3] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 36

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [6,5,7,1,4,3,2] => ([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 16

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => 8

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [6,5,4,7,3,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 16

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [6,5,4,7,2,3,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 16

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [6,5,4,7,2,1,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 32

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [6,5,4,7,1,3,2] => ([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 24

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 16

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [6,5,4,3,7,1,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 32

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 32

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 64

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [6,5,4,3,1,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 48

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [6,5,4,2,7,3,1] => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [6,5,4,2,7,1,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 48

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [6,5,4,2,1,7,3] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 72

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [6,5,4,1,7,3,2] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 32

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [6,5,3,7,4,2,1] => ([(2,6),(3,6),(4,5),(4,6)],7) => 12

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [6,5,3,7,4,1,2] => ([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 24

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [6,5,3,7,2,4,1] => ([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [6,5,3,7,2,1,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 48

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [6,5,3,7,1,4,2] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 36

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [6,5,3,2,7,4,1] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [6,5,3,2,7,1,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 72

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [6,5,3,2,1,7,4] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [6,5,3,1,7,4,2] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [6,5,2,7,4,3,1] => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 16

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [6,5,2,7,4,1,3] => ([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 32

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [6,5,2,7,1,4,3] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 48

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [6,5,2,1,7,4,3] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 64

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [6,5,1,7,4,3,2] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 20

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [6,4,7,5,3,2,1] => ([(3,6),(4,5),(4,6)],7) => 6

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [6,4,7,5,2,1,3] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 24

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [6,4,7,3,5,2,1] => ([(2,6),(3,5),(4,5),(4,6)],7) => 12

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [6,4,7,3,5,1,2] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 24

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [6,4,7,3,2,5,1] => ([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [6,4,7,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 48

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [6,4,7,3,1,5,2] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 36

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [6,4,7,2,5,1,3] => ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 36

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [6,4,7,2,1,5,3] => ([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 54

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [6,4,3,7,5,2,1] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [6,4,3,7,5,1,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 36

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [6,4,3,7,2,5,1] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 36

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [6,4,3,7,2,1,5] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 72

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [6,4,3,7,1,5,2] => ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 54

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [6,4,3,2,7,5,1] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 54

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [6,4,3,2,7,1,5] => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [6,4,3,2,1,7,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 162

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [6,4,3,1,7,5,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 72

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [6,4,2,7,5,1,3] => ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [6,4,2,7,1,5,3] => ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 72

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [6,4,2,1,7,5,3] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [6,3,7,5,4,2,1] => ([(2,6),(3,4),(3,5),(3,6)],7) => 8

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [6,3,7,5,2,1,4] => ([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 32

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [6,3,7,2,5,4,1] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [6,3,7,2,5,1,4] => ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [6,3,7,2,1,5,4] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 72

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [6,3,2,7,5,4,1] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 32

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [6,3,2,7,5,1,4] => ([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 64

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [6,3,2,7,1,5,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [6,3,2,1,7,5,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 128

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [6,2,7,5,4,3,1] => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [6,1,7,5,4,3,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 12

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [5,7,6,4,3,2,1] => ([(4,5),(4,6)],7) => 3

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [5,7,6,4,3,1,2] => ([(2,6),(3,4),(3,5)],7) => 6

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [5,7,6,4,2,3,1] => ([(2,6),(3,4),(3,5)],7) => 6

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [5,7,6,4,2,1,3] => ([(1,6),(2,6),(3,4),(3,5)],7) => 12

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [5,7,6,3,4,2,1] => ([(2,6),(3,4),(3,5)],7) => 6

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [5,7,6,3,2,4,1] => ([(1,6),(2,6),(3,4),(3,5)],7) => 12

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [5,7,6,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 24

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [5,7,6,2,1,4,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 27

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [5,7,4,6,3,2,1] => ([(3,6),(4,5),(4,6)],7) => 6

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [5,7,4,6,2,1,3] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 24

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [5,7,4,3,6,2,1] => ([(2,6),(3,6),(4,5),(4,6)],7) => 12

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [5,7,4,3,6,1,2] => ([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 24

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [5,7,4,3,2,6,1] => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [5,7,4,3,2,1,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 48

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [5,7,4,3,1,6,2] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 36

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [5,7,4,2,6,1,3] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 36

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [5,7,4,2,1,6,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 54

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [5,7,3,6,2,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 36

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [5,7,3,2,6,4,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 27

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [5,7,3,2,6,1,4] => ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 54

