Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000097: Graphs ⟶ ℤ
Values
[1,0] => [1] => [1] => ([],1) => 1
[1,0,1,0] => [2,1] => [2] => ([],2) => 1
[1,1,0,0] => [1,2] => [2] => ([],2) => 1
[1,0,1,0,1,0] => [2,3,1] => [3] => ([],3) => 1
[1,0,1,1,0,0] => [2,1,3] => [3] => ([],3) => 1
[1,1,0,0,1,0] => [1,3,2] => [1,2] => ([(1,2)],3) => 2
[1,1,0,1,0,0] => [3,1,2] => [3] => ([],3) => 1
[1,1,1,0,0,0] => [1,2,3] => [3] => ([],3) => 1
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4] => ([],4) => 1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [4] => ([],4) => 1
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4] => ([],4) => 1
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [4] => ([],4) => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,3] => ([(2,3)],4) => 2
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3] => ([(2,3)],4) => 2
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [4] => ([],4) => 1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [4] => ([],4) => 1
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,3] => ([(2,3)],4) => 2
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4] => ([],4) => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4] => ([],4) => 1
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5] => ([],5) => 1
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [5] => ([],5) => 1
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [5] => ([],5) => 1
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [5] => ([],5) => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [5] => ([],5) => 1
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [5] => ([],5) => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [5] => ([],5) => 1
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [5] => ([],5) => 1
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,4] => ([(3,4)],5) => 2
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4] => ([(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,2,2] => ([(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] => [1,4] => ([(3,4)],5) => 2
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,4] => ([(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [5] => ([],5) => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [5] => ([],5) => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [5] => ([],5) => 1
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [5] => ([],5) => 1
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,2,2] => ([(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] => [1,4] => ([(3,4)],5) => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,4] => ([(3,4)],5) => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [5] => ([],5) => 1
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [5] => ([],5) => 1
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,4] => ([(3,4)],5) => 2
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [5] => ([],5) => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5] => ([],5) => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6] => ([],6) => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [6] => ([],6) => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [6] => ([],6) => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [6] => ([],6) => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [6] => ([],6) => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [6] => ([],6) => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [6] => ([],6) => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [6] => ([],6) => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,2,2] => ([(1,5),(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] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [6] => ([],6) => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [6] => ([],6) => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [6] => ([],6) => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [6] => ([],6) => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,2,2] => ([(1,5),(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] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [6] => ([],6) => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [6] => ([],6) => 1
>>> Load all 1072 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [6] => ([],6) => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [6] => ([],6) => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,5] => ([(4,5)],6) => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,5] => ([(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [2,2,2] => ([(1,5),(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] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [6] => ([],6) => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [6] => ([],6) => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [6] => ([],6) => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [6] => ([],6) => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [2,2,2] => ([(1,5),(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] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [6] => ([],6) => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [6] => ([],6) => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [6] => ([],6) => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [6] => ([],6) => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,5] => ([(4,5)],6) => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5] => ([(4,5)],6) => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,5] => ([(4,5)],6) => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,5] => ([(4,5)],6) => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [2,2,2] => ([(1,5),(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] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [6] => ([],6) => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [6] => ([],6) => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [6] => ([],6) => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [6] => ([],6) => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,5] => ([(4,5)],6) => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,5] => ([(4,5)],6) => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [6] => ([],6) => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [6] => ([],6) => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,5] => ([(4,5)],6) => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [6] => ([],6) => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6] => ([],6) => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [7] => ([],7) => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [7] => ([],7) => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [7] => ([],7) => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [7] => ([],7) => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [7] => ([],7) => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [7] => ([],7) => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [7] => ([],7) => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [7] => ([],7) => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [7] => ([],7) => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [7] => ([],7) => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [7] => ([],7) => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [7] => ([],7) => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [7] => ([],7) => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [7] => ([],7) => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [7] => ([],7) => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [7] => ([],7) => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [7] => ([],7) => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [7] => ([],7) => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [7] => ([],7) => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [7] => ([],7) => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [7] => ([],7) => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [7] => ([],7) => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [7] => ([],7) => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [7] => ([],7) => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [7] => ([],7) => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,6] => ([(5,6)],7) => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [7] => ([],7) => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [7] => ([],7) => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [7] => ([],7) => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [7] => ([],7) => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [7] => ([],7) => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [7] => ([],7) => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [7] => ([],7) => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [7] => ([],7) => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [7] => ([],7) => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [7] => ([],7) => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [7] => ([],7) => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [7] => ([],7) => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [7] => ([],7) => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [7] => ([],7) => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [7] => ([],7) => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [7] => ([],7) => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [7] => ([],7) => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [7] => ([],7) => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [7] => ([],7) => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [7] => ([],7) => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [7] => ([],7) => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [7] => ([],7) => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [7] => ([],7) => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [7] => ([],7) => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [7] => ([],7) => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [7] => ([],7) => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [7] => ([],7) => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [7] => ([],7) => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [7] => ([],7) => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [7] => ([],7) => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [2,5] => ([(4,6),(5,6)],7) => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,6] => ([(5,6)],7) => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [7] => ([],7) => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [7] => ([],7) => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,4,6,1,7,5,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [8] => ([],8) => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [8] => ([],8) => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,5,1,6,4,7,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [8] => ([],8) => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,1,4,7,5,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,1,4,8,5,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [8] => ([],8) => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => ([(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) => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,2,2,2] => ([(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) => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [8] => ([],8) => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,6,7,1,8,3,5] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [8] => ([],8) => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [8] => ([],8) => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,2,2,2] => ([(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) => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [2,2,2,2] => ([(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) => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [8] => ([],8) => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [8] => ([],8) => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [8] => ([],8) => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,2,2,2] => ([(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) => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,1,6,3,7,4,5,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [8] => ([],8) => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [8] => ([],8) => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [8] => ([],8) => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [8] => ([],8) => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [8] => ([],8) => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [8] => ([],8) => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [1,7] => ([(6,7)],8) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [1,7] => ([(6,7)],8) => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [1,7] => ([(6,7)],8) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,7] => ([(6,7)],8) => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,7] => ([(6,7)],8) => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [2,2,2,2] => ([(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) => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [2,2,2,2] => ([(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) => 4
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [8] => ([],8) => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [8] => ([],8) => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [8] => ([],8) => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [8] => ([],8) => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [8] => ([],8) => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [8] => ([],8) => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [2,2,2,2] => ([(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) => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [2,2,2,2] => ([(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) => 4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [8] => ([],8) => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [8] => ([],8) => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [8] => ([],8) => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [2,2,2,2] => ([(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) => 4
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [8] => ([],8) => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [8] => ([],8) => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [8] => ([],8) => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [1,7] => ([(6,7)],8) => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [1,7] => ([(6,7)],8) => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [1,7] => ([(6,7)],8) => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,7] => ([(6,7)],8) => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [2,2,2,2] => ([(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) => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [2,2,2,2] => ([(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) => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [8] => ([],8) => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [8] => ([],8) => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [8] => ([],8) => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [8] => ([],8) => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [8] => ([],8) => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [2,2,2,2] => ([(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) => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [8] => ([],8) => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [8] => ([],8) => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [8] => ([],8) => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [8] => ([],8) => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [8] => ([],8) => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [2,2,2,2] => ([(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) => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8] => ([],8) => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [8] => ([],8) => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [8] => ([],8) => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [8] => ([],8) => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [8] => ([],8) => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [8] => ([],8) => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [8] => ([],8) => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [8] => ([],8) => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [8] => ([],8) => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [2,6] => ([(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [8] => ([],8) => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [8] => ([],8) => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,7] => ([(6,7)],8) => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [8] => ([],8) => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [8] => ([],8) => 1
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 8\ q + 6\ q^{2}$
$F_{5} = 16\ q + 24\ q^{2} + 2\ q^{3}$
$F_{6} = 32\ q + 80\ q^{2} + 20\ q^{3}$
$F_{7} = 64\ q + 240\ q^{2} + 120\ q^{3} + 5\ q^{4}$
Description
The order of the largest clique of the graph.
A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.
A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.
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
DEX composition
Description
The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.
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