Identifier
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
[1,0] => [1] => [1] => ([],1)
[1,0,1,0] => [1,2] => [2,1] => ([],2)
[1,1,0,0] => [2,1] => [1,2] => ([(0,1)],2)
[1,0,1,0,1,0] => [1,2,3] => [2,3,1] => ([(1,2)],3)
[1,0,1,1,0,0] => [1,3,2] => [3,2,1] => ([],3)
[1,1,0,0,1,0] => [2,1,3] => [1,3,2] => ([(0,1),(0,2)],3)
[1,1,0,1,0,0] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
[1,1,1,0,0,0] => [3,2,1] => [2,1,3] => ([(0,2),(1,2)],3)
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,4,3,1] => ([(1,2),(1,3)],4)
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [4,2,3,1] => ([(2,3)],4)
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,2,1] => ([],4)
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [5,3,4,2,1] => ([(3,4)],5)
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,2,1] => ([],5)
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => ([(1,4),(4,5),(5,2),(5,3)],6)
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => ([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => ([(1,5),(4,3),(5,2),(5,4)],6)
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => ([(1,5),(5,2),(5,3),(5,4)],6)
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => ([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [2,6,3,5,4,1] => ([(1,4),(1,5),(5,2),(5,3)],6)
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [2,6,4,3,5,1] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [2,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(5,2)],6)
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6)
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => ([(1,5),(2,5),(5,3),(5,4)],6)
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6)
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,2,3,5,4,1] => ([(2,3),(3,4),(3,5)],6)
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,2,4,3,6,1] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [6,2,4,3,5,1] => ([(2,3),(2,4),(3,5),(4,5)],6)
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [6,2,4,5,3,1] => ([(2,3),(2,4),(4,5)],6)
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,2,5,4,3,1] => ([(2,3),(2,4),(2,5)],6)
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6)
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6)
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6)
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6)
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6)
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(3,4),(3,5)],6)
>>> Load all 1856 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6)
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [6,5,3,4,2,1] => ([(4,5)],6)
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([],6)
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,3,5,4,6,2] => ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,3,6,4,5,2] => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,6,3,5,4,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,6,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [1,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,2,5,4,6,3] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,2,6,5,4,3] => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,2,3,6,5,4] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,3,2,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,3,2,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,3,2,4,6,5] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [1,3,4,2,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,4,3,2,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,1,4,6,5,3] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,1,5,4,6,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,1,6,4,5,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [2,1,3,6,5,4] => ([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [2,1,3,5,4,6] => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [2,1,4,3,5,6] => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,1,5,4,3,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,3,1,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,3,5,4,1,6] => ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,4,3,1,6,5] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [2,4,3,1,5,6] => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,4,3,5,1,6] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [2,5,3,4,1,6] => ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,5,4,3,1,6] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,2,1,5,6,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [3,2,1,6,5,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,1,4,6,5] => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,1,5,4,6] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,2,4,1,6,5] => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [3,2,5,4,1,6] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [4,2,3,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [5,2,4,3,1,6] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [2,3,4,5,7,6,1] => ([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,3,4,6,5,7,1] => ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [2,3,4,7,5,6,1] => ([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [2,3,4,7,6,5,1] => ([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,3,5,4,6,7,1] => ([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,3,5,4,7,6,1] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [2,3,6,4,5,7,1] => ([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [2,3,7,4,5,6,1] => ([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [2,3,7,4,6,5,1] => ([(1,6),(5,3),(5,4),(6,2),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [2,3,6,5,4,7,1] => ([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [2,3,7,5,4,6,1] => ([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [2,3,7,5,6,4,1] => ([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [2,3,7,6,5,4,1] => ([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,4,3,5,6,7,1] => ([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,4,3,5,7,6,1] => ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,4,3,6,5,7,1] => ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [2,4,3,7,5,6,1] => ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [2,4,3,7,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [2,5,3,4,6,7,1] => ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [2,5,3,4,7,6,1] => ([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [2,6,3,4,5,7,1] => ([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [2,7,3,4,5,6,1] => ([(1,3),(1,6),(4,5),(5,2),(6,4)],7)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [2,7,3,4,6,5,1] => ([(1,4),(1,5),(5,6),(6,2),(6,3)],7)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [2,6,3,5,4,7,1] => ([(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [2,7,3,5,4,6,1] => ([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [2,7,3,5,6,4,1] => ([(1,4),(1,6),(5,3),(6,2),(6,5)],7)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [2,7,3,6,5,4,1] => ([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [2,5,4,3,6,7,1] => ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [2,5,4,3,7,6,1] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [2,6,4,3,5,7,1] => ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [2,7,4,3,5,6,1] => ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [2,7,4,3,6,5,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [2,6,4,5,3,7,1] => ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [2,7,4,5,3,6,1] => ([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [2,7,4,5,6,3,1] => ([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [2,7,4,6,5,3,1] => ([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [2,6,5,4,3,7,1] => ([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [2,7,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [2,7,5,4,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [2,7,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [2,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,2,4,5,7,6,1] => ([(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [3,2,4,6,5,7,1] => ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,2,4,7,5,6,1] => ([(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [3,2,4,7,6,5,1] => ([(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [3,2,5,4,6,7,1] => ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [3,2,5,4,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,2,6,4,5,7,1] => ([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [3,2,7,4,5,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [3,2,7,4,6,5,1] => ([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [3,2,6,5,4,7,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [3,2,7,5,4,6,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [3,2,7,5,6,4,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [3,2,7,6,5,4,1] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [4,2,3,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [4,2,3,5,7,6,1] => ([(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [4,2,3,6,5,7,1] => ([(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [4,2,3,7,5,6,1] => ([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [4,2,3,7,6,5,1] => ([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [5,2,3,4,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [5,2,3,4,7,6,1] => ([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [7,2,3,4,5,6,1] => ([(2,6),(4,5),(5,3),(6,4)],7)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,2,3,4,6,5,1] => ([(2,5),(5,6),(6,3),(6,4)],7)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,2,3,5,4,7,1] => ([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [7,2,3,5,4,6,1] => ([(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [7,2,3,5,6,4,1] => ([(2,6),(5,4),(6,3),(6,5)],7)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,2,3,6,5,4,1] => ([(2,6),(6,3),(6,4),(6,5)],7)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,2,4,3,6,7,1] => ([(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [5,2,4,3,7,6,1] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [6,2,4,3,5,7,1] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [7,2,4,3,5,6,1] => ([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [7,2,4,3,6,5,1] => ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [6,2,4,5,3,7,1] => ([(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [7,2,4,5,3,6,1] => ([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [7,2,4,5,6,3,1] => ([(2,4),(2,6),(5,3),(6,5)],7)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [7,2,4,6,5,3,1] => ([(2,5),(2,6),(6,3),(6,4)],7)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,2,5,4,3,7,1] => ([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [7,2,5,4,3,6,1] => ([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [7,2,5,4,6,3,1] => ([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [7,2,6,4,5,3,1] => ([(2,4),(2,5),(2,6),(6,3)],7)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,2,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,3,2,5,7,6,1] => ([(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,3,2,6,5,7,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,3,2,7,5,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [4,3,2,7,6,5,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [5,3,2,4,7,6,1] => ([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [7,3,2,4,6,5,1] => ([(2,6),(3,6),(6,4),(6,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [6,3,2,5,4,7,1] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [7,3,2,5,4,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [7,3,2,5,6,4,1] => ([(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,3,2,6,5,4,1] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [5,3,4,2,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [6,3,4,2,5,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [7,3,4,2,5,6,1] => ([(2,6),(3,4),(4,6),(6,5)],7)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [7,3,4,2,6,5,1] => ([(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [7,3,4,5,2,6,1] => ([(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [7,3,4,6,5,2,1] => ([(3,4),(4,5),(4,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [6,3,5,4,2,7,1] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [7,3,5,4,2,6,1] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [7,3,5,4,6,2,1] => ([(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [7,3,6,4,5,2,1] => ([(3,4),(3,5),(5,6)],7)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [7,3,6,5,4,2,1] => ([(3,4),(3,5),(3,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [5,4,3,2,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [7,4,3,2,6,5,1] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [7,4,3,6,5,2,1] => ([(3,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [7,5,3,4,6,2,1] => ([(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [7,6,3,5,4,2,1] => ([(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [7,6,4,5,3,2,1] => ([(5,6)],7)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,2,1] => ([],7)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,3,4,5,7,6,2] => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,3,4,6,5,7,2] => ([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,3,4,7,5,6,2] => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [1,3,4,7,6,5,2] => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,3,5,4,6,7,2] => ([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,3,5,4,7,6,2] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,3,6,4,5,7,2] => ([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,3,7,4,5,6,2] => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [1,3,7,4,6,5,2] => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [1,3,6,5,4,7,2] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [1,3,7,5,4,6,2] => ([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [1,3,7,5,6,4,2] => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [1,3,7,6,5,4,2] => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => ([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => ([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [1,4,3,7,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,5,3,4,6,7,2] => ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,5,3,4,7,6,2] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(3,5),(3,6),(4,1)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,6,3,4,5,7,2] => ([(0,2),(0,3),(0,5),(1,6),(3,6),(4,1),(5,4)],7)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,7,3,4,5,6,2] => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [1,7,3,4,6,5,2] => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [1,6,3,5,4,7,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [1,7,3,5,4,6,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [1,7,3,5,6,4,2] => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [1,7,3,6,5,4,2] => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [1,5,4,3,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [1,5,4,3,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [1,6,4,3,5,7,2] => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [1,7,4,3,5,6,2] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [1,7,4,3,6,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [1,6,4,5,3,7,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [1,7,4,5,3,6,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [1,7,4,5,6,3,2] => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [1,7,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [1,6,5,4,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [1,7,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [1,7,5,4,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [1,7,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [1,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [1,2,4,6,5,7,3] => ([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [1,2,4,7,5,6,3] => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [1,2,4,7,6,5,3] => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [1,2,5,4,6,7,3] => ([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [1,2,5,4,7,6,3] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [1,2,6,4,5,7,3] => ([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [1,2,7,4,5,6,3] => ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [1,2,7,4,6,5,3] => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [1,2,6,5,4,7,3] => ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [1,2,7,5,4,6,3] => ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [1,2,7,5,6,4,3] => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [1,2,7,6,5,4,3] => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [1,2,3,5,7,6,4] => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [1,2,3,6,5,7,4] => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [1,2,3,7,5,6,4] => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [1,2,3,7,6,5,4] => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [1,2,3,4,7,6,5] => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [1,2,3,5,4,7,6] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [1,2,3,6,5,4,7] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [1,2,4,3,6,7,5] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [1,2,4,3,7,6,5] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [1,2,4,3,5,7,6] => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [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)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [1,2,4,5,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [1,2,4,6,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [1,2,5,4,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [1,2,5,4,3,6,7] => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [1,2,5,4,6,3,7] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [1,2,6,4,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [1,2,6,5,4,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [1,3,2,5,6,7,4] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [1,3,2,5,7,6,4] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [1,3,2,6,5,7,4] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [1,3,2,7,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [1,3,2,7,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [1,3,2,4,6,7,5] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [1,3,2,4,7,6,5] => ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [1,3,2,4,5,7,6] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [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)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [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)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [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)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [1,3,2,6,5,4,7] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [1,3,4,2,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [1,3,4,2,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [1,3,4,2,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [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)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [1,3,4,5,2,7,6] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [1,3,4,6,5,2,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [1,3,5,4,2,7,6] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [1,3,5,4,2,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [1,3,5,4,6,2,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [1,3,6,4,5,2,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [1,3,6,5,4,2,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [1,4,3,2,6,7,5] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [1,4,3,2,7,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [1,4,3,2,5,7,6] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [1,4,3,2,5,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [1,4,3,2,6,5,7] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [1,4,3,5,2,7,6] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [1,4,3,5,2,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [1,4,3,5,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [1,4,3,6,5,2,7] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [1,5,3,4,2,7,6] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [1,5,3,4,2,6,7] => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [1,5,3,4,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [1,6,3,4,5,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [1,6,3,5,4,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [1,5,4,3,2,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [1,5,4,3,2,6,7] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [1,5,4,3,6,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [1,6,4,3,5,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [1,6,4,5,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,1,4,5,6,7,3] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,1,4,5,7,6,3] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,1,4,6,5,7,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,1,4,7,5,6,3] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,1,4,7,6,5,3] => ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,1,5,4,6,7,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(5,3),(6,3)],7)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,1,5,4,7,6,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,1,6,4,5,7,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(5,2),(6,3)],7)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,1,7,4,5,6,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(6,2)],7)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,1,7,4,6,5,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,1,6,5,4,7,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,1,7,5,4,6,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,1,7,5,6,4,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,1,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [2,1,3,5,6,7,4] => ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [2,1,3,5,7,6,4] => ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [2,1,3,6,5,7,4] => ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [2,1,3,7,5,6,4] => ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [2,1,3,7,6,5,4] => ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [2,1,3,4,6,7,5] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [2,1,3,4,7,6,5] => ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [2,1,3,4,5,7,6] => ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [2,1,3,4,6,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [2,1,3,5,4,7,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [2,1,3,5,4,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [2,1,3,5,6,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [2,1,3,6,5,4,7] => ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [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)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [2,1,4,3,7,6,5] => ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [2,1,4,3,5,7,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [2,1,4,3,5,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [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)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [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)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [2,1,4,5,3,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [2,1,4,5,6,3,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [2,1,4,6,5,3,7] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [2,1,5,4,3,7,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [2,1,5,4,3,6,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [2,1,5,4,6,3,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [2,1,6,4,5,3,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [2,1,6,5,4,3,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,3,1,5,6,7,4] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,3,1,5,7,6,4] => ([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,3,1,6,5,7,4] => ([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [2,3,1,7,5,6,4] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [2,3,1,7,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,3,1,4,6,7,5] => ([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [2,3,1,4,7,6,5] => ([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,3,1,4,5,7,6] => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [2,3,1,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [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)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [2,3,1,5,4,6,7] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,3,1,5,6,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [2,3,1,6,5,4,7] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,3,4,1,7,6,5] => ([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,4,1,5,7,6] => ([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [2,3,4,1,6,5,7] => ([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,5,1,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [2,3,4,6,5,1,7] => ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [2,3,5,4,1,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [2,3,5,4,1,6,7] => ([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,3,5,4,6,1,7] => ([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [2,3,6,4,5,1,7] => ([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [2,3,6,5,4,1,7] => ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [2,4,3,1,6,7,5] => ([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [2,4,3,1,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [2,4,3,1,5,7,6] => ([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [2,4,3,1,5,6,7] => ([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [2,4,3,1,6,5,7] => ([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,4,3,5,1,7,6] => ([(0,2),(0,3),(1,4),(1,5),(2,6),(3,6),(6,4),(6,5)],7)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,4,3,5,1,6,7] => ([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,3,5,6,1,7] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [2,4,3,6,5,1,7] => ([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [2,5,3,4,1,7,6] => ([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [2,5,3,4,1,6,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [2,5,3,4,6,1,7] => ([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [2,6,3,4,5,1,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [2,6,3,5,4,1,7] => ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,5,4,3,1,7,6] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [2,5,4,3,1,6,7] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [2,5,4,3,6,1,7] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [2,6,4,3,5,1,7] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [2,6,4,5,3,1,7] => ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,6,5,4,3,1,7] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [3,2,1,5,6,7,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [3,2,1,5,7,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [3,2,1,6,5,7,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,1,7,5,6,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [3,2,1,7,6,5,4] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,1,4,6,7,5] => ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,1,4,7,6,5] => ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [3,2,1,4,5,7,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [3,2,1,4,6,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,1,5,4,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [3,2,1,5,4,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,1,5,6,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [3,2,1,6,5,4,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,2,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [3,2,4,1,7,6,5] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,4,1,5,7,6] => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,4,1,6,5,7] => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,4,5,1,7,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [3,2,4,6,5,1,7] => ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [3,2,5,4,1,7,6] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,5,4,1,6,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,2,5,4,6,1,7] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,6,4,5,1,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [3,2,6,5,4,1,7] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,2,3,1,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [4,2,3,1,7,6,5] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,2,3,1,5,7,6] => ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [4,2,3,1,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,2,3,5,1,7,6] => ([(0,6),(1,4),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,2,3,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [4,2,3,6,5,1,7] => ([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [5,2,3,4,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [6,2,3,5,4,1,7] => ([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [5,2,4,3,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [5,2,4,3,1,6,7] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [5,2,4,3,6,1,7] => ([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [6,2,4,3,5,1,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [6,2,4,5,3,1,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [6,2,5,4,3,1,7] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [4,3,2,1,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [4,3,2,1,7,6,5] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [4,3,2,1,5,7,6] => ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [4,3,2,1,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [4,3,2,5,1,7,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [4,3,2,6,5,1,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [5,3,2,4,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [6,3,2,5,4,1,7] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [5,3,4,2,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [5,4,3,2,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,1] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,8,7,1] => ([(1,6),(4,5),(5,7),(6,4),(7,2),(7,3)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,3,4,5,7,6,8,1] => ([(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [2,3,4,5,8,6,7,1] => ([(1,6),(4,7),(5,2),(6,4),(7,3),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [2,3,4,5,8,7,6,1] => ([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,3,4,6,5,7,8,1] => ([(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,3,4,6,5,8,7,1] => ([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [2,3,4,7,5,6,8,1] => ([(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [2,3,4,8,5,6,7,1] => ([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [2,3,4,8,5,7,6,1] => ([(1,5),(5,7),(6,3),(6,4),(7,2),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [2,3,4,7,6,5,8,1] => ([(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [2,3,4,8,6,5,7,1] => ([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [2,3,4,8,6,7,5,1] => ([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [2,3,4,8,7,6,5,1] => ([(1,6),(6,7),(7,2),(7,3),(7,4),(7,5)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,3,5,4,6,7,8,1] => ([(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [2,3,5,4,7,6,8,1] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [2,3,5,4,8,6,7,1] => ([(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4),(7,2)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [2,3,5,4,8,7,6,1] => ([(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [2,3,6,4,5,7,8,1] => ([(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [2,3,6,4,5,8,7,1] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [2,3,7,4,5,6,8,1] => ([(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [2,3,8,4,5,6,7,1] => ([(1,7),(4,6),(5,4),(6,2),(7,3),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [2,3,7,4,6,5,8,1] => ([(1,6),(2,7),(3,7),(4,7),(5,3),(5,4),(6,2),(6,5)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [2,3,8,4,6,7,5,1] => ([(1,7),(5,4),(6,3),(6,5),(7,2),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [2,3,6,5,4,7,8,1] => ([(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [2,3,7,5,4,6,8,1] => ([(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [2,3,8,5,4,6,7,1] => ([(1,6),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [2,3,7,5,6,4,8,1] => ([(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [2,3,8,5,6,4,7,1] => ([(1,6),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [2,3,8,5,6,7,4,1] => ([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [2,3,8,5,7,6,4,1] => ([(1,7),(6,4),(6,5),(7,2),(7,3),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [2,3,7,6,5,4,8,1] => ([(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [2,3,8,6,5,4,7,1] => ([(1,6),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [2,3,8,7,6,5,4,1] => ([(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,4,3,5,6,7,8,1] => ([(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,4,3,5,6,8,7,1] => ([(1,4),(1,5),(4,7),(5,7),(6,2),(6,3),(7,6)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [2,4,3,5,7,6,8,1] => ([(1,2),(1,3),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [2,4,3,5,8,6,7,1] => ([(1,3),(1,4),(3,7),(4,7),(6,2),(7,5),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,4,3,6,5,7,8,1] => ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,4,3,6,5,8,7,1] => ([(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [2,4,3,7,5,6,8,1] => ([(1,3),(1,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(7,2)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [2,4,3,8,5,6,7,1] => ([(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,5)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [2,4,3,8,5,7,6,1] => ([(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [2,4,3,7,6,5,8,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [2,4,3,8,6,5,7,1] => ([(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [2,4,3,8,7,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [2,5,3,4,6,7,8,1] => ([(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [2,5,3,4,6,8,7,1] => ([(1,3),(1,6),(2,7),(3,7),(6,2),(7,4),(7,5)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [2,5,3,4,7,6,8,1] => ([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [2,5,3,4,8,6,7,1] => ([(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,2)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [2,5,3,4,8,7,6,1] => ([(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [2,6,3,4,5,7,8,1] => ([(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [2,6,3,4,5,8,7,1] => ([(1,3),(1,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [2,8,3,4,5,6,7,1] => ([(1,3),(1,7),(4,6),(5,4),(6,2),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [2,8,3,4,5,7,6,1] => ([(1,4),(1,6),(5,7),(6,5),(7,2),(7,3)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [2,6,3,5,4,7,8,1] => ([(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [2,6,3,5,4,8,7,1] => ([(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [2,7,3,5,4,6,8,1] => ([(1,2),(1,5),(2,7),(3,6),(4,6),(5,3),(5,4),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [2,8,3,5,4,7,6,1] => ([(1,2),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,7,5,6,3,8] => [2,7,3,5,6,4,8,1] => ([(1,4),(1,6),(2,7),(3,7),(4,7),(5,3),(6,2),(6,5)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [2,8,3,5,6,7,4,1] => ([(1,4),(1,7),(5,6),(6,3),(7,2),(7,5)],8)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,8,6,7,5,3] => [2,8,3,7,5,6,4,1] => ([(1,5),(1,7),(6,4),(7,2),(7,3),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [2,8,3,7,6,5,4,1] => ([(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [2,5,4,3,6,7,8,1] => ([(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [2,5,4,3,6,8,7,1] => ([(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [2,5,4,3,7,6,8,1] => ([(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [2,5,4,3,8,6,7,1] => ([(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [2,5,4,3,8,7,6,1] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,4,6,3,7,8] => [2,6,4,3,5,7,8,1] => ([(1,3),(1,4),(1,5),(3,7),(4,6),(5,6),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,4,6,3,8,7] => [2,6,4,3,5,8,7,1] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [2,7,4,3,5,6,8,1] => ([(1,2),(1,3),(1,5),(2,7),(3,7),(4,6),(5,6),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [2,8,4,3,5,6,7,1] => ([(1,3),(1,4),(1,5),(4,7),(5,7),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [2,8,4,3,5,7,6,1] => ([(1,2),(1,3),(1,4),(3,7),(4,7),(7,5),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,4,7,6,3,8] => [2,7,4,3,6,5,8,1] => ([(1,2),(1,3),(1,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [2,8,4,3,6,5,7,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [2,8,4,3,6,7,5,1] => ([(1,3),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [2,8,4,3,7,6,5,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [2,6,4,5,3,7,8,1] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [2,8,4,5,3,6,7,1] => ([(1,2),(1,4),(1,6),(3,7),(4,7),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,7,4,5,6,3,8] => [2,7,4,5,6,3,8,1] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [2,8,4,5,6,3,7,1] => ([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [2,8,4,5,6,7,3,1] => ([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,7,4,6,5,3,8] => [2,7,4,6,5,3,8,1] => ([(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,7,4,6,5,8,3] => [2,8,4,6,5,3,7,1] => ([(1,2),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [2,8,4,7,6,5,3,1] => ([(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [2,6,5,4,3,7,8,1] => ([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [2,6,5,4,3,8,7,1] => ([(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [2,8,5,4,3,6,7,1] => ([(1,2),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [2,8,5,4,3,7,6,1] => ([(1,2),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => [2,7,5,4,6,3,8,1] => ([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [2,8,5,4,6,7,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,7),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [2,8,5,4,7,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,7,5,6,4,3,8] => [2,7,6,4,5,3,8,1] => ([(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2)],8)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [2,8,7,4,5,6,3,1] => ([(1,3),(1,4),(1,5),(1,7),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,8,5,7,6,4,3] => [2,8,7,4,6,5,3,1] => ([(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [2,7,6,5,4,3,8,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [2,8,7,5,4,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [2,8,7,5,6,4,3,1] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [2,8,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,2,4,5,6,7,8,1] => ([(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [3,2,4,5,6,8,7,1] => ([(1,7),(2,7),(5,6),(6,3),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [3,2,4,5,7,6,8,1] => ([(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,3)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,2,4,5,8,6,7,1] => ([(1,7),(2,7),(5,4),(6,3),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [3,2,4,6,5,8,7,1] => ([(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [3,2,4,7,5,6,8,1] => ([(1,6),(2,6),(3,7),(4,5),(5,7),(6,3),(6,4)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [3,2,4,8,5,6,7,1] => ([(1,7),(2,7),(5,3),(6,5),(7,4),(7,6)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [3,2,4,7,6,5,8,1] => ([(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [3,2,4,8,6,7,5,1] => ([(1,7),(2,7),(6,3),(7,4),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [3,2,4,8,7,6,5,1] => ([(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [3,2,5,4,6,7,8,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,4,6,8,7] => [3,2,5,4,6,8,7,1] => ([(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [3,2,5,4,7,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,2,5,4,8,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [3,2,8,4,5,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [3,2,7,4,6,5,8,1] => ([(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [3,2,8,4,6,5,7,1] => ([(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(6,3),(6,4)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [3,2,6,5,4,8,7,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [3,2,8,5,4,6,7,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(6,4),(7,4)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [3,2,8,5,4,7,6,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,7,5,6,4,8] => [3,2,7,5,6,4,8,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [3,2,8,5,6,4,7,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,3),(7,4)],8)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [3,2,8,5,7,6,4,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [3,2,7,6,5,4,8,1] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [3,2,8,6,5,7,4,1] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [3,2,8,7,5,6,4,1] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [3,2,8,7,6,5,4,1] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [4,2,3,5,6,7,8,1] => ([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [4,2,3,5,6,8,7,1] => ([(1,7),(2,5),(5,7),(6,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [4,2,3,5,8,7,6,1] => ([(1,7),(2,3),(3,7),(7,4),(7,5),(7,6)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [4,2,3,6,5,8,7,1] => ([(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [4,2,3,7,5,6,8,1] => ([(1,5),(1,7),(2,4),(3,6),(4,5),(4,7),(5,6),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [4,2,3,8,5,6,7,1] => ([(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [4,2,3,8,5,7,6,1] => ([(1,6),(1,7),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [4,2,3,7,6,5,8,1] => ([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [4,2,3,8,7,6,5,1] => ([(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [5,2,3,4,6,7,8,1] => ([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [5,2,3,4,8,6,7,1] => ([(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [5,2,3,4,8,7,6,1] => ([(1,5),(1,6),(1,7),(2,3),(3,4),(4,5),(4,6),(4,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [6,2,3,4,5,7,8,1] => ([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [6,2,3,4,5,8,7,1] => ([(1,3),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [7,2,3,4,5,6,8,1] => ([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [8,2,3,4,5,6,7,1] => ([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [8,2,3,4,5,7,6,1] => ([(2,6),(5,7),(6,5),(7,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [8,2,3,4,7,6,5,1] => ([(2,6),(6,7),(7,3),(7,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,5,2,7,8] => [6,2,3,5,4,7,8,1] => ([(1,7),(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [8,2,3,5,4,6,7,1] => ([(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [8,2,3,5,4,7,6,1] => ([(2,3),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [8,2,3,5,6,7,4,1] => ([(2,7),(5,6),(6,4),(7,3),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [8,2,3,6,5,4,7,1] => ([(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,8,6,7,5,2] => [8,2,3,7,5,6,4,1] => ([(2,7),(6,5),(7,3),(7,4),(7,6)],8)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [8,2,3,7,6,5,4,1] => ([(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [5,2,4,3,7,6,8,1] => ([(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,4,2,8,7,6] => [5,2,4,3,8,7,6,1] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [7,2,4,3,6,5,8,1] => ([(1,7),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [8,2,4,3,6,5,7,1] => ([(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [8,2,4,3,7,6,5,1] => ([(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [7,2,4,5,3,6,8,1] => ([(1,6),(2,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [8,2,4,5,3,7,6,1] => ([(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [8,2,4,5,6,7,3,1] => ([(2,4),(2,7),(5,6),(6,3),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,7,4,6,5,2,8] => [7,2,4,6,5,3,8,1] => ([(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [8,2,4,7,5,6,3,1] => ([(2,5),(2,7),(6,4),(7,3),(7,6)],8)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,8,4,7,6,5,2] => [8,2,4,7,6,5,3,1] => ([(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [6,2,5,4,3,7,8,1] => ([(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [8,2,5,4,3,7,6,1] => ([(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [8,2,5,4,7,6,3,1] => ([(2,3),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,5,6,4,2,8] => [7,2,6,4,5,3,8,1] => ([(1,7),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,8,5,6,4,7,2] => [8,2,6,4,5,7,3,1] => ([(2,3),(2,5),(2,6),(4,7),(5,7),(6,4)],8)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [8,2,7,4,5,6,3,1] => ([(2,4),(2,5),(2,7),(6,3),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [8,2,7,4,6,5,3,1] => ([(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [7,2,6,5,4,3,8,1] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [8,2,7,5,4,6,3,1] => ([(2,3),(2,4),(2,5),(2,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [8,2,7,5,6,4,3,1] => ([(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,2,7,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [4,3,2,5,6,7,8,1] => ([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [4,3,2,5,6,8,7,1] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [4,3,2,5,7,6,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [4,3,2,5,8,7,6,1] => ([(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,3,2,6,5,7,8] => [4,3,2,6,5,7,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [4,3,2,6,5,8,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [4,3,2,7,5,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [4,3,2,8,5,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [4,3,2,8,5,7,6,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [4,3,2,7,6,5,8,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [4,3,2,8,6,7,5,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [4,3,2,8,7,6,5,1] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [5,3,2,4,6,7,8,1] => ([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [7,3,2,4,5,6,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [8,3,2,4,5,6,7,1] => ([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [8,3,2,4,6,5,7,1] => ([(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [8,3,2,4,6,7,5,1] => ([(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [8,3,2,4,7,6,5,1] => ([(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [6,3,2,5,4,7,8,1] => ([(1,7),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [8,3,2,5,4,7,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,3,7,5,6,2,8] => [7,3,2,5,6,4,8,1] => ([(1,7),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [8,3,2,5,6,7,4,1] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [8,3,2,5,7,6,4,1] => ([(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [8,3,2,6,5,7,4,1] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [8,3,2,7,5,6,4,1] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,3,2,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [5,3,4,2,6,7,8,1] => ([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,5,3,4,2,7,6,8] => [5,3,4,2,7,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [5,3,4,2,8,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [8,3,4,2,5,6,7,1] => ([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,5,3,4,7,6,2,8] => [7,3,4,2,6,5,8,1] => ([(1,7),(2,5),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,5,3,4,7,6,8,2] => [8,3,4,2,6,5,7,1] => ([(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [6,3,4,5,2,7,8,1] => ([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,6,3,4,5,7,8,2] => [8,3,4,5,2,6,7,1] => ([(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [8,3,4,5,2,7,6,1] => ([(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [7,3,4,5,6,2,8,1] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [8,3,4,5,6,2,7,1] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [8,3,4,5,6,7,2,1] => ([(3,4),(4,7),(6,5),(7,6)],8)
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8,3,4,5,7,6,2] => [8,3,4,5,7,6,2,1] => ([(3,4),(4,7),(7,5),(7,6)],8)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [8,3,4,7,6,5,2,1] => ([(3,4),(4,5),(4,6),(4,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [6,3,5,4,2,7,8,1] => ([(1,7),(2,7),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,6,3,5,4,7,8,2] => [8,3,5,4,2,6,7,1] => ([(2,7),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [8,3,5,4,2,7,6,1] => ([(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [7,3,5,4,6,2,8,1] => ([(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [8,3,5,4,6,7,2,1] => ([(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [8,3,5,4,7,6,2,1] => ([(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7,3,5,6,4,8,2] => [8,3,6,4,5,2,7,1] => ([(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [8,3,7,4,5,6,2,1] => ([(3,4),(3,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [8,3,7,4,6,5,2,1] => ([(3,4),(3,5),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [7,3,6,5,4,2,8,1] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [8,3,6,5,4,2,7,1] => ([(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [8,3,6,5,4,7,2,1] => ([(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8,3,6,5,7,4,2] => [8,3,7,5,4,6,2,1] => ([(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [8,3,7,5,6,4,2,1] => ([(3,4),(3,5),(3,6),(6,7)],8)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [8,3,7,6,5,4,2,1] => ([(3,4),(3,5),(3,6),(3,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [5,4,3,2,6,7,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [5,4,3,2,7,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [5,4,3,2,8,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [5,4,3,2,8,7,6,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [7,4,3,2,5,6,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [8,4,3,2,5,6,7,1] => ([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [8,4,3,2,5,7,6,1] => ([(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [8,4,3,2,6,5,7,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [8,4,3,2,7,6,5,1] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [8,4,3,5,2,7,6,1] => ([(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [8,4,3,5,6,7,2,1] => ([(3,7),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [8,4,3,5,7,6,2,1] => ([(3,7),(4,7),(7,5),(7,6)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,7,4,3,6,5,2,8] => [7,4,3,6,5,2,8,1] => ([(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [8,4,3,7,5,6,2,1] => ([(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,8,4,3,7,6,5,2] => [8,4,3,7,6,5,2,1] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [6,5,3,4,2,7,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [8,5,3,4,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [8,5,3,4,6,7,2,1] => ([(3,7),(4,5),(5,7),(7,6)],8)
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,8,4,5,3,7,6,2] => [8,5,3,4,7,6,2,1] => ([(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => [7,6,3,4,5,2,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [8,6,3,4,5,2,7,1] => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [8,7,3,4,5,6,2,1] => ([(4,5),(5,7),(7,6)],8)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,8,4,5,7,6,3,2] => [8,7,3,4,6,5,2,1] => ([(4,5),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [7,6,3,5,4,2,8,1] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7,4,6,5,3,8,2] => [8,6,3,5,4,2,7,1] => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [8,6,3,5,4,7,2,1] => ([(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [8,7,3,5,4,6,2,1] => ([(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,8,4,7,5,6,3,2] => [8,7,3,5,6,4,2,1] => ([(4,5),(4,6),(6,7)],8)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [8,7,3,6,5,4,2,1] => ([(4,5),(4,6),(4,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [6,5,4,3,2,7,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [6,5,4,3,2,8,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,5,4,3,7,2,8] => [7,5,4,3,2,6,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [8,5,4,3,2,6,7,1] => ([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [8,5,4,3,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [7,5,4,3,6,2,8,1] => ([(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [8,5,4,3,6,2,7,1] => ([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [8,5,4,3,6,7,2,1] => ([(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [8,5,4,3,7,6,2,1] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7,5,4,6,3,8,2] => [8,6,4,3,5,2,7,1] => ([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [8,6,4,3,5,7,2,1] => ([(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [8,7,4,3,5,6,2,1] => ([(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [8,7,4,3,6,5,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [7,6,4,5,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7,6,4,5,3,8,2] => [8,6,4,5,3,2,7,1] => ([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [8,7,4,5,3,6,2,1] => ([(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [8,7,4,5,6,3,2,1] => ([(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [8,7,4,6,5,3,2,1] => ([(5,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [8,6,5,4,3,2,7,1] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [8,6,5,4,3,7,2,1] => ([(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [8,7,5,4,3,6,2,1] => ([(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [8,7,5,4,6,3,2,1] => ([(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [8,7,6,4,5,3,2,1] => ([(6,7)],8)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,2,1] => ([],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [1,3,4,5,6,8,7,2] => ([(0,3),(0,6),(4,5),(5,7),(6,4),(7,1),(7,2)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [1,3,4,5,7,6,8,2] => ([(0,3),(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [1,3,4,5,8,6,7,2] => ([(0,3),(0,6),(4,7),(5,2),(6,4),(7,1),(7,5)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [1,3,4,5,8,7,6,2] => ([(0,4),(0,6),(5,7),(6,5),(7,1),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [1,3,4,6,5,7,8,2] => ([(0,4),(0,5),(1,7),(2,7),(5,6),(6,1),(6,2),(7,3)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [1,3,4,8,5,6,7,2] => ([(0,3),(0,6),(4,5),(5,2),(6,7),(7,1),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [1,3,4,8,7,6,5,2] => ([(0,5),(0,6),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6,8] => [1,3,5,4,7,6,8,2] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [1,3,5,4,8,7,6,2] => ([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,1),(4,2)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,5,6,4,7,8] => [1,3,6,4,5,7,8,2] => ([(0,4),(0,6),(1,7),(2,7),(5,2),(6,1),(6,5),(7,3)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [1,3,6,4,5,8,7,2] => ([(0,3),(0,5),(1,6),(1,7),(2,6),(2,7),(4,2),(5,1),(5,4)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [1,3,8,4,5,6,7,2] => ([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [1,3,8,4,6,5,7,2] => ([(0,4),(0,6),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [1,3,8,4,6,7,5,2] => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [1,3,6,5,4,8,7,2] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,1),(5,2),(5,3)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [1,3,8,5,4,6,7,2] => ([(0,5),(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [1,3,8,5,4,7,6,2] => ([(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(5,1),(5,2),(5,3)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [1,3,8,5,6,7,4,2] => ([(0,4),(0,7),(5,6),(6,3),(7,1),(7,2),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [1,3,8,5,7,6,4,2] => ([(0,5),(0,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [1,3,8,6,5,7,4,2] => ([(0,5),(0,6),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4)],8)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [1,3,8,7,5,6,4,2] => ([(0,5),(0,7),(6,4),(7,1),(7,2),(7,3),(7,6)],8)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [1,3,8,7,6,5,4,2] => ([(0,6),(0,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [1,4,3,5,6,7,8,2] => ([(0,2),(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [1,4,3,5,8,6,7,2] => ([(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [1,4,3,5,8,7,6,2] => ([(0,4),(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [1,4,3,6,5,7,8,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [1,4,3,6,5,8,7,2] => ([(0,1),(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [1,4,3,8,5,6,7,2] => ([(0,2),(0,3),(0,4),(3,6),(3,7),(4,6),(4,7),(5,1),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [1,4,3,8,5,7,6,2] => ([(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [1,4,3,8,6,5,7,2] => ([(0,1),(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [1,4,3,8,6,7,5,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1)],8)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [1,4,3,8,7,