- FindStat

Identifier

Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ 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] => [2,3,1] => ([(1,2)],3) => ([(0,1)],2) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,0,1,0,1,0,0] => [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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,1,0,1,0,0,0] => [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

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

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

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

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

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

[1,1,1,1,1,0,0,0,0,0] => [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] => [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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 817 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,0,1,0,1,0,1,0,0] => [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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,1,0,1,0,1,0,0,0] => [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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,1,0,1,0,0,0,0] => [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

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

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

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

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

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

[1,1,1,1,1,0,1,0,0,0,0,0] => [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

[1,1,1,1,1,1,0,0,0,0,0,0] => [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] => [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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => ([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7) => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 5

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => ([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 5

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 5

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

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

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => ([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 5

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

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

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

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

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

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

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

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => 5

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => ([(0,5),(1,3),(3,6),(4,2),(5,4),(5,6)],7) => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => 5

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

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => ([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7) => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 5

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => ([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7) => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10) => 5

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => 5

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 5

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

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

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

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => 5

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => ([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7) => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => ([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => ([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

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

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

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

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

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 5

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => ([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7) => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 5

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 5

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => ([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => 5

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11) => 5

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => 5

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

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

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => ([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7) => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 5

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => ([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => 5

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

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

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

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

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

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

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

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

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => ([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7) => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 5

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

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

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => 5

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => ([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7) => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10) => 5

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => ([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 5

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 5

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 5

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 5

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

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => ([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 5

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => ([(0,5),(1,3),(3,6),(4,2),(5,4),(5,6)],7) => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10) => 5

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => 5

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [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

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 5

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

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

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

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

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

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

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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

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

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

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

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

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

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [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

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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] => [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

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

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

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

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

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

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

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

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

[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => ([(0,6),(0,7),(1,5),(2,6),(5,2),(5,7),(6,3),(7,4)],8) => ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => ([(0,6),(0,7),(1,5),(1,7),(2,6),(3,4),(4,2),(5,3)],8) => ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10) => 6

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

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

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

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

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

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

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

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

[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => ([(0,3),(0,7),(1,6),(1,7),(2,6),(3,2),(3,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => 6

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

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

[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => ([(0,2),(0,7),(1,5),(1,7),(2,3),(2,6),(3,4),(3,5),(6,4),(7,6)],8) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => 6

[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => 6

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

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

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

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,4),(6,5),(7,2)],8) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8) => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9) => 6

[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(3,5),(4,5),(6,3),(7,4)],8) => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9) => 6

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => ([(0,7),(1,6),(1,7),(4,5),(5,2),(6,4),(7,3)],8) => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => 6

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

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

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

[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8) => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 5

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

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

[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => ([(0,7),(1,4),(1,7),(3,6),(4,3),(5,2),(5,6),(7,5)],8) => ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10) => 6

[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,4),(6,5),(7,2)],8) => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 5

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

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

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

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

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

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

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

[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => 6

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

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

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

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

[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => ([(0,4),(0,5),(1,6),(4,6),(4,7),(5,1),(5,7),(6,2),(7,3)],8) => ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 6

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

[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => ([(0,3),(0,5),(2,6),(3,6),(3,7),(4,1),(5,2),(5,7),(7,4)],8) => ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 6

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

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

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

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

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => ([(0,5),(1,3),(1,7),(2,7),(3,6),(4,2),(5,4),(7,6)],8) => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10) => 6

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,3),(0,6),(2,10),(3,7),(4,5),(4,9),(5,2),(5,8),(6,4),(6,7),(7,9),(8,10),(9,8),(10,1)],11) => 6

[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => ([(0,5),(1,3),(2,6),(3,6),(3,7),(4,2),(4,7),(5,4)],8) => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10) => 6

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

[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => ([(0,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6),(7,2)],8) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => 6

[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => 6

[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => ([(0,4),(0,7),(1,5),(3,7),(4,6),(5,3),(5,6),(7,2)],8) => ([(0,4),(0,6),(1,10),(2,9),(3,8),(4,7),(5,2),(5,8),(6,1),(6,7),(7,10),(8,9),(10,3),(10,5)],11) => 6

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

[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => ([(0,5),(1,4),(1,6),(3,6),(4,7),(5,3),(5,7),(7,2)],8) => ([(0,4),(0,6),(1,10),(2,9),(3,8),(4,7),(5,2),(5,8),(6,1),(6,7),(7,10),(8,9),(10,3),(10,5)],11) => 6