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [5,7,3,2,1,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 81

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [5,4,7,6,3,2,1] => ([(3,5),(3,6),(4,5),(4,6)],7) => 9

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [5,4,7,6,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [5,4,7,6,2,3,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 18

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [5,4,7,6,2,1,3] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 36

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [5,4,7,6,1,3,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 27

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [5,4,7,3,6,2,1] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [5,4,7,3,6,1,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 36

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [5,4,7,3,2,6,1] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [5,4,7,3,2,1,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 72

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [5,4,7,3,1,6,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 54

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [5,4,7,2,6,3,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 27

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [5,4,7,2,6,1,3] => ([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 54

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [5,4,7,2,1,6,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 81

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [5,4,7,1,6,3,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 36

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [5,4,3,7,6,2,1] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 27

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [5,4,3,7,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 54

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [5,4,3,7,2,6,1] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 54

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [5,4,3,7,2,1,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [5,4,3,7,1,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 81

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [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

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [5,4,3,2,7,1,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 162

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [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

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [5,4,3,1,7,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 108

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [5,4,2,7,6,3,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 36

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [5,4,2,7,6,1,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 72

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [5,4,2,7,1,6,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 108

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [5,4,2,1,7,6,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 144

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [5,4,1,7,6,3,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 45

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [5,3,7,6,2,4,1] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [5,3,7,6,2,1,4] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 48

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [5,3,7,2,6,1,4] => ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 72

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [5,3,7,2,1,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 108

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [5,3,2,7,6,1,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [5,3,2,7,1,6,4] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 144

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [5,3,2,1,7,6,4] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 192

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [4,7,6,5,3,2,1] => ([(3,4),(3,5),(3,6)],7) => 4

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [4,7,6,5,3,1,2] => ([(1,6),(2,3),(2,4),(2,5)],7) => 8

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [4,7,6,5,2,3,1] => ([(1,6),(2,3),(2,4),(2,5)],7) => 8

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [4,7,6,5,2,1,3] => ([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 16

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [4,7,6,3,5,2,1] => ([(2,6),(3,4),(3,5),(3,6)],7) => 8

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [4,7,6,3,2,5,1] => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 16

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [4,7,6,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 32

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [4,7,6,2,1,5,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 36

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [4,7,3,6,2,1,5] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 48

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [4,7,3,2,6,5,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 36

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [4,7,3,2,6,1,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 72

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [4,7,3,2,1,6,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 108

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [4,3,7,6,2,5,1] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 32

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [4,3,7,6,2,1,5] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 64

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [4,3,7,2,6,1,5] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 96

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [4,3,7,2,1,6,5] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 144

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [4,3,2,7,6,1,5] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 128

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [4,3,2,7,1,6,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 192

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [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

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [3,7,6,5,4,2,1] => ([(2,3),(2,4),(2,5),(2,6)],7) => 5

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [3,7,6,5,4,1,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 10

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [3,7,6,5,2,4,1] => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 10

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [3,7,6,5,2,1,4] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 20

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [3,7,6,2,1,5,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 45

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [2,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 6

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [2,7,6,5,4,1,3] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 12

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 7

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + 2\ q^{2} + q^{3} + q^{4}$

$F_{4} = q + 3\ q^{2} + 2\ q^{3} + 4\ q^{4} + 2\ q^{6} + q^{8} + q^{9}$

$F_{5} = q + 4\ q^{2} + 3\ q^{3} + 8\ q^{4} + q^{5} + 6\ q^{6} + 6\ q^{8} + 3\ q^{9} + 5\ q^{12} + 2\ q^{16} + 2\ q^{18} + q^{27}$

$F_{6} = q + 5\ q^{2} + 4\ q^{3} + 13\ q^{4} + 2\ q^{5} + 13\ q^{6} + 16\ q^{8} + 6\ q^{9} + 2\ q^{10} + 18\ q^{12} + 2\ q^{15} + 11\ q^{16} + 9\ q^{18} + 2\ q^{20} + 8\ q^{24} + q^{25} + 4\ q^{27} + 3\ q^{32} + 6\ q^{36} + 2\ q^{48} + 2\ q^{54} + q^{64} + q^{81}$

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 321-avoiding permutation (Krattenthaler)

Description

Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength

$n$ in an

$n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.

Map

complement

Description

Sents a permutation to its complement.
The complement of a permutation

$\sigma$ of length

$n$ is the permutation

$\tau$ with

$\tau(i) = n+1-\sigma(i)$