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [1,5,3,4,6,7,8,2] => ([(0,3),(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,5)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [1,5,3,4,8,6,7,2] => ([(0,3),(0,4),(0,5),(2,6),(2,7),(4,6),(4,7),(5,2),(7,1)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [1,6,3,4,5,8,7,2] => ([(0,2),(0,3),(0,5),(1,6),(1,7),(3,6),(3,7),(4,1),(5,4)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [1,7,3,4,5,6,8,2] => ([(0,2),(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [1,8,3,4,5,6,7,2] => ([(0,2),(0,3),(0,7),(4,6),(5,4),(6,1),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [1,8,3,4,6,7,5,2] => ([(0,3),(0,4),(0,6),(5,2),(6,7),(7,1),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [1,8,3,4,7,6,5,2] => ([(0,4),(0,5),(0,6),(6,7),(7,1),(7,2),(7,3)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [1,6,3,5,4,8,7,2] => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(4,6),(4,7),(5,1),(5,2)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [1,8,3,5,4,6,7,2] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(6,1),(6,2),(7,3)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [1,8,3,5,4,7,6,2] => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(5,1),(5,2)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,7,5,6,8,3] => [1,8,3,5,6,4,7,2] => ([(0,3),(0,4),(0,6),(1,7),(2,7),(5,2),(6,1),(6,5)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [1,8,3,5,6,7,4,2] => ([(0,3),(0,4),(0,7),(5,6),(6,2),(7,1),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [1,8,3,5,7,6,4,2] => ([(0,4),(0,5),(0,7),(6,2),(6,3),(7,1),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,7,6,5,3,8] => [1,7,3,6,5,4,8,2] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(5,7),(6,1),(6,2),(6,3)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [1,8,3,6,5,4,7,2] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3)],8)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [1,8,3,7,5,6,4,2] => ([(0,4),(0,5),(0,7),(6,3),(7,1),(7,2),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [1,8,3,7,6,5,4,2] => ([(0,5),(0,6),(0,7),(7,1),(7,2),(7,3),(7,4)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [1,5,4,3,6,7,8,2] => ([(0,2),(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [1,5,4,3,6,8,7,2] => ([(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [1,5,4,3,8,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [1,6,4,3,5,8,7,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [1,8,4,3,5,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [1,8,4,3,5,7,6,2] => ([(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1),(7,2)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,4,7,6,3,8] => [1,7,4,3,6,5,8,2] => ([(0,1),(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [1,8,4,3,6,5,7,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [1,8,4,3,6,7,5,2] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [1,6,4,5,3,8,7,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(3,6),(3,7),(4,6),(4,7),(5,1)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,6,4,5,7,3,8] => [1,7,4,5,3,6,8,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,7),(4,6),(5,1),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [1,8,4,5,3,6,7,2] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1),(7,2)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,7,4,5,6,3,8] => [1,7,4,5,6,3,8,2] => ([(0,2),(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,7,4,5,6,8,3] => [1,8,4,5,6,3,7,2] => ([(0,2),(0,3),(0,4),(0,6),(1,7),(4,7),(5,1),(6,5)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [1,8,4,5,6,7,3,2] => ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [1,8,4,6,5,3,7,2] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(5,7),(6,1),(6,2)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [1,8,4,6,5,7,3,2] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(6,1),(6,2)],8)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [1,8,4,7,6,5,3,2] => ([(0,4),(0,5),(0,6),(0,7),(7,1),(7,2),(7,3)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [1,6,5,4,3,8,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [1,8,5,4,3,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [1,8,5,4,3,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,7,5,4,6,8,3] => [1,8,5,4,6,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [1,8,5,4,6,7,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1)],8)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [1,8,5,4,7,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [1,8,6,4,5,3,7,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(4,7),(5,7),(6,1)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [1,8,6,4,5,7,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1)],8)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [1,8,7,4,5,6,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [1,8,7,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(7,1),(7,2)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [1,7,6,5,4,3,8,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [1,8,6,5,4,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [1,8,6,5,4,7,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [1,8,7,5,4,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [1,8,7,5,6,4,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [1,8,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [1,2,4,5,6,7,8,3] => ([(0,7),(3,4),(4,6),(5,3),(6,1),(7,2),(7,5)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [1,2,4,5,6,8,7,3] => ([(0,7),(4,5),(5,6),(6,2),(6,3),(7,1),(7,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [1,2,4,5,8,6,7,3] => ([(0,7),(4,6),(5,3),(6,2),(6,5),(7,1),(7,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [1,2,4,5,8,7,6,3] => ([(0,6),(5,7),(6,4),(6,5),(7,1),(7,2),(7,3)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [1,2,4,6,5,8,7,3] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [1,2,4,7,5,6,8,3] => ([(0,6),(2,7),(3,7),(4,3),(5,2),(5,4),(6,1),(6,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [1,2,4,8,5,6,7,3] => ([(0,7),(4,5),(5,3),(6,2),(6,4),(7,1),(7,6)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [1,2,4,8,6,5,7,3] => ([(0,5),(3,7),(4,7),(5,2),(5,6),(6,1),(6,3),(6,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [1,2,4,8,7,6,5,3] => ([(0,6),(6,5),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [1,2,5,4,6,7,8,3] => ([(0,6),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,5)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [1,2,5,4,7,6,8,3] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [1,2,5,4,8,6,7,3] => ([(0,5),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [1,2,6,4,5,7,8,3] => ([(0,6),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [1,2,7,4,5,6,8,3] => ([(0,6),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [1,2,8,4,5,6,7,3] => ([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [1,2,8,4,6,7,5,3] => ([(0,7),(5,4),(6,3),(6,5),(7,1),(7,2),(7,6)],8)
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [1,2,8,4,7,6,5,3] => ([(0,7),(6,3),(6,4),(6,5),(7,1),(7,2),(7,6)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [1,2,6,5,4,7,8,3] => ([(0,6),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [1,2,6,5,4,8,7,3] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [1,2,7,5,4,6,8,3] => ([(0,5),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [1,2,8,5,4,6,7,3] => ([(0,6),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [1,2,8,5,4,7,6,3] => ([(0,5),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,7,5,6,8,4] => [1,2,8,5,6,4,7,3] => ([(0,6),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [1,2,8,5,6,7,4,3] => ([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [1,2,7,6,5,4,8,3] => ([(0,6),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [1,2,8,6,5,4,7,3] => ([(0,6),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [1,2,8,6,5,7,4,3] => ([(0,6),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [1,2,8,7,5,6,4,3] => ([(0,7),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],8)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [1,2,8,7,6,5,4,3] => ([(0,7),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [1,2,3,5,6,7,8,4] => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [1,2,3,5,6,8,7,4] => ([(0,5),(4,7),(5,6),(6,3),(6,4),(7,1),(7,2)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [1,2,3,5,7,6,8,4] => ([(0,4),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [1,2,3,5,8,6,7,4] => ([(0,5),(4,3),(5,6),(6,2),(6,7),(7,1),(7,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [1,2,3,5,8,7,6,4] => ([(0,5),(5,6),(6,4),(6,7),(7,1),(7,2),(7,3)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [1,2,3,6,5,7,8,4] => ([(0,5),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [1,2,3,6,5,8,7,4] => ([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [1,2,3,7,5,6,8,4] => ([(0,5),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [1,2,3,8,5,6,7,4] => ([(0,6),(4,5),(5,3),(6,7),(7,1),(7,2),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [1,2,3,8,5,7,6,4] => ([(0,5),(5,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [1,2,3,7,6,5,8,4] => ([(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [1,2,3,8,6,5,7,4] => ([(0,5),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [1,2,3,8,6,7,5,4] => ([(0,6),(5,4),(6,7),(7,1),(7,2),(7,3),(7,5)],8)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [1,2,3,8,7,6,5,4] => ([(0,6),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [1,2,3,4,6,7,8,5] => ([(0,6),(3,7),(4,5),(5,1),(6,3),(7,2),(7,4)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [1,2,3,4,6,8,7,5] => ([(0,5),(4,7),(5,4),(6,2),(6,3),(7,1),(7,6)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [1,2,3,4,7,6,8,5] => ([(0,5),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [1,2,3,4,8,6,7,5] => ([(0,6),(4,7),(5,3),(6,4),(7,1),(7,2),(7,5)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [1,2,3,4,8,7,6,5] => ([(0,6),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [1,2,3,4,5,7,8,6] => ([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [1,2,3,4,5,8,7,6] => ([(0,6),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,6,8,7] => ([(0,6),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [1,2,3,4,5,7,6,8] => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [1,2,3,4,6,5,8,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,3),(5,1),(5,2)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [1,2,3,4,6,5,7,8] => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [1,2,3,4,6,7,5,8] => ([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [1,2,3,4,7,6,5,8] => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [1,2,3,5,4,7,8,6] => ([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3),(7,1)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [1,2,3,5,4,8,7,6] => ([(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,1),(4,2)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [1,2,3,5,4,6,8,7] => ([(0,5),(1,7),(2,7),(5,6),(6,1),(6,2),(7,3),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [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)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [1,2,3,5,4,7,6,8] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2),(5,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [1,2,3,5,6,4,8,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,2),(4,5),(5,1),(5,3)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [1,2,3,5,6,4,7,8] => ([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [1,2,3,5,6,7,4,8] => ([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [1,2,3,5,7,6,4,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [1,2,3,6,5,4,8,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [1,2,3,6,5,4,7,8] => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [1,2,3,6,5,7,4,8] => ([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [1,2,3,7,5,6,4,8] => ([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [1,2,3,7,6,5,4,8] => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [1,2,4,3,6,7,8,5] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(5,3),(7,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [1,2,4,3,6,8,7,5] => ([(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4),(7,1),(7,2)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [1,2,4,3,7,6,8,5] => ([(0,1),(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [1,2,4,3,8,6,7,5] => ([(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3),(7,1)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [1,2,4,3,8,7,6,5] => ([(0,1),(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [1,2,4,3,5,7,8,6] => ([(0,6),(2,7),(3,7),(5,1),(6,2),(6,3),(7,4),(7,5)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [1,2,4,3,5,6,8,7] => ([(0,6),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,5)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [1,2,4,3,5,6,7,8] => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [1,2,4,3,6,5,8,7] => ([(0,1),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [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)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [1,2,4,3,6,7,5,8] => ([(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(4,3),(5,6),(7,1)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [1,2,4,5,3,7,8,6] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4),(7,1)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [1,2,4,5,3,8,7,6] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,2),(4,1),(4,3)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [1,2,4,5,3,7,6,8] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,7,4,5,6,1,8] => [1,2,4,5,6,3,8,7] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,2),(5,1),(5,3)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [1,2,4,5,6,3,7,8] => ([(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4),(7,3)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [1,2,4,5,6,7,3,8] => ([(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,2),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [1,2,4,6,5,3,7,8] => ([(0,6),(1,7),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5),(7,4)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [1,2,5,4,3,7,8,6] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [1,2,5,4,3,8,7,6] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(4,2),(4,3)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [1,2,5,4,3,6,7,8] => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [1,2,5,4,6,7,3,8] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [1,2,6,4,5,3,7,8] => ([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [1,2,6,5,4,3,7,8] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,8,6,5,7,4,1] => [1,2,7,5,4,6,3,8] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [1,2,7,6,5,4,3,8] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [1,3,2,5,6,7,8,4] => ([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(4,1),(5,4),(7,5)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [1,3,2,5,6,8,7,4] => ([(0,3),(0,4),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(7,5)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [1,3,2,5,8,7,6,4] => ([(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2),(7,3)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [1,3,2,6,5,7,8,4] => ([(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(6,4),(7,4)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [1,3,2,6,5,8,7,4] => ([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [1,3,2,8,5,7,6,4] => ([(0,3),(0,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1),(7,2)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [1,3,2,8,6,5,7,4] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [1,3,2,8,6,7,5,4] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(7,1)],8)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [1,3,2,8,7,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [1,3,2,4,6,7,8,5] => ([(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,2),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [1,3,2,4,6,8,7,5] => ([(0,4),(0,5),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [1,3,2,4,7,6,8,5] => ([(0,4),(0,5),(2,6),(3,6),(4,7),(5,7),(7,1),(7,2),(7,3)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [1,3,2,4,8,6,7,5] => ([(0,4),(0,5),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [1,3,2,4,8,7,6,5] => ([(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,3,5,6,1,7,8] => [1,3,2,4,5,7,8,6] => ([(0,3),(0,4),(3,7),(4,7),(5,2),(6,1),(6,5),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [1,3,2,4,5,8,7,6] => ([(0,4),(0,5),(4,7),(5,7),(6,1),(6,2),(6,3),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [1,3,2,4,5,6,8,7] => ([(0,3),(0,4),(3,7),(4,7),(5,6),(6,1),(6,2),(7,5)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [1,3,2,4,5,6,7,8] => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [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)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,3,5,7,6,1,8] => [1,3,2,4,6,5,8,7] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(7,1),(7,2)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [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)