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

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

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

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

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

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

[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,5),(3,7),(4,2),(6,5)],8) => ([(0,5),(0,6),(1,10),(3,7),(4,8),(5,9),(6,1),(6,9),(7,8),(8,2),(9,3),(9,10),(10,4),(10,7)],11) => 6

[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,7),(4,2),(6,5),(7,5)],8) => ([(0,5),(0,6),(1,10),(3,7),(4,8),(5,9),(6,1),(6,9),(7,8),(8,2),(9,3),(9,10),(10,4),(10,7)],11) => 6

[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8) => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10) => 6

[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => ([(0,4),(0,6),(1,3),(1,7),(3,6),(4,5),(4,7),(6,5),(7,2)],8) => ([(0,4),(0,5),(1,8),(2,10),(3,7),(4,9),(5,9),(6,3),(6,10),(7,8),(9,2),(9,6),(10,1),(10,7)],11) => 6

[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10) => 6

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

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

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

[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(3,5),(4,5),(6,3),(7,4)],8) => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9) => 6

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

[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8) => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9) => 6

[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => ([(0,4),(0,6),(1,3),(1,7),(3,6),(4,5),(4,7),(6,5),(7,2)],8) => ([(0,4),(0,5),(1,8),(2,10),(3,7),(4,9),(5,9),(6,3),(6,10),(7,8),(9,2),(9,6),(10,1),(10,7)],11) => 6

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

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

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

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

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

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

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

[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => ([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8) => ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10) => 6

[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => ([(0,4),(0,5),(1,7),(2,6),(2,7),(3,1),(3,6),(4,2),(5,3)],8) => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9) => 6

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

[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => ([(0,3),(0,5),(2,6),(3,6),(3,7),(4,1),(5,2),(5,7),(7,4)],8) => ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 6

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

[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => ([(0,4),(0,5),(1,6),(2,7),(3,2),(4,3),(4,6),(5,1),(5,7)],8) => ([(0,6),(1,8),(2,9),(3,10),(4,7),(5,3),(5,9),(6,2),(6,5),(7,8),(9,4),(9,10),(10,1),(10,7)],11) => 6

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

[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => ([(0,4),(0,5),(1,6),(4,6),(4,7),(5,1),(5,7),(6,2),(7,3)],8) => ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 6

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

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

[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => ([(0,7),(1,4),(1,7),(3,6),(4,3),(5,2),(5,6),(7,5)],8) => ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10) => 6

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

[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,5),(6,7),(7,2)],8) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9) => 6

[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10) => 6

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => ([(0,5),(1,6),(3,7),(4,3),(5,4),(6,2),(6,7)],8) => ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13) => 6

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13) => 6

[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => 5

[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => 6

[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => ([(0,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6),(7,2)],8) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => 6

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

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

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

[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => ([(0,2),(0,7),(1,5),(1,7),(2,3),(2,6),(3,4),(3,5),(6,4),(7,6)],8) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => 6

[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => ([(0,3),(0,7),(1,6),(1,7),(2,6),(3,2),(3,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => 6

[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => ([(0,5),(1,4),(1,6),(3,6),(4,7),(5,3),(5,7),(7,2)],8) => ([(0,4),(0,6),(1,10),(2,9),(3,8),(4,7),(5,2),(5,8),(6,1),(6,7),(7,10),(8,9),(10,3),(10,5)],11) => 6

[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,7),(4,2),(6,5),(7,5)],8) => ([(0,5),(0,6),(1,10),(3,7),(4,8),(5,9),(6,1),(6,9),(7,8),(8,2),(9,3),(9,10),(10,4),(10,7)],11) => 6

[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,5),(3,7),(4,2),(6,5)],8) => ([(0,5),(0,6),(1,10),(3,7),(4,8),(5,9),(6,1),(6,9),(7,8),(8,2),(9,3),(9,10),(10,4),(10,7)],11) => 6

[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => ([(0,6),(0,7),(1,5),(2,6),(5,2),(5,7),(6,3),(7,4)],8) => ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 6

[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => ([(0,4),(0,7),(1,5),(3,7),(4,6),(5,3),(5,6),(7,2)],8) => ([(0,4),(0,6),(1,10),(2,9),(3,8),(4,7),(5,2),(5,8),(6,1),(6,7),(7,10),(8,9),(10,3),(10,5)],11) => 6

