Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001622: Lattices ⟶ ℤ
Values
[1,0] => [1] => ([],1) => ([],1) => 0
[1,0,1,0] => [2,1] => ([],2) => ([],1) => 0
[1,1,0,0] => [1,2] => ([(0,1)],2) => ([(0,1)],2) => 1
[1,0,1,0,1,0] => [3,2,1] => ([],3) => ([],1) => 0
[1,0,1,1,0,0] => [2,3,1] => ([(1,2)],3) => ([(0,1)],2) => 1
[1,1,0,0,1,0] => [3,1,2] => ([(1,2)],3) => ([(0,1)],2) => 1
[1,1,0,1,0,0] => [2,1,3] => ([(0,2),(1,2)],3) => ([],1) => 0
[1,1,1,0,0,0] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,0,1,0] => [4,3,2,1] => ([],4) => ([],1) => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => ([(2,3)],4) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => ([(2,3)],4) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => ([(1,3),(2,3)],4) => ([],1) => 0
[1,0,1,1,1,0,0,0] => [2,3,4,1] => ([(1,2),(2,3)],4) => ([(0,2),(2,1)],3) => 2
[1,1,0,0,1,0,1,0] => [4,3,1,2] => ([(2,3)],4) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => ([(1,3),(2,3)],4) => ([],1) => 0
[1,1,0,1,0,1,0,0] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => ([],1) => 0
[1,1,0,1,1,0,0,0] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => ([(1,2),(2,3)],4) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,1,0,0] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([],1) => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => ([],5) => ([],1) => 0
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => ([(3,4)],5) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => ([(3,4)],5) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => ([],1) => 0
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => ([(3,4)],5) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => ([],1) => 0
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => ([],1) => 0
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => ([(3,4)],5) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => ([],1) => 0
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([],1) => 0
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([],1) => 0
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([],1) => 0
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([],1) => 0
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,1)],2) => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([],1) => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => ([],6) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => ([(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => ([(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => ([],1) => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => ([(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => ([],1) => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => ([],1) => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => ([],1) => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => ([(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => ([],1) => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([],1) => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => ([],1) => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => ([],1) => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
>>> Load all 902 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => ([],1) => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => ([(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => ([],1) => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([],1) => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => ([],1) => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],1) => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([],1) => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([],1) => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => ([],1) => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([],1) => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => ([],1) => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([],1) => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([],1) => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([],1) => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => ([],1) => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([],1) => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([],1) => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([],1) => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,1)],2) => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([],1) => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => ([],7) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => ([(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => ([(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => ([(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => ([(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => ([(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => ([(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => ([(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => ([(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => ([(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => ([],1) => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => ([(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([],1) => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => ([(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([],1) => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => ([(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([],1) => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => ([(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => ([(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => ([(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => ([(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => ([],1) => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => ([],1) => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => ([],1) => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => ([(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12) => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12) => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => ([(0,6),(1,3),(2,4),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => ([(0,6),(1,3),(2,4),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([],1) => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => ([(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([],1) => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([],1) => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => ([],1) => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([],1) => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([],1) => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([],1) => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([],1) => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([],1) => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12) => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => ([(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => ([],1) => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => ([],1) => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => ([(2,6),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([],1) => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => ([(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => ([(0,6),(1,3),(2,4),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([],1) => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([],1) => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => ([(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => ([(0,6),(1,3),(2,4),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => ([(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => ([(2,6),(3,6),(4,5),(6,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([],1) => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([],1) => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => ([],1) => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([],1) => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => ([],1) => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([],1) => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([],1) => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([],1) => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => ([],1) => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => ([],1) => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => ([],8) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => ([(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => ([(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => ([(4,5),(5,7),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => ([(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => ([(4,5),(5,7),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => ([(3,4),(4,7),(6,5),(7,6)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => ([(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => ([],1) => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => ([(2,7),(3,6),(4,6),(5,7),(6,5)],8) => ([],1) => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => ([(4,5),(5,7),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => ([(3,4),(4,7),(6,5),(7,6)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => ([(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => ([],1) => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => ([],1) => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => ([],1) => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => ([(2,7),(3,6),(4,6),(5,7),(6,5)],8) => ([],1) => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => ([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => ([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => ([],1) => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => ([(4,5),(5,7),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => ([(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => ([(3,4),(4,7),(6,5),(7,6)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => ([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => ([(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16) => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => ([(0,7),(1,7),(2,5),(3,4),(7,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8) => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16) => 5
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => ([(0,7),(1,7),(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => ([(0,7),(1,6),(2,4),(3,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => ([(0,7),(1,7),(2,5),(3,4),(7,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => ([(0,7),(1,5),(2,6),(3,7),(6,3),(7,4)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8) => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16) => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => ([(0,7),(1,7),(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => ([(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => ([(0,7),(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => ([(0,7),(1,6),(2,4),(3,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => ([(0,7),(1,5),(2,6),(3,7),(6,3),(7,4)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => ([(0,7),(1,7),(2,4),(5,3),(6,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => ([(5,7),(6,7)],8) => ([],1) => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => ([(2,7),(3,7),(4,6),(5,6)],8) => ([],1) => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => ([(0,7),(1,7),(2,6),(4,5),(5,3),(6,4)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => ([],1) => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([],1) => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => ([(0,7),(1,7),(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([],1) => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => ([],1) => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => ([(0,7),(1,7),(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => ([(0,7),(1,6),(2,4),(3,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => ([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => ([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => ([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => ([(2,7),(3,7),(4,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => ([(0,7),(1,7),(2,5),(3,4),(7,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => ([(0,6),(1,6),(2,7),(3,7),(6,5),(7,4)],8) => ([],1) => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => ([(0,7),(1,7),(2,6),(5,3),(6,5),(7,4)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => ([(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7)],8) => ([(0,1)],2) => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => ([],1) => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([],1) => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([],1) => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => ([],1) => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => ([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => ([(0,7),(1,5),(2,6),(3,7),(6,3),(7,4)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => ([(4,5),(5,7),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => ([(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8) => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16) => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => ([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => ([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => ([(0,7),(1,7),(2,6),(5,3),(6,5),(7,4)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => ([(0,7),(1,7),(2,4),(3,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => ([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => ([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => ([(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => ([(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => ([(2,7),(3,6),(4,6),(5,7),(6,5)],8) => ([],1) => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => ([(0,7),(1,6),(2,6),(3,4),(5,7),(6,5)],8) => ([(0,1)],2) => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([],1) => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => ([(0,7),(1,7),(2,7),(3,4),(5,6),(7,5)],8) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => ([(3,4),(4,7),(6,5),(7,6)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => ([(0,7),(1,7),(2,6),(4,5),(5,3),(6,4)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => ([(0,7),(1,6),(2,4),(3,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => ([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => ([(0,7),(1,5),(2,6),(3,7),(6,3),(7,4)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => ([(0,7),(1,7),(2,4),(5,3),(6,5),(7,6)],8) => ([(0,1)],2) => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8) => ([],1) => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 7
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([],1) => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9) => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([],1) => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 9
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 7
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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:
1,1 2,2,1 5,5,3,1 13,15,9,4,1 35,46,31,14,5,1 97,143,108,54,20,6,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 2 + 2\ q + q^{2}$
$F_{4} = 5 + 5\ q + 3\ q^{2} + q^{3}$
$F_{5} = 13 + 15\ q + 9\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 35 + 46\ q + 31\ q^{2} + 14\ q^{3} + 5\ q^{4} + q^{5}$
$F_{7} = 97 + 143\ q + 108\ q^{2} + 54\ q^{3} + 20\ q^{4} + 6\ q^{5} + q^{6}$
Description
The number of join-irreducible elements of a lattice.
An element $j$ of a lattice $L$ is join irreducible if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.
An element $j$ of a lattice $L$ is join irreducible if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
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