- FindStat

Identifier

Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1051 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8) => ([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)

[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => ([(0,4),(0,6),(1,3),(1,7),(3,6),(4,5),(4,7),(6,5),(7,2)],8) => ([(0,3),(1,4),(1,7),(2,5),(3,5),(3,7),(4,2),(4,6),(7,6)],8)

[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8) => ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)

[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => ([(0,4),(1,6),(1,7),(4,7),(5,2),(6,5),(7,3)],8) => ([(0,5),(1,6),(3,7),(4,2),(5,3),(6,4),(6,7)],8)

[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(6,5),(7,4),(7,5)],8) => ([(0,3),(1,4),(1,6),(3,6),(4,5),(4,7),(6,5),(6,7),(7,2)],8)

[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => ([(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(6,4),(7,5)],8) => ([(0,3),(0,7),(1,4),(2,5),(2,7),(3,5),(3,6),(4,2),(7,6)],8)

[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => ([(0,6),(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2)],8) => ([(0,5),(1,3),(2,6),(3,6),(3,7),(4,2),(4,7),(5,4)],8)

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => ([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8)

[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)

[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => ([(0,1),(0,2),(1,7),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8) => ([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,1),(7,5)],8)

[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => ([(0,3),(0,4),(1,5),(2,5),(2,6),(3,7),(4,2),(4,7),(7,1),(7,6)],8) => ([(0,3),(0,7),(1,6),(1,7),(2,4),(3,6),(5,4),(6,2),(6,5),(7,5)],8)

[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => ([(0,3),(0,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6),(5,7),(7,1)],8) => ([(0,3),(1,6),(1,7),(2,4),(3,6),(3,7),(5,4),(6,5),(7,2),(7,5)],8)

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)

[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => ([(0,4),(0,5),(1,7),(2,6),(2,7),(3,1),(3,6),(4,2),(5,3)],8) => ([(0,6),(0,7),(1,2),(1,7),(2,6),(3,5),(4,5),(6,3),(7,4)],8)

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => ([(0,1),(0,3),(1,2),(1,5),(2,6),(2,7),(3,5),(3,7),(5,6),(6,4),(7,4)],8) => ([(0,1),(0,3),(1,2),(1,5),(2,6),(2,7),(3,5),(3,7),(5,6),(6,4),(7,4)],8)

[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => ([(0,3),(0,5),(2,6),(3,6),(3,7),(4,1),(5,2),(5,7),(7,4)],8) => ([(0,3),(0,7),(1,4),(2,5),(2,7),(3,5),(4,2),(5,6),(7,6)],8)

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => ([(0,1),(0,3),(1,2),(1,7),(2,5),(2,6),(3,6),(3,7),(6,4),(7,4),(7,5)],8) => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8)

[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7),(7,1)],8) => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,1),(3,5),(4,2),(4,6),(6,7)],8) => ([(0,3),(0,7),(1,6),(1,7),(2,6),(3,2),(3,5),(5,4),(6,4),(7,5)],8)

[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => ([(0,4),(0,5),(1,6),(2,7),(3,2),(4,3),(4,6),(5,1),(5,7)],8) => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,7),(4,2),(6,5),(7,5)],8)

[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,1),(3,5),(4,2),(4,6),(6,7)],8) => ([(0,3),(0,7),(1,6),(1,7),(2,6),(3,2),(3,5),(5,4),(6,4),(7,5)],8)

[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => ([(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,3),(7,5)],8) => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)

[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => ([(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,2),(4,5),(5,6),(7,1)],8) => ([(0,3),(1,2),(1,5),(2,6),(2,7),(3,5),(3,7),(5,6),(6,4),(7,4)],8)

[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => ([(0,4),(0,5),(1,6),(4,6),(4,7),(5,1),(5,7),(6,2),(7,3)],8) => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => ([(0,3),(0,4),(1,6),(2,7),(3,5),(3,7),(4,2),(4,5),(5,6),(7,1)],8) => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => ([(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,3),(7,5)],8) => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)

[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => ([(0,3),(0,5),(2,7),(3,6),(3,7),(4,1),(5,2),(5,6),(7,4)],8) => ([(0,6),(0,7),(1,3),(2,7),(3,4),(4,2),(4,6),(6,5),(7,5)],8)

[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => ([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8) => ([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)

[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => ([(0,6),(1,2),(1,6),(2,3),(2,7),(3,4),(3,5),(6,7),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(3,2),(3,4),(5,4),(6,5),(7,3),(7,5)],8)

[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8) => ([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)

[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => ([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8) => ([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)

