- FindStat

Identifier

Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000093: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1037 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,2,5,6,8,7] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,4,1,5,2,7,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,4,1,5,7,2,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,4,1,5,2,6,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,5,1,7,2,8,6] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,5,2,4,6,8,7] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,7,2,4,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7

[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,3,8,7] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,6,3,7,8,5] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,6,7,3,8,5] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,4,2,5,6,3,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,4,2,5,3,7,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,4,2,5,3,6,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,4,5,6,2,3,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,6,3,7,8,5] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,6,7,3,8,5] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,5,7,2,3,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,5,2,3,6,8,7] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,7,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,5,7,1,2,3,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,6,7,2,3,8,5] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,6,1,2,3,7,8,5] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,6,1,2,7,3,8,5] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,6,1,7,2,3,8,5] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,6,7,1,2,3,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,7,1,2,3,5,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7

[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,2,5,6,3,4,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,5,2,6,7,3,8,4] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,5,6,2,7,3,8,4] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,3,6,4,8,7] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,6,2,3,4,8,7] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,7,2,3,4,8,6] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7

[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,6,2,3,4,7,8,5] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7

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Description

The cardinality of a maximal independent set of vertices of a graph.
An independent set of a graph is a set of pairwise non-adjacent vertices. A maximum independent set is an independent set of maximum cardinality. This statistic is also called the independence number or stability number $\alpha(G)$ of $G$.

Map

to threshold graph

Description

The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.

Map

to 321-avoiding permutation (Billey-Jockusch-Stanley)

Description

The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.

Map

descent composition

Description

The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.