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [1,3,2,4,7,6,5,8] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [1,3,2,5,4,7,8,6] => ([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(5,1),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [1,3,2,5,4,8,7,6] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [1,3,2,5,4,6,7,8] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7),(7,4)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [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)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,3,7,5,6,1,8] => [1,3,2,5,6,4,8,7] => ([(0,2),(0,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(6,1),(7,4),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [1,3,2,5,6,4,7,8] => ([(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,2),(7,1)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [1,3,2,5,6,7,4,8] => ([(0,2),(0,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [1,3,2,5,7,6,4,8] => ([(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,1),(6,2)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [1,3,2,6,5,4,8,7] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [1,3,2,6,5,4,7,8] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7),(7,1)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [1,3,2,6,5,7,4,8] => ([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [1,3,2,7,6,5,4,8] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [1,3,4,2,6,7,8,5] => ([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(7,4)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,3,4,1,7,8,6] => [1,3,4,2,8,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(7,1)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [1,3,4,2,8,7,6,5] => ([(0,1),(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [1,3,4,2,5,6,8,7] => ([(0,4),(0,5),(3,7),(4,7),(5,3),(6,1),(6,2),(7,6)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [1,3,4,2,5,6,7,8] => ([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [1,3,4,2,5,7,6,8] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,3,4,7,6,1,8] => [1,3,4,2,6,5,8,7] => ([(0,1),(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [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)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [1,3,4,5,2,7,8,6] => ([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4),(7,1)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,3,4,5,1,8,7] => [1,3,4,5,2,8,7,6] => ([(0,2),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,1),(4,3)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [1,3,4,5,2,6,7,8] => ([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [1,3,4,5,2,7,6,8] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [1,3,4,5,6,2,8,7] => ([(0,2),(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,1),(5,3)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,7,3,4,5,6,8,1] => [1,3,4,5,6,2,7,8] => ([(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4),(7,2)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [1,3,4,5,6,7,2,8] => ([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [1,3,4,5,7,6,2,8] => ([(0,3),(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,6,3,5,4,1,7,8] => [1,3,5,4,2,7,8,6] => ([(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(7,1)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [1,3,5,4,2,7,6,8] => ([(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(4,2),(6,5),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [1,3,5,4,7,6,2,8] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,1),(4,2),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,7,3,5,6,4,1,8] => [1,3,6,4,5,2,8,7] => ([(0,3),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,2),(5,1),(5,4)],8)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [1,3,7,4,5,6,2,8] => ([(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(6,1),(6,4)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [1,3,6,5,4,2,8,7] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,8,3,6,5,4,7,1] => [1,3,6,5,4,7,2,8] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [1,4,3,2,6,7,8,5] => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(7,5)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [1,4,3,2,6,8,7,5] => ([(0,3),(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [1,4,3,2,7,6,8,5] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [1,4,3,2,8,6,7,5] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [1,4,3,2,8,7,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,4,3,6,1,7,8] => [1,4,3,2,5,7,8,6] => ([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [1,4,3,2,5,8,7,6] => ([(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [1,4,3,2,5,6,8,7] => ([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(6,2),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [1,4,3,2,5,6,7,8] => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [1,4,3,2,5,7,6,8] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [1,4,3,2,6,7,5,8] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,1)],8)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [1,4,3,2,7,6,5,8] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [1,4,3,5,2,7,6,8] => ([(0,1),(0,2),(0,3),(1,7),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [1,4,3,5,6,2,7,8] => ([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,7),(6,2),(7,1)],8)
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [1,4,3,5,7,6,2,8] => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [1,4,3,6,5,2,7,8] => ([(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [1,4,3,6,5,7,2,8] => ([(0,1),(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [1,5,3,4,2,7,8,6] => ([(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(7,1)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [1,5,3,4,2,8,7,6] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => [1,5,3,4,2,6,7,8] => ([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,7,4,5,3,6,1,8] => [1,5,3,4,6,2,8,7] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(3,7),(4,1),(5,6),(5,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [1,5,3,4,6,7,2,8] => ([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,6),(5,1),(7,2)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [1,6,3,4,5,2,7,8] => ([(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5),(7,2)],8)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [1,7,3,4,5,6,2,8] => ([(0,2),(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,1),(6,4)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [1,6,3,5,4,2,7,8] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,7),(6,1),(6,2),(7,3)],8)
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,8,4,6,5,7,3,1] => [1,7,3,5,4,6,2,8] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [1,7,3,6,5,4,2,8] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [1,5,4,3,2,8,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [1,5,4,3,2,6,7,8] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [1,5,4,3,2,7,6,8] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [1,5,4,3,6,2,7,8] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [1,5,4,3,6,7,2,8] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,6),(7,1)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [1,6,4,3,5,2,7,8] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [1,6,4,5,3,2,7,8] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [1,7,4,6,5,3,2,8] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [1,6,5,4,3,2,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [1,6,5,4,3,2,7,8] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,8,6,5,4,7,3,1] => [1,7,5,4,3,6,2,8] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [1,7,6,4,5,3,2,8] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [1,7,6,5,4,3,2,8] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [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)
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,1,4,5,6,8,7,3] => ([(0,6),(0,7),(1,6),(1,7),(4,5),(5,2),(5,3),(7,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [2,1,4,5,8,6,7,3] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(5,4),(7,5)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,1,4,5,8,7,6,3] => ([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(5,4),(7,5)],8)
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [2,1,4,6,5,8,7,3] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(7,2),(7,3)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [2,1,4,8,5,6,7,3] => ([(0,6),(0,7),(1,6),(1,7),(4,5),(5,3),(7,2),(7,4)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [2,1,4,8,5,7,6,3] => ([(0,6),(0,7),(1,6),(1,7),(5,3),(5,4),(7,2),(7,5)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,1,4,7,6,5,8,3] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [2,1,4,8,6,5,7,3] => ([(0,6),(0,7),(1,6),(1,7),(3,5),(4,5),(7,2),(7,3),(7,4)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [2,1,4,8,6,7,5,3] => ([(0,6),(0,7),(1,6),(1,7),(5,4),(7,2),(7,3),(7,5)],8)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,1,4,8,7,6,5,3] => ([(0,6),(0,7),(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,1,5,4,6,7,8,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(4,2),(6,4),(7,4)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,5,4,6,8,7] => [2,1,5,4,6,8,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(4,3),(6,4),(7,4)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,1,5,4,7,6,8,3] => ([(0,3),(0,6),(0,7),(1,3),(1,6),(1,7),(4,2),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,1,5,4,7,8,6] => [2,1,5,4,8,6,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,1,5,4,8,7,6] => [2,1,5,4,8,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(6,2),(6,3),(6,4),(7,2),(7,3),(7,4)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,1,6,4,5,7,8,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(6,3),(7,4)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [2,1,6,4,5,8,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(6,2),(7,3),(7,4)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,1,8,4,5,6,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(7,3)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [2,1,8,4,5,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(4,3),(7,4)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [2,1,7,4,6,5,8,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [2,1,8,4,6,5,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(7,2),(7,3)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [2,1,8,4,6,7,5,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,3),(7,2),(7,4)],8)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [2,1,8,4,7,6,5,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [2,1,6,5,4,8,7,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [2,1,8,5,4,6,7,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(3,2),(6,3),(7,3)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [2,1,8,5,4,7,6,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [2,1,7,5,6,4,8,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(4,7),(5,7),(6,2)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [2,1,8,5,6,4,7,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(6,2),(7,3)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [2,1,8,5,6,7,4,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(7,2)],8)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [2,1,8,5,7,6,4,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,1,7,6,5,4,8,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [2,1,8,6,5,4,7,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [2,1,8,6,5,7,4,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(6,2),(7,2)],8)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [2,1,8,7,5,6,4,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,1,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [2,1,3,5,6,7,8,4] => ([(0,7),(1,7),(4,5),(5,2),(6,4),(7,3),(7,6)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [2,1,3,5,8,6,7,4] => ([(0,7),(1,7),(5,3),(6,2),(6,5),(7,4),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [2,1,3,6,5,8,7,4] => ([(0,7),(1,7),(3,5),(3,6),(4,5),(4,6),(7,2),(7,3),(7,4)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [2,1,3,8,5,6,7,4] => ([(0,7),(1,7),(5,2),(6,5),(7,3),(7,4),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [2,1,3,8,5,7,6,4] => ([(0,7),(1,7),(6,2),(6,3),(7,4),(7,5),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [2,1,3,8,6,5,7,4] => ([(0,7),(1,7),(4,6),(5,6),(7,2),(7,3),(7,4),(7,5)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [2,1,3,8,6,7,5,4] => ([(0,7),(1,7),(6,2),(7,3),(7,4),(7,5),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [2,1,3,8,7,6,5,4] => ([(0,7),(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [2,1,3,4,6,7,8,5] => ([(0,7),(1,7),(4,5),(5,3),(6,2),(6,4),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [2,1,3,4,8,6,7,5] => ([(0,7),(1,7),(5,4),(6,2),(6,3),(6,5),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [2,1,3,4,8,7,6,5] => ([(0,7),(1,7),(6,2),(6,3),(6,4),(6,5),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [2,1,3,4,5,7,8,6] => ([(0,7),(1,7),(4,3),(5,6),(6,2),(6,4),(7,5)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [2,1,3,4,5,6,8,7] => ([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [2,1,3,4,5,6,7,8] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [2,1,3,4,5,7,6,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,2),(5,3),(7,4)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [2,1,3,4,6,5,8,7] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(7,4)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [2,1,3,4,6,5,7,8] => ([(0,6),(1,6),(3,7),(4,7),(5,3),(5,4),(6,5),(7,2)],8)
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [2,1,3,5,4,8,7,6] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,2),(7,3)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,2,4,6,5,7,1,8] => [2,1,3,5,4,6,8,7] => ([(0,7),(1,7),(2,6),(3,6),(6,4),(6,5),(7,2),(7,3)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,7,5,6,1,8] => [2,1,3,5,6,4,8,7] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,3),(7,2),(7,4)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,2,4,7,6,5,1,8] => [2,1,3,6,5,4,8,7] => ([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [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)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [2,1,4,3,6,8,7,5] => ([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [2,1,4,3,7,6,8,5] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,3),(6,2),(6,4),(6,5),(7,2),(7,4),(7,5)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [2,1,4,3,8,6,7,5] => ([(0,6),(0,7),(1,6),(1,7),(5,2),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [2,1,4,3,8,7,6,5] => ([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [2,1,4,3,5,7,8,6] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,7),(6,7),(7,2),(7,4)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [2,1,4,3,5,8,7,6] => ([(0,5),(0,6),(1,5),(1,6),(5,7),(6,7),(7,2),(7,3),(7,4)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [2,1,4,3,5,6,8,7] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,4),(6,5),(7,5)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [2,1,4,3,5,6,7,8] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,7),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [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)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [2,1,4,3,6,5,7,8] => ([(0,6),(0,7),(1,6),(1,7),(3,2),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [2,1,4,3,6,7,5,8] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,2),(5,4),(6,3),(6,5),(7,3),(7,5)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [2,1,4,5,3,8,7,6] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(6,2),(7,3),(7,4),(7,5)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,6,4,5,7,1,8] => [2,1,4,5,3,6,8,7] => ([(0,5),(0,6),(1,5),(1,6),(4,7),(5,7),(6,4),(7,2),(7,3)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [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)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [2,1,4,5,6,7,3,8] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,2),(6,5),(7,3)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [2,1,4,6,5,3,8,7] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [2,1,4,6,5,3,7,8] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3),(7,4)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [2,1,5,4,3,8,7,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [2,1,5,4,3,6,8,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7),(7,2),(7,3)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [2,1,5,4,3,7,6,8] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,2),(7,2)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [2,1,5,4,6,3,8,7] => ([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(4,6),(5,6),(6,2),(6,3),(7,2),(7,3)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [2,1,5,4,6,7,3,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,2),(5,4),(6,3),(7,3)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [2,1,6,4,5,3,8,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [2,1,6,5,4,3,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [2,1,7,6,5,4,3,8] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,3,1,5,6,7,8,4] => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(7,5)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [2,3,1,5,7,6,8,4] => ([(0,6),(0,7),(1,2),(2,6),(2,7),(3,5),(4,5),(7,3),(7,4)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [2,3,1,6,5,8,7,4] => ([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [2,3,1,8,5,6,7,4] => ([(0,5),(0,6),(0,7),(1,3),(3,5),(3,6),(3,7),(4,2),(7,4)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [2,3,1,7,6,5,8,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [2,3,1,8,6,7,5,4] => ([(0,3),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(3,7),(7,2)],8)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [2,3,1,8,7,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [2,3,1,4,6,7,8,5] => ([(0,7),(1,3),(3,7),(5,2),(6,5),(7,4),(7,6)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [2,3,1,4,8,7,6,5] => ([(0,7),(1,2),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [2,3,1,4,5,7,8,6] => ([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [2,3,1,4,5,6,8,7] => ([(0,7),(1,4),(4,7),(5,6),(6,2),(6,3),(7,5)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [2,3,1,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [2,3,1,4,5,7,6,8] => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,3),(5,4),(7,5)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,2,3,5,7,6,1,8] => [2,3,1,4,6,5,8,7] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(4,5),(4,6),(7,3),(7,4)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [2,3,1,5,4,7,6,8] => ([(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [2,3,1,5,6,4,7,8] => ([(0,5),(0,7),(1,2),(2,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [2,3,1,5,6,7,4,8] => ([(0,6),(0,7),(1,3),(2,5),(3,6),(3,7),(4,2),(6,5),(7,4)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,2,3,7,6,5,1,8] => [2,3,1,6,5,4,8,7] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [2,3,1,6,5,4,7,8] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7),(7,2)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,3,8,6,5,7,1] => [2,3,1,6,5,7,4,8] => ([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [2,3,1,7,5,6,4,8] => ([(0,3),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,2)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [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)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [2,3,4,1,6,8,7,5] => ([(0,6),(0,7),(1,5),(4,6),(4,7),(5,4),(7,2),(7,3)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,3,4,1,7,6,8] => [2,3,4,1,7,6,8,5] => ([(0,2),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [2,3,4,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,4),(3,5),(3,6),(3,7),(4,3),(7,2)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [2,3,4,1,8,7,6,5] => ([(0,2),(1,4),(1,5),(1,6),(1,7),(2,3),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [2,3,4,1,5,7,8,6] => ([(0,7),(1,5),(3,7),(5,3),(6,2),(7,4),(7,6)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [2,3,4,1,5,8,7,6] => ([(0,7),(1,6),(2,7),(6,2),(7,3),(7,4),(7,5)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [2,3,4,1,5,6,8,7] => ([(0,7),(1,5),(4,7),(5,4),(6,2),(6,3),(7,6)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [2,3,4,1,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,2,3,4,6,8,7,1] => [2,3,4,1,5,7,6,8] => ([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(7,3),(7,4)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [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)