[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,5),(6,7),(7,2)],8) => ([(0,4),(1,3),(1,7),(3,5),(4,5),(4,7),(5,6),(7,2),(7,6)],8)

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => ([(0,5),(1,6),(3,7),(4,3),(5,4),(6,2),(6,7)],8) => ([(0,7),(1,6),(1,7),(4,5),(5,2),(6,4),(7,3)],8)

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => ([(0,5),(1,6),(1,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,3),(1,6),(1,7),(3,7),(4,5),(5,2),(6,4)],8)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8) => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)

[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8) => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)

[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => ([(0,5),(1,6),(3,7),(4,2),(4,7),(5,3),(6,4)],8) => ([(0,7),(1,5),(1,7),(4,2),(5,4),(6,3),(7,6)],8)

[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8) => ([(0,7),(3,5),(4,6),(5,2),(6,1),(7,3),(7,4)],8)

[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8) => ([(0,4),(0,5),(1,6),(4,6),(4,7),(5,1),(5,7),(6,2),(7,3)],8)

[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8) => ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)

[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => ([(0,5),(1,6),(3,7),(4,2),(5,3),(6,4),(6,7)],8) => ([(0,4),(1,6),(1,7),(4,7),(5,2),(6,5),(7,3)],8)

[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => ([(0,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6),(7,2)],8) => ([(0,6),(0,7),(1,5),(2,6),(5,2),(5,7),(6,3),(7,4)],8)

[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8) => ([(0,6),(3,4),(4,1),(5,2),(6,7),(7,3),(7,5)],8)

[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8) => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)

[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => ([(0,2),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,3),(5,2),(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] => [4,1,2,6,3,8,5,7] => ([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8) => ([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)

[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => ([(0,2),(0,7),(1,5),(1,7),(2,3),(2,6),(3,4),(3,5),(6,4),(7,6)],8) => ([(0,2),(0,7),(1,5),(1,7),(2,3),(2,6),(3,4),(3,5),(6,4),(7,6)],8)

[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => ([(0,3),(0,7),(1,6),(1,7),(2,6),(3,2),(3,4),(6,5),(7,4),(7,5)],8) => ([(0,3),(0,7),(1,6),(1,7),(2,6),(3,2),(3,4),(6,5),(7,4),(7,5)],8)

[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => ([(0,5),(1,4),(1,6),(3,6),(4,7),(5,3),(5,7),(7,2)],8) => ([(0,5),(1,4),(1,6),(3,6),(4,7),(5,3),(5,7),(7,2)],8)

[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,7),(4,2),(6,5),(7,5)],8) => ([(0,4),(0,5),(1,6),(2,7),(3,2),(4,3),(4,6),(5,1),(5,7)],8)

[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => ([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8) => ([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)

[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => ([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8) => ([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8)

[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,5),(3,7),(4,2),(6,5)],8) => ([(0,6),(0,7),(1,4),(1,7),(2,6),(3,2),(4,3),(4,5),(7,5)],8)

[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => ([(0,6),(0,7),(1,5),(2,6),(5,2),(5,7),(6,3),(7,4)],8) => ([(0,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6),(7,2)],8)

[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => ([(0,4),(0,7),(1,5),(3,7),(4,6),(5,3),(5,6),(7,2)],8) => ([(0,4),(0,7),(1,5),(3,7),(4,6),(5,3),(5,6),(7,2)],8)

[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => ([(0,4),(0,7),(1,5),(1,6),(3,7),(4,6),(5,3),(7,2)],8) => ([(0,5),(1,3),(1,7),(2,7),(3,6),(4,2),(5,4),(5,6)],8)

[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8) => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8) => ([(0,6),(3,7),(4,5),(5,1),(6,3),(7,2),(7,4)],8)

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8) => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)

[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [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) => ([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)

[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [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) => ([(0,6),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,5)],8)

[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [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) => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(6,5),(7,5)],8)

[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [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) => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7),(7,4)],8)

[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => ([(0,4),(1,6),(2,6),(2,7),(3,1),(3,7),(4,5),(5,2),(5,3)],8) => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,5)],8)

[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => ([(0,5),(2,7),(3,1),(4,3),(4,7),(5,6),(6,2),(6,4)],8) => ([(0,3),(1,4),(1,7),(3,7),(4,6),(5,2),(6,5),(7,6)],8)

[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)

[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => ([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3),(7,1)],8) => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(6,5),(7,5)],8)

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)

[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)

[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => ([(0,3),(0,5),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,1)],8) => ([(0,7),(1,3),(2,6),(3,4),(3,7),(4,2),(4,5),(5,6),(7,5)],8)

