Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001337: Graphs ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [1] => ([],1) => 1
[1,1,0,0] => [2,1] => [1] => ([],1) => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2] => ([],2) => 2
[1,0,1,1,0,0] => [1,3,2] => [1,2] => ([],2) => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1] => ([(0,1)],2) => 1
[1,1,0,1,0,0] => [2,3,1] => [2,1] => ([(0,1)],2) => 1
[1,1,1,0,0,0] => [3,2,1] => [2,1] => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3] => ([],3) => 3
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,3] => ([],3) => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2] => ([(1,2)],3) => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,3,2] => ([(1,2)],3) => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,2] => ([(1,2)],3) => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3] => ([(1,2)],3) => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,3] => ([(1,2)],3) => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [2,3,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 1
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4] => ([],4) => 4
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,4] => ([],4) => 4
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3] => ([(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,4,3] => ([(2,3)],4) => 3
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,3] => ([(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4] => ([(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,4] => ([(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,3,4,2] => ([(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,3,4,2] => ([(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4] => ([(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,4] => ([(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3] => ([(0,3),(1,2)],4) => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,4,3] => ([(0,3),(1,2)],4) => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4) => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4] => ([(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,3,1,4] => ([(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5] => ([],5) => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,5] => ([],5) => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4] => ([(3,4)],5) => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,5,4] => ([(3,4)],5) => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,4] => ([(3,4)],5) => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5] => ([(3,4)],5) => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,5] => ([(3,4)],5) => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5] => ([(3,4)],5) => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,5] => ([(3,4)],5) => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
>>> Load all 932 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5] => ([(3,4)],5) => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,5] => ([(3,4)],5) => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => ([],6) => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6] => ([],6) => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5] => ([(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,6,5] => ([(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,6,5] => ([(4,5)],6) => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6] => ([(4,5)],6) => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,6] => ([(4,5)],6) => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6] => ([(4,5)],6) => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,6] => ([(4,5)],6) => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,5,4,6,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,5,4,6,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,5,4,6,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6] => ([(4,5)],6) => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,6] => ([(4,5)],6) => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,3,5,4,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,3,5,4,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,3,5,4,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,3,5,4,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,3,5,4,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,3,5,6,4,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,3,5,6,4,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,3,5,6,4,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,3,5,6,4,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,4,3,5,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,4,3,5,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,4,3,5,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,4,3,5,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,4,3,5,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,4,5,3,2,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,4,5,3,2,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,4,5,3,6,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,4,5,3,6,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,4,5,3,6,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,5,4,3,2,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,5,4,3,6,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,5,4,3,6,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,5,4,3,6,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,5,4,6,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,5,4,6,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,5,4,6,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,5,4,6,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => ([(4,5)],6) => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,6] => ([(4,5)],6) => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,5,4,3,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,5,4,6,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,5,4,6,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,5,4,6,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [2,3,5,4,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [2,3,5,4,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [2,4,3,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [2,4,3,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [2,4,3,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [2,4,3,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [2,4,3,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [2,4,3,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [2,4,3,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [2,4,5,3,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [2,4,5,3,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,1,5,4,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,5,6,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,1,5,6,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,1,5,6,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,4,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,2,4,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,4,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,2,5,4,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,5,4,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [3,4,2,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [3,4,2,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [3,4,2,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [3,4,2,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [3,5,4,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [3,5,4,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,3,2,5,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [4,5,3,2,6,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [4,5,3,2,6,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,4,3,2,6,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => ([],7) => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ([],7) => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7) => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => 6
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,5,7,6,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,2,3,5,7,6,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,5,7,6,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,6,5,7,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,6,5,7,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,2,3,6,7,5,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,2,3,6,7,5,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,2,3,6,7,5,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,2,4,6,5,3,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [1,2,4,6,7,5,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,4,7,6,5,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,5,4,6,7,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,2,5,6,4,7,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,2,5,6,7,4,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,6,5,4,7,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,2,6,7,5,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,3,4,2,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,3,4,2,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [1,3,4,5,7,6,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,3,4,5,7,6,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [1,3,4,6,7,5,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,3,4,7,6,5,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,3,5,6,7,4,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,3,5,7,6,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [1,3,6,5,7,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,4,3,2,6,7,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [1,4,3,2,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,4,3,2,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,4,3,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,4,3,6,5,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [1,4,3,7,6,5,2] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,4,3,7,6,5,2] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,4,5,3,6,7,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [1,4,7,6,5,3,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [1,4,7,6,5,3,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,5,4,3,6,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [1,5,6,4,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [1,5,6,4,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,5,7,6,4,3,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,6,5,4,3,7,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,6,7,5,4,3,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,6,7,5,4,3,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [1,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => ([(5,6)],7) => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,7] => ([(5,6)],7) => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [2,1,3,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7) => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,7,6,5] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,4,3,7,6,5] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,5] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,4,5,6,3,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [2,1,4,5,7,6,3] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,4,5,7,6,3] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,4,6,5,3,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,4,6,5,7,3] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,4,7,6,5,3] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,5,4,6,3,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,5,4,7,6,3] => ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,5,6,4,3,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [2,1,5,6,7,4,3] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,6,5,7,4,3] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,6,5,7,4,3] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [2,1,6,5,7,4,3] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [2,1,6,7,5,4,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,6,7,5,4,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,6,7,5,4,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,7,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,7,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,3,1,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [2,3,1,4,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [2,3,1,4,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,3,1,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,3,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [2,3,1,7,6,5,4] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [2,3,4,1,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [2,3,4,1,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [2,3,4,1,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [2,3,4,1,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [2,3,4,5,7,6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [2,3,4,6,5,1,7] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [2,3,4,7,6,5,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [2,3,5,4,1,7,6] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [2,3,5,4,7,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [2,3,5,6,7,4,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [2,3,5,6,7,4,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [2,3,6,5,4,1,7] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [2,4,3,1,6,5,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [2,4,3,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [2,4,3,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [2,4,3,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [2,4,3,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [2,4,3,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [2,4,3,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [2,4,3,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [2,4,3,6,5,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [2,4,3,6,5,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [2,4,3,6,5,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [2,4,3,7,6,5,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [2,4,5,3,1,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [2,4,5,3,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [2,4,6,7,5,3,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [2,4,7,6,5,3,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [2,5,4,3,1,7,6] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [2,5,4,3,6,7,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [2,5,4,3,6,7,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [2,5,4,3,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [2,5,4,3,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [2,5,4,3,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [2,5,4,6,7,3,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [2,5,4,7,6,3,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [2,5,6,7,4,3,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [2,6,7,5,4,3,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => ([(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [3,2,1,4,6,7,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,2,1,4,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [3,2,1,4,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [3,2,1,4,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [3,2,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,2,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [3,2,1,5,7,6,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [3,2,1,5,7,6,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [3,2,1,5,7,6,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,2,1,6,5,7,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,6,5,7,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [3,2,1,6,7,5,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [3,2,1,6,7,5,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [3,2,1,6,7,5,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,2,1,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [3,2,1,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [3,2,1,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [3,2,1,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [3,2,4,1,5,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [3,2,4,1,5,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [3,2,4,1,5,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,2,4,1,5,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,4,1,6,5,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [3,2,4,1,6,5,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [3,2,4,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [3,2,4,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,2,4,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,2,4,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,2,4,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [3,2,4,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [3,2,4,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [3,2,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [3,2,4,5,7,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [3,2,4,7,6,5,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [3,2,5,4,1,6,7] => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,2,5,4,1,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [3,2,5,4,6,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [3,2,5,4,7,6,1] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [3,2,5,4,7,6,1] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [3,2,6,5,4,7,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [3,2,6,5,7,4,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [3,2,6,7,5,4,1] => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [3,2,7,6,5,4,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [3,4,2,1,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [3,4,2,1,6,7,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [3,4,2,1,6,7,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [3,4,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [3,4,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [3,4,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [3,4,2,5,1,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [3,4,2,5,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [3,4,2,6,7,5,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [3,4,2,7,6,5,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [3,4,5,2,1,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [3,4,5,7,6,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [3,4,7,6,5,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [3,4,7,6,5,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [3,5,4,2,1,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [3,5,4,2,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [3,5,4,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [3,5,6,7,4,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [3,5,7,6,4,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [3,6,5,4,2,1,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,3,2,1,5,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [4,3,2,1,6,7,5] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,3,2,1,6,7,5] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,3,2,1,6,7,5] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [4,3,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [4,3,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,3,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [4,3,2,5,1,7,6] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,3,2,5,6,1,7] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [4,3,2,7,6,5,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [4,3,2,7,6,5,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [4,3,5,2,1,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [4,3,5,2,6,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [4,3,5,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [4,3,5,6,2,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [4,3,6,5,2,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [4,3,6,5,2,7,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [4,3,6,5,7,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [4,3,6,5,7,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [4,5,3,2,1,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [4,5,3,2,6,1,7] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [4,5,3,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [4,5,3,6,2,1,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [4,5,6,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,7,6] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,7,6] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [5,4,3,2,6,1,7] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [5,4,3,2,6,7,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [5,4,3,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [5,4,3,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [5,4,3,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [5,4,3,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [5,4,3,6,2,1,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [5,6,4,3,2,1,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,6,7,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,7] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
3,2 4,8,2 5,20,15,2 6,40,60,24,2 7,70,175,140,35,2
$F_{2} = 2\ q$
$F_{3} = 3\ q + 2\ q^{2}$
$F_{4} = 4\ q + 8\ q^{2} + 2\ q^{3}$
$F_{5} = 5\ q + 20\ q^{2} + 15\ q^{3} + 2\ q^{4}$
$F_{6} = 6\ q + 40\ q^{2} + 60\ q^{3} + 24\ q^{4} + 2\ q^{5}$
$F_{7} = 7\ q + 70\ q^{2} + 175\ q^{3} + 140\ q^{4} + 35\ q^{5} + 2\ q^{6}$
Description
The upper domination number of a graph.
This is the maximum cardinality of a minimal dominating set of $G$.
The smallest graph with different upper irredundance number and upper domination number has eight vertices. It is obtained from the disjoint union of two copies of $K_4$ by joining three of the four vertices of the first with three of the four vertices of the second. For bipartite graphs the two parameters always coincide [1].
This is the maximum cardinality of a minimal dominating set of $G$.
The smallest graph with different upper irredundance number and upper domination number has eight vertices. It is obtained from the disjoint union of two copies of $K_4$ by joining three of the four vertices of the first with three of the four vertices of the second. For bipartite graphs the two parameters always coincide [1].
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to 312-avoiding permutation
Description
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
This map is undefined for the empty permutation.
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