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [2,3,4,1,6,7,5,8] => ([(0,6),(0,7),(1,4),(2,6),(2,7),(3,5),(4,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [2,3,4,1,7,6,5,8] => ([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,3,4,5,1,7,8,6] => ([(0,6),(0,7),(1,5),(3,6),(3,7),(4,3),(5,4),(7,2)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [2,3,4,5,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,4),(2,5),(2,6),(2,7),(3,2),(4,3)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [2,3,4,5,1,6,8,7] => ([(0,7),(1,6),(2,7),(5,2),(6,5),(7,3),(7,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,5,1,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [2,3,4,5,1,7,6,8] => ([(0,6),(0,7),(1,4),(2,6),(2,7),(3,2),(4,3),(6,5),(7,5)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [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)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,1,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [2,3,4,5,7,6,1,8] => ([(0,7),(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,2,3,4,6,5,8,1] => [2,3,4,6,5,1,7,8] => ([(0,7),(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8,2,3,4,6,5,7,1] => [2,3,4,6,5,7,1,8] => ([(0,7),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8,2,3,4,6,7,5,1] => [2,3,4,7,5,6,1,8] => ([(0,7),(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [2,3,4,7,6,5,1,8] => ([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [2,3,5,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [2,3,5,4,1,6,8,7] => ([(0,7),(1,6),(2,7),(3,7),(6,2),(6,3),(7,4),(7,5)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [2,3,5,4,1,6,7,8] => ([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,2,3,5,4,8,7,1] => [2,3,5,4,1,7,6,8] => ([(0,6),(0,7),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(6,5),(7,5)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [2,3,5,4,6,7,1,8] => ([(0,6),(1,5),(2,7),(3,7),(4,6),(5,2),(5,3),(7,4)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [2,3,6,4,5,1,8,7] => ([(0,6),(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,2,3,5,6,4,8,1] => [2,3,6,4,5,1,7,8] => ([(0,7),(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [2,3,6,5,4,1,8,7] => ([(0,6),(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8,2,3,6,5,7,4,1] => [2,3,7,5,4,6,1,8] => ([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [2,3,7,5,6,4,1,8] => ([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [2,3,7,6,5,4,1,8] => ([(0,7),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [2,4,3,1,6,7,8,5] => ([(0,6),(0,7),(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,5)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [2,4,3,1,6,8,7,5] => ([(0,6),(0,7),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [2,4,3,1,7,6,8,5] => ([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [2,4,3,1,8,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [2,4,3,1,5,8,7,6] => ([(0,7),(1,2),(1,3),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [5,2,4,3,6,7,8,1] => [2,4,3,1,5,6,7,8] => ([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [2,4,3,1,6,5,8,7] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [2,4,3,1,6,5,7,8] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [2,4,3,5,1,8,7,6] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,2,4,3,5,8,7,1] => [2,4,3,5,1,7,6,8] => ([(0,2),(0,3),(1,5),(1,6),(2,7),(3,7),(5,4),(6,4),(7,5),(7,6)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [2,4,3,6,5,1,8,7] => ([(0,6),(0,7),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [2,4,3,6,5,1,7,8] => ([(0,7),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,4,3,6,5,7,1,8] => ([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [2,5,3,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,2,4,5,3,7,8,1] => [2,5,3,4,1,6,7,8] => ([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8,2,4,5,3,6,7,1] => [2,5,3,4,6,7,1,8] => ([(0,6),(1,3),(1,5),(2,7),(3,7),(4,6),(5,2),(7,4)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,2,4,5,6,3,8,1] => [2,6,3,4,5,1,7,8] => ([(0,7),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [2,7,3,4,5,6,1,8] => ([(0,7),(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [2,6,3,5,4,1,8,7] => ([(0,6),(0,7),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [2,7,3,6,5,4,1,8] => ([(0,7),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [2,5,4,3,1,7,8,6] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [2,5,4,3,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [2,5,4,3,1,6,8,7] => ([(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [2,5,4,3,1,6,7,8] => ([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,2,5,4,3,8,7,1] => [2,5,4,3,1,7,6,8] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [2,5,4,3,6,1,8,7] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [2,5,4,3,6,7,1,8] => ([(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,2,5,4,6,3,1,8] => [2,6,4,3,5,1,8,7] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [2,6,4,5,3,1,7,8] => ([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [2,7,4,5,6,3,1,8] => ([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [2,7,4,6,5,3,1,8] => ([(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [2,6,5,4,3,1,8,7] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [2,7,6,5,4,3,1,8] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [3,2,1,5,6,7,8,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [3,2,1,5,6,8,7,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(7,3)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [3,2,1,5,7,6,8,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(7,3),(7,4)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,1,5,8,6,7,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(4,5),(7,3),(7,4)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [3,2,1,5,8,7,6,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [3,2,1,6,5,7,8,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(6,4),(7,4)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [3,2,1,6,5,8,7,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [3,2,1,7,5,6,8,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,4),(7,3)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [3,2,1,8,5,6,7,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(7,3)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [3,2,1,8,5,7,6,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [3,2,1,7,6,5,8,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(5,3),(6,3),(7,3)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [3,2,1,8,6,5,7,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [3,2,1,8,6,7,5,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [3,2,1,8,7,6,5,4] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,1,4,6,7,8,5] => ([(0,7),(1,7),(2,7),(5,3),(6,5),(7,4),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [3,2,1,4,6,8,7,5] => ([(0,7),(1,7),(2,7),(6,3),(6,4),(7,5),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,3,2,5,1,7,6,8] => [3,2,1,4,7,6,8,5] => ([(0,7),(1,7),(2,7),(4,6),(5,6),(7,3),(7,4),(7,5)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [3,2,1,4,8,6,7,5] => ([(0,7),(1,7),(2,7),(6,3),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [3,2,1,4,8,7,6,5] => ([(0,7),(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [3,2,1,4,5,7,8,6] => ([(0,7),(1,7),(2,7),(5,4),(6,3),(6,5),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [3,2,1,4,5,8,7,6] => ([(0,7),(1,7),(2,7),(6,3),(6,4),(6,5),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [3,2,1,4,5,6,8,7] => ([(0,7),(1,7),(2,7),(5,6),(6,3),(6,4),(7,5)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [3,2,1,4,5,6,7,8] => ([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [3,2,1,4,5,7,6,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(7,3)],8)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [3,2,1,4,7,6,5,8] => ([(0,6),(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [3,2,1,5,4,6,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(5,3),(6,5),(7,5)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [3,2,1,5,4,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [3,2,1,5,6,4,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [3,2,1,5,7,6,4,8] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [3,2,1,6,5,4,8,7] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(5,3),(5,4),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [3,2,1,6,5,4,7,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,4)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,2,8,6,5,7,1] => [3,2,1,6,5,7,4,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,4),(6,3),(7,3)],8)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,2,1,7,5,6,4,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,3),(6,4),(7,4)],8)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [3,2,1,7,6,5,4,8] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [3,2,4,1,6,7,8,5] => ([(0,6),(0,7),(1,5),(2,5),(3,4),(5,6),(5,7),(7,3)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [3,2,4,1,6,8,7,5] => ([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [3,2,4,1,7,6,8,5] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(5,3),(6,3),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3,2,4,1,7,8,6] => [3,2,4,1,8,6,7,5] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(6,3),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [3,2,4,1,8,7,6,5] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(7,3),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [3,2,4,1,5,7,8,6] => ([(0,7),(1,6),(2,6),(4,5),(6,7),(7,3),(7,4)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [3,2,4,1,5,8,7,6] => ([(0,7),(1,6),(2,6),(6,7),(7,3),(7,4),(7,5)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,3,2,4,6,7,1,8] => [3,2,4,1,5,6,8,7] => ([(0,7),(1,6),(2,6),(3,4),(3,5),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [3,2,4,1,5,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,3,2,4,5,1,8,7] => [3,2,4,5,1,8,7,6] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,3)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,3,2,4,5,7,8,1] => [3,2,4,5,1,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,4,5,6,1,7,8] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,7,1,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [3,2,5,4,1,7,8,6] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [3,2,5,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [3,2,5,4,1,6,8,7] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [3,2,5,4,1,6,7,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [3,2,5,4,1,7,6,8] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [3,2,5,4,6,1,8,7] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,1,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,3),(5,4),(6,3),(6,4)],8)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [3,2,7,4,5,6,1,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(5,7),(6,3)],8)
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [3,2,7,4,6,5,1,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8,3,2,6,5,4,7,1] => [3,2,6,5,4,7,1,8] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [3,2,7,5,4,6,1,8] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,3),(6,3)],8)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [3,2,7,5,6,4,1,8] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [3,2,7,6,5,4,1,8] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [4,2,3,1,6,7,8,5] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [4,2,3,1,6,8,7,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,3,4,2,1,7,6,8] => [4,2,3,1,7,6,8,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [4,2,3,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [4,2,3,1,8,7,6,5] => ([(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,3,4,2,6,1,7,8] => [4,2,3,1,5,7,8,6] => ([(0,7),(1,7),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [4,2,3,1,5,8,7,6] => ([(0,7),(1,7),(2,3),(3,7),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [4,2,3,1,5,6,7,8] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [4,2,3,1,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [4,2,3,1,6,5,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,3,4,2,5,1,7,8] => [4,2,3,5,1,7,8,6] => ([(0,7),(1,5),(1,6),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [4,2,3,5,1,8,7,6] => ([(0,3),(1,7),(2,4),(2,5),(2,6),(3,7),(7,4),(7,5),(7,6)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [6,3,4,2,5,7,1,8] => [4,2,3,5,1,6,8,7] => ([(0,7),(1,6),(2,3),(3,7),(6,4),(6,5),(7,6)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [4,2,3,5,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8,3,4,2,6,7,5,1] => [4,2,3,7,5,6,1,8] => ([(0,7),(1,5),(1,6),(2,4),(3,7),(4,5),(4,6),(5,7),(6,3)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [5,2,3,4,1,7,8,6] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [5,2,3,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(4,5),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [5,2,3,4,1,6,8,7] => ([(0,7),(1,7),(2,6),(3,7),(6,3),(7,4),(7,5)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [5,2,3,4,1,6,7,8] => ([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,3,4,5,2,6,1,8] => [5,2,3,4,6,1,8,7] => ([(0,5),(1,6),(1,7),(2,3),(3,4),(4,5),(5,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [5,2,3,4,6,1,7,8] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [5,2,3,4,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [5,2,3,4,7,6,1,8] => ([(0,7),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [6,2,3,4,5,1,8,7] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [6,2,3,4,5,1,7,8] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [6,2,3,4,5,7,1,8] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [7,2,3,4,5,6,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [7,2,3,4,6,5,1,8] => ([(0,7),(1,7),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [6,2,3,5,4,1,8,7] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,5,2,7,1] => [6,2,3,5,4,7,1,8] => ([(0,3),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8,3,4,6,5,7,2,1] => [7,2,3,5,4,6,1,8] => ([(0,3),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8,3,4,7,5,6,2,1] => [7,2,3,5,6,4,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,7),(5,4),(6,3),(6,5)],8)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [7,2,3,6,5,4,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [5,2,4,3,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [5,2,4,3,1,6,8,7] => ([(0,7),(1,7),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [5,2,4,3,1,6,7,8] => ([(0,7),(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [5,2,4,3,1,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [5,2,4,3,6,1,8,7] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,3,5,4,2,6,8,1] => [5,2,4,3,6,1,7,8] => ([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [5,2,4,3,6,7,1,8] => ([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [5,2,4,3,7,6,1,8] => ([(0,5),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [6,2,4,3,5,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,5),(4,5),(5,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [7,2,4,3,6,5,1,8] => ([(0,7),(1,7),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [6,2,4,5,3,1,7,8] => ([(0,7),(1,7),(2,4),(2,6),(3,7),(4,7),(6,3),(7,5)],8)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => [7,2,4,5,3,6,1,8] => ([(0,7),(1,7),(2,3),(2,4),(3,5),(4,6),(5,6),(6,7)],8)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [7,2,4,6,5,3,1,8] => ([(0,7),(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [6,2,5,4,3,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [6,2,5,4,3,1,7,8] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [6,2,5,4,3,7,1,8] => ([(0,7),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [7,2,5,4,3,6,1,8] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [7,2,6,4,5,3,1,8] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [7,2,6,5,4,3,1,8] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [4,3,2,1,6,7,8,5] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [4,3,2,1,6,8,7,5] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [4,3,2,1,7,6,8,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [4,3,2,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [4,3,2,1,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [4,3,2,1,5,7,8,6] => ([(0,7),(1,7),(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [4,3,2,1,5,8,7,6] => ([(0,7),(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [4,3,2,1,5,6,8,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [4,3,2,1,5,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [4,3,2,1,5,7,6,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [4,3,2,1,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [4,3,2,1,6,5,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [4,3,2,1,6,7,5,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [4,3,2,1,7,6,5,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [4,3,2,5,1,7,8,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(6,4),(7,5),(7,6)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [4,3,2,5,1,8,7,6] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5),(7,6)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1,8] => [4,3,2,5,6,1,8,7] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,2,5,6,1,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,5),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [4,3,2,5,6,7,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [4,3,2,5,7,6,1,8] => ([(0,7),(1,6),(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [4,3,2,6,5,1,8,7] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [4,3,2,6,5,1,7,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [4,3,2,6,5,7,1,8] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,4),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [5,3,2,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(4,5),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [5,3,2,4,1,6,8,7] => ([(0,7),(1,7),(2,6),(3,6),(6,7),(7,4),(7,5)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,4,3,5,2,7,8,1] => [5,3,2,4,1,6,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,4,3,5,2,8,7,1] => [5,3,2,4,1,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [5,3,2,4,6,1,8,7] => ([(0,4),(1,4),(2,7),(3,5),(3,6),(4,7),(7,5),(7,6)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [5,3,2,4,6,1,7,8] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [5,3,2,4,7,6,1,8] => ([(0,4),(1,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [6,3,2,4,5,7,1,8] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [6,3,2,5,4,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [6,3,2,5,4,1,7,8] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8,4,3,6,5,2,7,1] => [6,3,2,5,4,7,1,8] => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8,4,3,6,5,7,2,1] => [7,3,2,5,4,6,1,8] => ([(0,7),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [5,3,4,2,1,7,8,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [5,3,4,2,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [5,3,4,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [5,3,4,2,6,1,8,7] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(4,7),(7,5),(7,6)],8)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [5,3,4,2,7,6,1,8] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [7,3,4,2,6,5,1,8] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [6,3,4,5,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [6,3,4,5,2,7,1,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [7,3,4,5,6,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [7,3,4,6,5,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [6,3,5,4,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [6,3,5,4,2,7,1,8] => ([(0,7),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [7,3,5,4,2,6,1,8] => ([(0,7),(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [7,3,5,4,6,2,1,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [7,3,6,4,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [5,4,3,2,1,7,8,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [5,4,3,2,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [5,4,3,2,1,6,8,7] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [5,4,3,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [5,4,3,2,1,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [5,4,3,2,6,1,8,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [5,4,3,2,6,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [5,4,3,2,6,7,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [5,4,3,2,7,6,1,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [6,4,3,2,5,1,8,7] => ([(0,5),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [6,4,3,2,5,1,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [7,4,3,2,6,5,1,8] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [6,4,3,5,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [7,4,3,5,2,6,1,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [7,4,3,6,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [6,5,3,4,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [6,5,3,4,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8,6,4,5,3,7,2,1] => [7,5,3,4,2,6,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [7,6,3,4,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [7,6,3,5,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [6,5,4,3,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [6,5,4,3,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [6,5,4,3,2,7,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [7,5,4,3,2,6,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [7,6,4,3,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [7,6,5,4,3,2,1,9,8] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,2,1] => ([],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [8,7,6,5,4,3,2,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [7,6,4,5,3,2,1,9,8] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [9,8,7,5,6,4,3,2,1] => ([(7,8)],9)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,2,1] => ([],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [9,8,7,6,5,4,3,2,1,11,10] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => [8,7,6,4,5,3,2,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(7,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => [7,6,4,3,5,2,1,9,8] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(5,6),(6,7),(6,8)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => [7,6,3,5,4,2,1,9,8] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,6),(5,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => [9,8,7,5,4,6,3,2,1] => ([(6,8),(7,8)],9)
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => [9,8,7,4,6,5,3,2,1] => ([(6,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => [10,9,8,7,5,6,4,3,2,1] => ([(8,9)],10)
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,2,1] => ([],11)
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [10,9,8,7,6,5,4,3,2,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,9,8,5,6,7,4,3,2] => [9,8,7,4,5,6,3,2,1] => ([(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,10,9,8,6,5,7,4,3,2] => [10,9,8,6,5,7,4,3,2,1] => ([(7,9),(8,9)],10)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,3,7,6,5,4,2,1,9] => [7,2,6,5,4,3,1,9,8] => ([(0,7),(0,8),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,9,8,5,4,6,7,3,2] => [9,8,5,4,6,7,3,2,1] => ([(5,8),(6,8),(8,7)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [1,7,6,5,4,3,2,9,8] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [6,5,4,3,2,1,9,8,7] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [1,9,8,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8)],9)
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [9,2,8,7,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [6,5,4,3,2,1,8,9,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(8,6)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,2,9,1] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,6,4,5,3,2,1,9,8] => [6,5,3,4,2,1,9,8,7] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(5,6),(5,7),(5,8)],9)
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,9,8,6,7,5,4,3] => [1,9,8,7,5,6,4,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(8,1)],9)
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [2,9,8,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [7,6,5,4,3,2,1,10,9,8] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,6,3,5,4,2,1,9,8] => [6,3,5,4,2,1,9,8,7] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [1,10,9,8,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9)],10)
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [10,2,9,8,7,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [7,6,5,4,3,2,1,9,10,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(9,7)],10)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,2,10,1] => ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,9,5,4,6,7,8,3,2] => [9,8,4,3,5,6,7,2,1] => ([(4,8),(5,8),(6,7),(8,6)],9)
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1,9,8,5,6,7,4,3] => [1,9,8,5,6,7,4,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,8),(7,1),(8,7)],9)
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,10,9,8,6,7,5,4,3] => [1,10,9,8,6,7,5,4,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(9,1)],10)
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [2,10,9,8,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9)],10)
[] => [] => [] => ([],0)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [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)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [1,2,3,4,5,6,8,7,9] => ([(0,6),(1,8),(2,8),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [1,2,3,4,5,7,6,8,9] => ([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [1,2,3,4,5,7,8,6,9] => ([(0,6),(1,8),(2,8),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => [1,2,3,4,6,5,7,8,9] => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => [1,2,3,5,4,6,7,8,9] => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => [1,2,3,5,6,7,8,4,9] => ([(0,6),(1,8),(2,8),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,6,4,5,7,8,9,1] => [1,2,4,5,3,6,7,8,9] => ([(0,7),(2,8),(3,8),(4,1),(5,3),(6,4),(7,2),(7,5),(8,6)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,3,7,4,5,6,8,9,1] => [1,2,4,5,6,3,7,8,9] => ([(0,7),(2,8),(3,8),(4,5),(5,3),(6,1),(7,2),(7,4),(8,6)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [1,3,2,4,5,6,7,8,9] => ([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,8,3,4,5,6,7,9,1] => [1,3,4,5,6,7,2,8,9] => ([(0,3),(0,7),(1,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,2)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [1,3,4,5,6,7,8,2,9] => ([(0,2),(0,7),(1,8),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5)],9)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [1,8,7,6,5,4,3,2,9] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [2,1,3,4,5,6,7,8,9] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => [2,1,4,3,6,5,8,7,9] => ([(0,7),(0,8),(1,7),(1,8),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,9,4,5,6,7,8,1] => [2,1,4,5,6,7,8,3,9] => ([(0,7),(0,8),(1,7),(1,8),(2,6),(3,5),(4,3),(5,2),(7,6),(8,4)],9)
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [2,1,8,7,6,5,4,3,9] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [2,3,1,4,5,6,7,8,9] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [7,2,3,4,5,6,9,8,1] => [2,3,4,5,6,1,8,7,9] => ([(0,7),(0,8),(1,5),(2,7),(2,8),(3,4),(4,2),(5,3),(7,6),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,7,1,8,9] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [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)
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9,2,3,4,5,6,8,7,1] => [2,3,4,5,6,8,7,1,9] => ([(0,8),(1,6),(2,8),(3,8),(4,5),(5,7),(6,4),(7,2),(7,3)],9)
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [2,8,7,6,5,4,3,1,9] => ([(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [3,2,1,4,5,6,7,8,9] => ([(0,8),(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1,9] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => [4,2,3,5,6,7,8,1,9] => ([(0,7),(1,8),(2,4),(3,7),(4,8),(5,3),(6,5),(8,6)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [8,2,3,4,5,6,7,1,9] => ([(0,8),(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [4,3,2,1,5,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(6,5),(7,6),(8,4)],9)
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => [4,3,2,1,8,7,6,5,9] => ([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(5,4),(6,4),(7,4),(8,4)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [5,4,3,2,1,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(7,6),(8,5)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [6,5,4,3,2,1,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,6)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [6,5,4,3,2,1,8,7,9] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(7,6),(8,6)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [6,5,4,3,2,7,1,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(7,6),(8,7)],9)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => [8,7,4,6,5,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [7,6,5,4,3,2,1,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => [8,7,5,4,6,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [8,7,6,4,5,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,1] => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,9,8,1] => ([(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [2,3,4,5,6,9,7,8,1] => ([(1,7),(4,5),(5,8),(6,2),(7,4),(8,3),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [2,3,4,5,9,6,7,8,1] => ([(1,7),(4,8),(5,6),(6,2),(7,4),(8,3),(8,5)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [2,3,4,9,5,6,7,8,1] => ([(1,7),(4,6),(5,4),(6,2),(7,8),(8,3),(8,5)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [2,3,9,4,5,6,7,8,1] => ([(1,8),(4,5),(5,7),(6,4),(7,2),(8,3),(8,6)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [2,9,3,4,5,6,7,8,1] => ([(1,3),(1,8),(4,5),(5,7),(6,4),(7,2),(8,6)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [9,2,3,4,5,6,7,8,1] => ([(2,8),(4,5),(5,7),(6,4),(7,3),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,1] => ([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,10,9,1] => ([(1,8),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(9,3)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [2,3,4,5,6,9,8,7,1] => ([(1,7),(5,6),(6,8),(7,5),(8,2),(8,3),(8,4)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [2,3,4,5,6,7,10,8,9,1] => ([(1,8),(4,6),(5,4),(6,9),(7,2),(8,5),(9,3),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [2,3,4,5,9,7,6,8,1] => ([(1,6),(3,8),(4,8),(5,7),(6,5),(7,2),(7,3),(7,4)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [2,3,4,5,6,10,7,8,9,1] => ([(1,8),(4,5),(5,9),(6,7),(7,2),(8,4),(9,3),(9,6)],10)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [2,3,4,9,6,5,7,8,1] => ([(1,6),(3,8),(4,8),(6,7),(7,2),(7,3),(7,4),(8,5)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [2,3,4,5,10,6,7,8,9,1] => ([(1,8),(4,7),(5,9),(6,4),(7,2),(8,5),(9,3),(9,6)],10)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [2,3,9,5,4,6,7,8,1] => ([(1,7),(4,8),(5,8),(6,3),(7,2),(7,4),(7,5),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [2,3,4,10,5,6,7,8,9,1] => ([(1,8),(4,5),(5,7),(6,4),(7,2),(8,9),(9,3),(9,6)],10)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [2,9,4,3,5,6,7,8,1] => ([(1,3),(1,4),(1,5),(4,8),(5,8),(6,2),(7,6),(8,7)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [2,3,10,4,5,6,7,8,9,1] => ([(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(9,3),(9,7)],10)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [9,3,2,4,5,6,7,8,1] => ([(2,8),(3,8),(4,7),(6,5),(7,6),(8,4)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [2,10,3,4,5,6,7,8,9,1] => ([(1,3),(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [10,2,3,4,5,6,7,8,9,1] => ([(2,9),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [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)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,1] => ([(1,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,3,4,5,6,7,8,9,11,10,1] => ([(1,9),(4,6),(5,4),(6,8),(7,5),(8,10),(9,7),(10,2),(10,3)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [2,3,4,5,6,7,10,9,8,1] => ([(1,8),(5,7),(6,5),(7,9),(8,6),(9,2),(9,3),(9,4)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [2,3,4,5,9,7,8,6,1] => ([(1,7),(5,8),(6,4),(7,5),(8,2),(8,3),(8,6)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,9,2] => [9,3,4,2,5,6,7,8,1] => ([(2,8),(3,4),(4,8),(5,6),(6,7),(8,5)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,10,2] => [10,3,2,4,5,6,7,8,9,1] => ([(2,9),(3,9),(5,7),(6,5),(7,4),(8,6),(9,8)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [2,1,3,4,5,6,7,8,9,10] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [11,2,3,4,5,6,7,8,9,10,1] => ([(2,10),(4,5),(5,7),(6,4),(7,9),(8,6),(9,3),(10,8)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,2,3,4,5,6,7,8,9,10,11] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => [2,3,4,5,6,10,8,9,7,1] => ([(1,8),(5,6),(6,9),(7,2),(8,5),(9,3),(9,4),(9,7)],10)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => [2,3,4,9,6,7,8,5,1] => ([(1,7),(5,6),(6,4),(7,8),(8,2),(8,3),(8,5)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,6,3,4,5,7,8,9,2] => [9,3,4,5,2,6,7,8,1] => ([(2,8),(3,4),(4,7),(5,6),(7,8),(8,5)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,10,1] => [2,3,1,4,5,6,7,8,9,10] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [3,2,1,4,5,6,7,8,9,10] => ([(0,9),(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [2,1,3,4,5,6,7,8,9,10,11] => ([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,5,10,7,8,9,6] => [2,3,4,5,10,7,8,9,6,1] => ([(1,8),(5,9),(6,7),(7,2),(8,5),(9,3),(9,4),(9,6)],10)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => [2,3,9,5,6,7,8,4,1] => ([(1,8),(5,7),(6,4),(7,6),(8,2),(8,3),(8,5)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,4,10,6,7,8,9,5] => [2,3,4,10,6,7,8,9,5,1] => ([(1,8),(5,7),(6,5),(7,2),(8,9),(9,3),(9,4),(9,6)],10)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => [2,9,4,5,6,7,8,3,1] => ([(1,3),(1,4),(1,8),(5,7),(6,5),(7,2),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,2,3,4,5,7,8,9,10,1] => [2,3,4,5,1,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [4,3,2,1,5,6,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(5,7),(6,5),(7,4),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,3,10,5,6,7,8,9,4] => [2,3,10,5,6,7,8,9,4,1] => ([(1,9),(5,6),(6,8),(7,5),(8,2),(9,3),(9,4),(9,7)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [9,3,4,5,6,7,8,2,1] => ([(3,8),(5,7),(6,5),(7,4),(8,6)],9)
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [2,3,9,8,7,6,5,4,1] => ([(1,8),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,10,4,5,6,7,8,9,3] => [2,10,4,5,6,7,8,9,3,1] => ([(1,3),(1,4),(1,9),(5,6),(6,8),(7,5),(8,2),(9,7)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [5,4,3,2,1,6,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(7,6),(8,7),(9,5)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => [10,3,4,5,6,7,8,9,2,1] => ([(3,9),(5,6),(6,8),(7,5),(8,4),(9,7)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [2,3,4,5,6,7,8,1,9,10] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,3,4,5,6,8,7,9,1] => ([(1,6),(2,8),(3,8),(4,5),(5,7),(6,4),(7,2),(7,3)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [2,3,4,5,7,6,8,9,1] => ([(1,6),(2,8),(3,8),(5,7),(6,5),(7,2),(7,3),(8,4)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [2,3,4,6,5,7,8,9,1] => ([(1,5),(3,8),(4,8),(5,7),(6,2),(7,3),(7,4),(8,6)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [2,4,3,5,6,7,8,9,1] => ([(1,3),(1,4),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,8,7,6,5,4,3,9] => [2,8,7,6,5,4,3,9,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,2,4,5,6,7,8,9,1] => ([(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [3,2,5,4,7,6,9,8,1] => ([(1,7),(1,8),(2,7),(2,8),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [3,2,9,8,7,6,5,4,1] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [4,3,2,5,6,7,8,9,1] => ([(1,8),(2,8),(3,8),(4,7),(6,5),(7,6),(8,4)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => [5,4,3,2,9,8,7,6,1] => ([(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,6,5,4,3,2,8,9] => [7,6,5,4,3,2,8,9,1] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(8,7)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [7,6,5,4,3,2,9,8,1] => ([(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [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)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [1,3,4,5,6,7,9,8,2] => ([(0,3),(0,7),(4,6),(5,4),(6,8),(7,5),(8,1),(8,2)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [1,3,4,5,6,8,7,9,2] => ([(0,3),(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2)],9)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [1,4,3,5,6,7,8,9,2] => ([(0,2),(0,3),(0,4),(3,8),(4,8),(5,6),(6,1),(7,5),(8,7)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [1,4,3,6,5,8,7,9,2] => ([(0,1),(0,2),(0,3),(2,7),(2,8),(3,7),(3,8),(5,4),(6,4),(7,5),(7,6),(8,5),(8,6)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [2,1,4,5,6,7,8,9,3] => ([(0,7),(0,8),(1,7),(1,8),(3,4),(4,6),(5,3),(6,2),(8,5)],9)
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [2,1,9,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [3,2,1,5,6,7,8,9,4] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [3,2,1,9,8,7,6,5,4] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [4,3,2,1,6,7,8,9,5] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(6,5),(8,4)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [4,3,2,1,9,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [5,4,3,2,1,7,8,9,6] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(8,5)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [5,4,3,2,1,9,8,7,6] => ([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [2,3,4,5,7,6,8,9,10,1] => ([(1,6),(3,9),(4,9),(5,8),(6,5),(7,2),(8,3),(8,4),(9,7)],10)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [2,3,4,6,5,7,8,9,10,1] => ([(1,6),(3,9),(4,9),(5,2),(6,8),(7,5),(8,3),(8,4),(9,7)],10)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [2,4,3,6,5,8,7,10,9,1] => ([(1,2),(1,3),(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,2,4,5,6,7,8,9,10,1] => ([(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,8,10,9] => [3,2,4,5,6,7,8,10,9,1] => ([(1,9),(2,9),(5,6),(6,8),(7,5),(8,3),(8,4),(9,7)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [3,2,5,4,7,6,9,8,10,1] => ([(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)