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,6),(5,7)],8) => ([(0,3),(0,7),(1,6),(1,7),(2,4),(3,6),(5,4),(6,5),(7,2),(7,5)],8)

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(5,4),(5,6),(6,7),(7,1)],8) => ([(0,5),(1,7),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4),(6,7)],8)

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)

[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)

[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => ([(0,4),(0,5),(1,7),(2,6),(2,7),(3,1),(3,6),(4,2),(5,3)],8) => ([(0,6),(0,7),(1,2),(1,7),(2,6),(3,5),(4,5),(6,3),(7,4)],8)

[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => ([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4),(7,1)],8) => ([(0,6),(0,7),(1,3),(2,5),(3,6),(3,7),(4,2),(6,5),(7,4)],8)

[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,4)],8)

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,7),(4,3),(4,6),(6,7)],8) => ([(0,3),(0,7),(1,2),(1,6),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8)

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => ([(0,4),(0,5),(1,6),(2,7),(3,2),(4,3),(4,6),(5,1),(5,7)],8) => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,7),(4,2),(6,5),(7,5)],8)

[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => ([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4),(7,1)],8) => ([(0,6),(0,7),(1,3),(2,5),(3,6),(3,7),(4,2),(6,5),(7,4)],8)

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => ([(0,3),(0,5),(2,7),(3,6),(3,7),(4,2),(5,4),(5,6),(7,1)],8) => ([(0,6),(0,7),(1,4),(2,7),(3,2),(4,3),(4,6),(6,5),(7,5)],8)

[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => ([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8) => ([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8)

[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => ([(0,7),(1,4),(1,7),(3,6),(4,5),(5,2),(5,6),(7,3)],8) => ([(0,7),(1,4),(1,7),(3,6),(4,5),(5,2),(5,6),(7,3)],8)

[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => ([(0,7),(1,5),(1,7),(3,6),(4,2),(5,4),(5,6),(7,3)],8) => ([(0,5),(0,7),(1,3),(3,7),(4,2),(4,6),(5,4),(7,6)],8)

[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => ([(0,7),(1,5),(1,7),(4,2),(5,4),(6,3),(7,6)],8) => ([(0,5),(1,6),(3,7),(4,2),(4,7),(5,3),(6,4)],8)

[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => ([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8) => ([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)

[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => ([(0,5),(1,3),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7)],8) => ([(0,6),(1,5),(1,6),(4,3),(5,4),(5,7),(6,7),(7,2)],8)

[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => ([(0,6),(1,4),(4,7),(5,2),(6,5),(6,7),(7,3)],8) => ([(0,6),(1,4),(4,7),(5,2),(6,5),(6,7),(7,3)],8)

[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => ([(0,5),(0,7),(1,3),(3,7),(4,2),(4,6),(5,4),(7,6)],8) => ([(0,7),(1,5),(1,7),(3,6),(4,2),(5,4),(5,6),(7,3)],8)

[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => ([(0,4),(1,6),(1,7),(4,7),(5,2),(6,5),(7,3)],8) => ([(0,5),(1,6),(3,7),(4,2),(5,3),(6,4),(6,7)],8)

[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => ([(0,5),(1,6),(3,7),(4,2),(4,7),(5,3),(6,4)],8) => ([(0,7),(1,5),(1,7),(4,2),(5,4),(6,3),(7,6)],8)

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => ([(0,5),(1,6),(3,7),(4,2),(5,3),(6,4),(6,7)],8) => ([(0,4),(1,6),(1,7),(4,7),(5,2),(6,5),(7,3)],8)

[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => ([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8) => ([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8)

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)

[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => ([(0,5),(1,3),(2,6),(3,6),(3,7),(4,2),(4,7),(5,4)],8) => ([(0,6),(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2)],8)

[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => ([(0,5),(1,6),(3,7),(4,3),(5,4),(6,2),(6,7)],8) => ([(0,7),(1,6),(1,7),(4,5),(5,2),(6,4),(7,3)],8)

[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => ([(0,6),(0,7),(1,4),(2,5),(2,7),(3,2),(4,3),(4,6),(6,5)],8) => ([(0,5),(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(6,4),(7,2)],8)

[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => ([(0,6),(0,7),(1,4),(1,7),(2,6),(3,2),(4,3),(4,5),(7,5)],8) => ([(0,3),(0,6),(1,4),(1,7),(2,6),(3,5),(3,7),(4,2),(6,5)],8)

[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => ([(0,5),(1,3),(1,7),(2,7),(3,6),(4,2),(5,4),(5,6)],8) => ([(0,4),(0,7),(1,5),(1,6),(3,7),(4,6),(5,3),(7,2)],8)