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

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

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

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

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

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

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

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => 6

[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11) => 6

[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => ([(0,4),(0,5),(1,7),(2,6),(2,7),(3,1),(3,6),(4,2),(5,3)],8) => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9) => 6

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

[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => ([(0,4),(0,5),(1,6),(2,7),(3,2),(4,3),(4,6),(5,1),(5,7)],8) => ([(0,6),(1,8),(2,9),(3,10),(4,7),(5,3),(5,9),(6,2),(6,5),(7,8),(9,4),(9,10),(10,1),(10,7)],11) => 6

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => 6

[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => ([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8) => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9) => 6

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13) => 6

[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => ([(0,5),(1,3),(2,6),(3,6),(3,7),(4,2),(4,7),(5,4)],8) => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10) => 6

[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => ([(0,5),(1,6),(3,7),(4,3),(5,4),(6,2),(6,7)],8) => ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13) => 6

[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => ([(0,6),(0,7),(1,4),(1,7),(2,6),(3,2),(4,3),(4,5),(7,5)],8) => ([(0,6),(1,8),(2,9),(3,10),(4,7),(5,3),(5,9),(6,2),(6,5),(7,8),(9,4),(9,10),(10,1),(10,7)],11) => 6

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => ([(0,5),(1,3),(1,7),(2,7),(3,6),(4,2),(5,4),(7,6)],8) => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10) => 6

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

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

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => 6

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => 6

[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => ([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8) => ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10) => 6

[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => ([(0,7),(1,6),(1,7),(4,5),(5,2),(6,4),(7,3)],8) => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => 6

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,3),(0,6),(2,10),(3,7),(4,5),(4,9),(5,2),(5,8),(6,4),(6,7),(7,9),(8,10),(9,8),(10,1)],11) => 6

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

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => ([(0,6),(0,7),(1,5),(1,7),(2,6),(3,4),(4,2),(5,3)],8) => ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10) => 6

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

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

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

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [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

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9) => ([(0,3),(0,7),(1,9),(3,8),(4,6),(4,10),(5,4),(5,12),(6,1),(6,11),(7,5),(7,8),(8,12),(9,2),(10,11),(11,9),(12,10)],13) => 7

[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9) => ([(0,6),(0,7),(2,5),(2,15),(3,12),(4,11),(5,4),(5,13),(6,2),(6,14),(7,3),(7,14),(8,1),(9,10),(10,8),(11,8),(12,9),(13,10),(13,11),(14,12),(14,15),(15,9),(15,13)],16) => 7

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [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) => ([(0,6),(0,7),(2,5),(2,16),(3,4),(3,15),(4,9),(5,10),(6,3),(6,14),(7,2),(7,14),(8,1),(9,11),(10,12),(11,8),(12,8),(13,11),(13,12),(14,15),(14,16),(15,9),(15,13),(16,10),(16,13)],17) => 7

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9) => ([(0,6),(0,7),(2,5),(2,15),(3,12),(4,11),(5,4),(5,13),(6,2),(6,14),(7,3),(7,14),(8,1),(9,10),(10,8),(11,8),(12,9),(13,10),(13,11),(14,12),(14,15),(15,9),(15,13)],16) => 7

[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7,9] => ([(0,6),(1,3),(1,8),(2,8),(3,7),(4,5),(5,2),(6,4),(8,7)],9) => ([(0,3),(0,7),(2,11),(3,8),(4,1),(5,6),(5,10),(6,2),(6,9),(7,5),(7,8),(8,10),(9,11),(10,9),(11,4)],12) => 7

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9) => ([(0,3),(0,7),(1,9),(3,8),(4,6),(4,10),(5,4),(5,12),(6,1),(6,11),(7,5),(7,8),(8,12),(9,2),(10,11),(11,9),(12,10)],13) => 7

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

[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 7

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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

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

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 8

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 7

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 8

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5

[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

[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [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) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 8

[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 8

[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => ([(0,8),(1,4),(1,8),(2,3),(2,7),(3,5),(4,2),(4,6),(6,7),(7,5),(8,6)],9) => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => 7

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => 7

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => ([(0,8),(1,4),(1,8),(2,3),(2,7),(3,5),(4,2),(4,6),(6,7),(7,5),(8,6)],9) => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => 7

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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 $x,y\in L$.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$

Map

maximal antichains

Description

The lattice of maximal antichains in a poset.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains 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 $A$.

Map

to 321-avoiding permutation (Billey-Jockusch-Stanley)

Description

The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.