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [3,2,10,9,8,7,6,5,4,1] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9)],10)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5,10,9,8] => [4,3,2,7,6,5,10,9,8,1] => ([(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(7,4),(7,5),(7,6),(8,4),(8,5),(8,6),(9,4),(9,5),(9,6)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [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)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [1,3,4,5,6,7,8,10,9,2] => ([(0,3),(0,8),(4,5),(5,7),(6,4),(7,9),(8,6),(9,1),(9,2)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [1,4,3,6,5,8,7,10,9,2] => ([(0,1),(0,2),(0,3),(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [1,4,3,6,5,10,9,8,7,2] => ([(0,1),(0,2),(0,3),(2,8),(2,9),(3,8),(3,9),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7)],10)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [1,6,5,4,3,10,9,8,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [1,8,7,6,5,4,3,10,9,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [2,1,4,5,6,7,8,9,10,3] => ([(0,8),(0,9),(1,8),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(9,6)],10)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [2,1,5,4,7,6,9,8,10,3] => ([(0,3),(0,8),(0,9),(1,3),(1,8),(1,9),(4,2),(5,2),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [2,1,10,9,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9)],10)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [3,2,1,5,6,7,8,9,10,4] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(4,5),(5,7),(6,4),(7,3),(9,6)],10)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [3,2,1,6,5,8,7,10,9,4] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(5,3),(5,4),(6,3),(6,4),(8,5),(8,6),(9,5),(9,6)],10)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [3,2,1,6,5,10,9,8,7,4] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(8,3),(8,4),(8,5),(8,6),(9,3),(9,4),(9,5),(9,6)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [3,2,1,8,7,6,5,10,9,4] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [3,2,1,10,9,8,7,6,5,4] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9)],10)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [4,3,2,1,6,7,8,9,10,5] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,7),(6,5),(7,6),(9,4)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [4,3,2,1,10,9,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [5,4,3,2,1,7,8,9,10,6] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(7,6),(9,5)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [5,4,3,2,1,10,9,8,7,6] => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [6,5,4,3,2,1,8,9,10,7] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(9,6)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [6,5,4,3,2,1,10,9,8,7] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [1,2,4,5,6,7,8,9,3] => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,2),(8,6)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [1,2,3,5,6,7,8,9,4] => ([(0,7),(3,4),(4,6),(5,3),(6,1),(7,8),(8,2),(8,5)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [1,2,3,4,6,7,8,9,5] => ([(0,7),(3,6),(4,8),(5,3),(6,1),(7,4),(8,2),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [1,2,3,4,5,7,8,9,6] => ([(0,7),(3,4),(4,8),(5,6),(6,1),(7,3),(8,2),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,6,8,9,7] => ([(0,7),(3,5),(4,3),(5,8),(6,1),(7,4),(8,2),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,7,9,8] => ([(0,7),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(8,2)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [1,2,4,5,6,7,8,9,10,3] => ([(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,2),(9,7)],10)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [1,2,3,5,6,7,8,9,10,4] => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,9),(9,2),(9,6)],10)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [1,2,3,4,6,7,8,9,10,5] => ([(0,8),(3,4),(4,7),(5,9),(6,3),(7,1),(8,5),(9,2),(9,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,5,7,8,9,10,6] => ([(0,8),(3,7),(4,5),(5,9),(6,3),(7,1),(8,4),(9,2),(9,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,6,8,9,10,7] => ([(0,8),(3,5),(4,3),(5,9),(6,7),(7,1),(8,4),(9,2),(9,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [1,2,3,4,5,7,6,9,8] => ([(0,5),(1,7),(1,8),(2,7),(2,8),(3,4),(4,6),(5,3),(6,1),(6,2)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,7,9,10,8] => ([(0,8),(3,4),(4,6),(5,3),(6,9),(7,1),(8,5),(9,2),(9,7)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,8,10,9] => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,1),(9,2)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [1,3,4,5,6,7,8,9,10,11,2] => ([(0,2),(0,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [1,2,3,4,5,6,7,9,8,10] => ([(0,7),(1,9),(2,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(8,2)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,7,1,9,8] => ([(0,7),(0,8),(1,6),(2,7),(2,8),(3,5),(4,3),(5,2),(6,4)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,6,1,8,9,7] => ([(0,7),(0,8),(1,6),(2,7),(2,8),(4,5),(5,2),(6,4),(8,3)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,2,3,4,5,1,7,8,9] => [2,3,4,5,1,7,8,9,6] => ([(0,7),(0,8),(1,6),(3,7),(3,8),(4,3),(5,2),(6,4),(8,5)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => [2,3,4,1,6,7,8,9,5] => ([(0,7),(0,8),(1,6),(3,7),(3,8),(4,5),(5,2),(6,3),(8,4)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [2,3,1,5,6,7,8,9,4] => ([(0,7),(0,8),(1,3),(3,7),(3,8),(4,6),(5,4),(6,2),(8,5)],9)
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [1,9,8,7,6,5,4,3,2,10] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [8,7,6,5,4,3,2,1,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(9,8)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [9,8,7,6,5,4,3,2,1,10,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(10,9)],11)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [2,1,3,5,6,7,8,9,4] => ([(0,8),(1,8),(4,6),(5,4),(6,2),(7,5),(8,3),(8,7)],9)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => [9,8,7,5,6,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2,3,4,5,6,1,9,8] => [2,3,4,5,6,1,9,8,7] => ([(0,6),(0,7),(0,8),(1,5),(2,6),(2,7),(2,8),(3,4),(4,2),(5,3)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,9,4,5,6,7,8,3] => [1,9,4,5,6,7,8,3,2] => ([(0,2),(0,3),(0,4),(0,8),(5,7),(6,1),(7,6),(8,5)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,8,3,4,5,6,7,1,9] => [1,3,4,5,6,7,2,9,8] => ([(0,2),(0,6),(1,7),(1,8),(2,7),(2,8),(3,5),(4,3),(5,1),(6,4)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => [1,3,4,5,6,7,8,9,2,10] => ([(0,2),(0,8),(1,9),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],10)
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [1,2,9,8,7,6,5,4,3] => ([(0,8),(8,1),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7)],9)
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,2,3,1,9,8,7,6,5] => [2,3,1,9,8,7,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,3,4,2,1,9,8,7,6] => [4,2,3,1,9,8,7,6,5] => ([(0,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,5,3,4,2,1,9,8,7] => [5,3,4,2,1,9,8,7,6] => ([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(4,5),(4,6),(4,7),(4,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [1,2,3,4,6,7,9,8,5] => ([(0,6),(4,8),(5,7),(6,4),(7,2),(7,3),(8,1),(8,5)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [1,2,3,5,4,6,7,8,9,10] => ([(0,7),(2,9),(3,9),(4,1),(5,4),(6,5),(7,8),(8,2),(8,3),(9,6)],10)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => [9,4,3,5,6,7,8,2,1] => ([(3,8),(4,8),(5,7),(7,6),(8,5)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [2,1,3,4,5,6,7,9,8] => ([(0,8),(1,8),(4,5),(5,7),(6,4),(7,2),(7,3),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,9,8,7] => ([(0,7),(4,6),(5,4),(6,8),(7,5),(8,1),(8,2),(8,3)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [1,9,3,4,5,6,7,8,2] => ([(0,2),(0,3),(0,8),(4,5),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [1,2,3,4,5,9,8,7,6] => ([(0,7),(5,6),(6,8),(7,5),(8,1),(8,2),(8,3),(8,4)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => [1,2,3,4,9,8,7,6,5] => ([(0,7),(6,8),(7,6),(8,1),(8,2),(8,3),(8,4),(8,5)],9)
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,9,5,6,7,8,4,3] => [1,9,8,4,5,6,7,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,8),(6,7),(7,1),(8,6)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [9,2,3,4,5,6,7,8,1,10] => ([(0,9),(1,9),(2,8),(3,9),(4,5),(5,7),(6,4),(7,3),(8,6)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,2,1,9,7,8,6,5] => [3,2,1,9,8,6,7,5,4] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(8,3)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [5,4,3,2,1,9,7,8,6] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(8,5)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10,8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,8)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,3,2,1,9,7,8,6] => [4,3,2,1,9,7,8,6,5] => ([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(8,4)],9)
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,1,9,8,6,7,5,4] => [2,1,9,8,6,7,5,4,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(8,2)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,6,7,5,8,9] => [2,3,4,7,5,6,8,9,1] => ([(1,6),(2,8),(3,8),(5,3),(6,7),(7,2),(7,5),(8,4)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => [1,2,3,4,6,5,7,8,9,10] => ([(0,7),(2,9),(3,9),(4,1),(5,8),(6,4),(7,5),(8,2),(8,3),(9,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [1,2,3,4,5,8,7,9,6] => ([(0,6),(2,8),(3,8),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [1,2,3,4,7,6,8,9,5] => ([(0,6),(2,8),(3,8),(5,7),(6,5),(7,1),(7,2),(7,3),(8,4)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,8,7,1,9] => [1,3,2,5,4,7,6,9,8] => ([(0,1),(0,2),(1,7),(1,8),(2,7),(2,8),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [1,2,5,4,7,6,9,8,3] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,8,7,1,10,9] => [1,3,2,5,4,7,6,10,9,8] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(6,8),(6,9),(7,8),(7,9),(8,3),(8,4),(8,5),(9,3),(9,4),(9,5)],10)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [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)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [1,2,5,4,7,6,9,8,10,3] => ([(0,2),(2,1),(2,3),(2,4),(3,8),(3,9),(4,8),(4,9),(6,5),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,8,9,1] => [1,2,3,4,5,6,8,9,7,10] => ([(0,7),(1,9),(2,9),(3,5),(4,3),(5,8),(6,1),(7,4),(8,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,10,7,8,9,1] => [1,2,3,4,5,7,8,9,6,10] => ([(0,7),(1,9),(2,9),(3,4),(4,8),(5,6),(6,1),(7,3),(8,2),(8,5)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [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)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [1,2,3,4,5,6,7,8,10,9,11] => ([(0,8),(1,10),(2,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,1),(9,2)],11)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1,11] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => [9,8,5,4,7,6,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10,5,4,3,2,9,8,7,6,1] => [5,4,3,2,9,8,7,6,1,10] => ([(0,9),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,9),(6,9),(7,9),(8,9)],10)
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,11,10,9,8,7,6,5,4,3] => [1,11,10,9,8,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10)],11)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,8,1,10,9] => ([(0,8),(0,9),(1,7),(2,8),(2,9),(3,4),(4,6),(5,3),(6,2),(7,5)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [2,3,4,5,9,6,8,7,1] => ([(1,6),(5,8),(6,5),(7,3),(7,4),(8,2),(8,7)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [2,1,9,4,5,6,7,8,3] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(3,5),(4,3),(5,2),(8,4)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => [7,6,5,4,3,2,9,8,1,10] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(8,7),(9,7)],10)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [4,2,3,5,6,7,8,9,1] => ([(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [1,10,3,4,5,6,7,8,9,2] => ([(0,2),(0,3),(0,9),(4,6),(5,4),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [1,2,9,4,5,6,7,8,3] => ([(0,8),(4,5),(5,7),(6,4),(7,1),(8,2),(8,3),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10,2,3,4,5,6,7,9,8,1] => [2,3,4,5,6,7,9,8,1,10] => ([(0,9),(1,7),(2,9),(3,9),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [1,2,3,4,5,10,7,8,9,6] => ([(0,8),(4,5),(5,9),(6,7),(7,1),(8,4),(9,2),(9,3),(9,6)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [2,3,4,5,8,6,7,9,1] => ([(1,6),(2,8),(3,8),(4,7),(5,2),(6,4),(7,3),(7,5)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [7,2,3,4,5,6,9,8,1] => ([(1,7),(1,8),(2,6),(3,7),(3,8),(4,5),(5,3),(6,4)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [1,2,3,4,5,6,7,8,9,11,10] => ([(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,1),(10,2)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [8,2,3,4,5,6,7,9,1] => ([(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,6,2,8,9,7] => [6,2,3,4,5,9,7,8,1] => ([(1,7),(1,8),(2,6),(4,7),(4,8),(5,4),(6,5),(8,3)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11] => [3,2,4,5,6,7,8,9,10,11,1] => ([(1,10),(2,10),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7),(10,9)],11)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,2,3,4,5,1,9,8,7] => [2,3,4,5,1,9,8,7,6] => ([(0,3),(1,5),(1,6),(1,7),(1,8),(2,4),(3,2),(4,5),(4,6),(4,7),(4,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [7,6,5,4,3,2,1,9,8,10] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(8,7),(9,7)],10)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [1,3,9,4,5,6,7,8,2] => ([(0,3),(0,8),(4,5),(5,7),(6,4),(7,1),(8,2),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,10,9,8] => ([(0,8),(4,5),(5,7),(6,4),(7,9),(8,6),(9,1),(9,2),(9,3)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,9,7,8,6] => ([(0,7),(4,5),(5,8),(6,1),(7,4),(8,2),(8,3),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1,11] => [2,3,4,5,6,7,8,9,1,11,10] => ([(0,9),(0,10),(1,8),(2,9),(2,10),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],11)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,11,3,4,5,6,7,8,9,10,2] => [11,3,4,5,6,7,8,9,10,2,1] => ([(3,10),(5,7),(6,5),(7,9),(8,6),(9,4),(10,8)],11)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [4,2,3,5,6,7,8,9,10,1] => ([(1,9),(2,4),(4,9),(5,7),(6,5),(7,3),(8,6),(9,8)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [9,2,3,4,5,6,7,8,10,1] => ([(1,9),(2,8),(3,9),(4,5),(5,7),(6,4),(7,3),(8,6)],10)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [2,6,3,4,5,7,8,9,10,1] => ([(1,4),(1,7),(3,9),(4,9),(5,2),(6,3),(7,6),(8,5),(9,8)],10)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [1,2,3,9,5,6,7,8,4] => ([(0,7),(4,6),(5,4),(6,1),(7,8),(8,2),(8,3),(8,5)],9)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,10,9,8,7,6,5,4,3,2,11] => [10,9,8,7,6,5,4,3,2,11,1] => ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,8,2,10,9] => [8,2,3,4,5,6,7,10,9,1] => ([(1,8),(1,9),(2,7),(3,8),(3,9),(4,6),(5,4),(6,3),(7,5)],10)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [2,1,4,3,6,5,8,7,9,10] => ([(0,8),(0,9),(1,8),(1,9),(3,2),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => [2,1,4,3,6,5,8,7,10,9] => ([(0,8),(0,9),(1,8),(1,9),(4,6),(4,7),(5,6),(5,7),(6,2),(6,3),(7,2),(7,3),(8,4),(8,5),(9,4),(9,5)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,9,1,10] => [2,1,3,4,5,6,7,8,10,9] => ([(0,9),(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3),(9,7)],10)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,8,1,9] => [2,3,1,4,5,6,7,9,8] => ([(0,8),(1,4),(4,8),(5,7),(6,5),(7,2),(7,3),(8,6)],9)
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => [3,2,9,8,7,6,5,4,1,10] => ([(0,9),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,2,1,10,7,6,9,8,5] => [3,2,1,10,7,6,9,8,5,4] => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(8,3),(8,4),(9,3),(9,4)],10)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [1,8,3,4,5,6,7,9,2] => ([(0,2),(0,3),(0,7),(1,8),(3,8),(4,6),(5,4),(6,1),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [7,6,5,4,3,2,1,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,7)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [6,5,4,3,2,1,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(8,7),(9,6)],10)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,9,4] => [3,2,9,4,5,6,7,8,1] => ([(1,7),(1,8),(2,7),(2,8),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [1,2,3,4,5,6,8,7,10,9] => ([(0,6),(1,8),(1,9),(2,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],10)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => [10,3,2,5,4,7,6,9,8,1] => ([(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,2,3,4,5,6,7,10,9,1] => [2,3,4,5,6,7,1,9,8,10] => ([(0,8),(0,9),(1,6),(2,8),(2,9),(3,5),(4,3),(5,2),(6,4),(8,7),(9,7)],10)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10,11,12] => [2,1,4,5,6,7,8,9,10,11,12,3] => ([(0,10),(0,11),(1,10),(1,11),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(11,8)],12)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [1,4,3,6,5,8,7,10,9,12,11,2] => ([(0,1),(0,2),(0,3),(2,10),(2,11),(3,10),(3,11),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,10,2,11] => [10,2,3,4,5,6,7,8,9,11,1] => ([(1,10),(2,9),(3,10),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7)],11)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => [3,2,5,4,7,6,9,8,1,10] => ([(0,9),(1,7),(1,8),(2,7),(2,8),(3,9),(4,9),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [9,8,7,6,5,4,3,2,1,12,11,10] => ([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,11,10,9,8,7,6,5,4,3] => [2,11,10,9,8,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10)],11)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [4,2,3,6,5,8,7,10,9,1] => ([(1,3),(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => [1,2,3,4,5,6,7,8,11,10,9] => ([(0,9),(4,6),(5,4),(6,8),(7,5),(8,10),(9,7),(10,1),(10,2),(10,3)],11)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [1,2,3,4,9,6,7,8,5] => ([(0,7),(4,8),(5,6),(6,1),(7,4),(8,2),(8,3),(8,5)],9)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,10,9,8,1] => [3,2,1,6,5,4,9,8,7,10] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(4,3),(5,3),(6,3),(7,4),(7,5),(7,6),(8,4),(8,5),(8,6),(9,4),(9,5),(9,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [1,2,3,4,5,6,10,8,9,7] => ([(0,8),(4,6),(5,4),(6,9),(7,1),(8,5),(9,2),(9,3),(9,7)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,11,10,12] => [3,2,5,4,7,6,9,8,11,10,12,1] => ([(1,10),(1,11),(2,10),(2,11),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => [9,6,5,4,3,8,7,2,1,10] => ([(0,9),(1,9),(2,9),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7,10,9] => [3,2,5,4,1,8,7,10,9,6] => ([(0,7),(0,8),(0,9),(1,5),(1,6),(2,5),(2,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(8,3),(8,4),(9,3),(9,4)],10)
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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