[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => ([(0,5),(1,6),(1,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,3),(1,6),(1,7),(3,7),(4,5),(5,2),(6,4)],8)

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8) => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)

[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)

[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => ([(0,4),(1,6),(2,6),(2,7),(3,1),(3,7),(4,5),(5,2),(5,3)],8) => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,5)],8)

[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => ([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8) => ([(0,6),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,5)],8)

[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(4,6),(5,3),(6,7)],8) => ([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,7),(7,4)],8)

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8)

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,4),(0,5),(1,7),(2,6),(3,2),(4,3),(5,1),(5,6),(6,7)],8)

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)

[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => ([(0,2),(0,5),(1,7),(2,6),(2,7),(3,4),(4,1),(4,6),(5,3)],8) => ([(0,6),(0,7),(1,3),(1,7),(2,5),(3,6),(4,2),(6,4),(7,5)],8)

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => ([(0,2),(0,5),(1,7),(2,6),(2,7),(3,4),(4,1),(5,3),(5,6)],8) => ([(0,6),(0,7),(1,4),(1,7),(2,6),(3,2),(4,3),(6,5),(7,5)],8)

[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => ([(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4),(7,2)],8) => ([(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,2),(6,4)],8)

[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => ([(0,7),(1,6),(1,7),(4,5),(5,2),(6,4),(7,3)],8) => ([(0,5),(1,6),(3,7),(4,3),(5,4),(6,2),(6,7)],8)

[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => ([(0,3),(1,6),(1,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,5),(1,6),(1,7),(3,7),(4,3),(5,4),(6,2)],8)

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8) => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => ([(0,6),(0,7),(1,5),(2,6),(2,7),(3,4),(4,2),(5,3)],8) => ([(0,6),(0,7),(1,6),(1,7),(3,5),(4,3),(5,2),(7,4)],8)

[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => ([(0,6),(0,7),(1,5),(2,7),(3,4),(4,2),(5,3),(5,6)],8) => ([(0,6),(0,7),(1,5),(1,6),(3,7),(4,3),(5,4),(7,2)],8)

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8) => ([(0,7),(3,4),(4,6),(5,3),(6,1),(7,2),(7,5)],8)

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => ([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8) => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [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) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)

[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => ([(0,5),(2,7),(3,1),(4,3),(4,7),(5,6),(6,2),(6,4)],8) => ([(0,3),(1,4),(1,7),(3,7),(4,6),(5,2),(6,5),(7,6)],8)

[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => ([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8) => ([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)

[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => ([(0,2),(0,6),(2,7),(3,5),(4,1),(5,4),(5,7),(6,3)],8) => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,6),(5,2),(7,5)],8)

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => ([(0,5),(1,3),(1,7),(2,7),(3,6),(4,2),(5,4),(7,6)],8)

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => ([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8) => ([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => ([(0,7),(1,5),(3,4),(4,6),(5,3),(6,2),(6,7)],8) => ([(0,7),(1,3),(1,7),(4,5),(5,2),(6,4),(7,6)],8)

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => ([(0,7),(1,5),(3,6),(4,2),(5,3),(6,4),(6,7)],8) => ([(0,4),(1,3),(1,7),(4,7),(5,2),(6,5),(7,6)],8)

[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => ([(0,7),(1,6),(3,5),(4,3),(5,2),(6,4),(6,7)],8) => ([(0,6),(1,4),(1,7),(2,7),(5,2),(6,5),(7,3)],8)

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8) => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => ([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8) => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8) => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8) => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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) => ([(0,7),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(8,2)],9)

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => ([(0,8),(1,6),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],9) => ([(0,8),(1,3),(1,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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) => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,1),(9,2)],10)

[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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) => ([(0,7),(3,5),(4,3),(5,8),(6,1),(7,4),(8,2),(8,6)],9)

[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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) => ([(0,8),(3,4),(4,6),(5,3),(6,9),(7,1),(8,5),(9,2),(9,7)],10)

[] => [] => ([],0) => ([],0)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => ([(0,8),(1,3),(4,5),(5,7),(6,4),(7,2),(8,6)],9) => ([(0,8),(1,3),(4,5),(5,7),(6,4),(7,2),(8,6)],9)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9) => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)

[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => ([(0,4),(1,3),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9) => ([(0,7),(3,4),(4,8),(5,2),(6,1),(7,3),(8,5),(8,6)],9)

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,9,6,8] => ([(0,2),(0,8),(1,7),(1,8),(2,6),(2,7),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6)],9) => ([(0,2),(0,8),(1,7),(1,8),(2,6),(2,7),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6)],9)

[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => ([(0,7),(3,5),(4,3),(5,8),(6,1),(7,4),(8,2),(8,6)],9)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => ([(0,8),(1,7),(4,6),(5,4),(6,3),(7,5),(8,2)],9) => ([(0,8),(1,7),(4,6),(5,4),(6,3),(7,5),(8,2)],9)

[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9) => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)

[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => ([(0,7),(1,6),(3,8),(4,8),(5,2),(6,3),(7,4),(8,5)],9) => ([(0,7),(3,5),(4,6),(5,2),(6,1),(7,8),(8,3),(8,4)],9)

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9) => ([(0,7),(3,4),(4,8),(5,6),(6,1),(7,3),(8,2),(8,5)],9)

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => ([(0,7),(1,8),(4,5),(5,2),(6,3),(7,6),(8,4)],9) => ([(0,7),(1,8),(4,5),(5,2),(6,3),(7,6),(8,4)],9)

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9) => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9) => ([(0,7),(3,6),(4,8),(5,3),(6,1),(7,4),(8,2),(8,5)],9)

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => ([(0,7),(1,8),(4,5),(5,2),(6,3),(7,6),(8,4)],9) => ([(0,7),(1,8),(4,5),(5,2),(6,3),(7,6),(8,4)],9)

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9) => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9) => ([(0,7),(3,4),(4,6),(5,3),(6,1),(7,8),(8,2),(8,5)],9)

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => ([(0,8),(1,7),(4,6),(5,4),(6,3),(7,5),(8,2)],9) => ([(0,8),(1,7),(4,6),(5,4),(6,3),(7,5),(8,2)],9)

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9) => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)

[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9) => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,2),(8,6)],9)

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => ([(0,8),(1,3),(4,5),(5,7),(6,4),(7,2),(8,6)],9) => ([(0,8),(1,3),(4,5),(5,7),(6,4),(7,2),(8,6)],9)

[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9) => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9) => ([(1,8),(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] => [2,3,4,5,6,7,8,1,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => ([(0,8),(1,6),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],9) => ([(0,8),(1,3),(1,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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) => ([(1,9),(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] => [2,3,4,5,6,7,8,9,1,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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) => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,2),(8,6)],9)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => ([(0,9),(1,3),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10) => ([(0,9),(1,3),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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) => ([(1,10),(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] => [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) => ([(0,2),(0,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9) => ([(0,7),(3,4),(4,6),(5,3),(6,1),(7,8),(8,2),(8,5)],9)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10) => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,9),(9,2),(9,6)],10)

[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9) => ([(0,7),(3,6),(4,8),(5,3),(6,1),(7,4),(8,2),(8,5)],9)

[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9) => ([(0,7),(3,4),(4,8),(5,6),(6,1),(7,3),(8,2),(8,5)],9)

[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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) => ([(0,8),(3,7),(4,5),(5,9),(6,3),(7,1),(8,4),(9,2),(9,6)],10)

[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => ([(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) => ([(0,7),(0,8),(1,7),(1,8),(4,2),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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) => ([(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)

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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) => ([(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)

[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => ([(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,2),(0,3),(2,8),(2,9),(3,8),(3,9),(5,1),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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) => ([(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)

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,1),(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)

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)

[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10) => ([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10) => ([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)

[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)

[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11) => ([(0,2),(0,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)

[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)

[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10) => ([(0,8),(3,4),(4,6),(5,3),(6,9),(7,1),(8,5),(9,2),(9,7)],10)

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => ([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10) => ([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10)

[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10) => ([(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,9),(9,2),(9,6)],10)

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10) => ([(0,8),(3,7),(4,5),(5,9),(6,3),(7,1),(8,4),(9,2),(9,6)],10)

[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => ([(1,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8)],11) => ([(1,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8)],11)

[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => ([(0,9),(1,7),(1,9),(4,5),(5,2),(6,3),(7,4),(8,6),(9,8)],10) => ([(0,7),(1,8),(3,9),(4,6),(5,3),(6,2),(6,9),(7,4),(8,5)],10)

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => ([(0,8),(1,9),(4,6),(5,4),(6,3),(7,2),(8,7),(9,5)],10) => ([(0,8),(1,9),(4,6),(5,4),(6,3),(7,2),(8,7),(9,5)],10)

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => ([(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) => ([(0,7),(0,8),(1,7),(1,8),(4,2),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)

[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => ([(0,2),(0,8),(1,7),(1,8),(2,7),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9) => ([(0,7),(0,8),(1,7),(1,8),(2,4),(5,2),(5,3),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)

[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => ([(0,2),(0,6),(1,6),(1,8),(2,7),(2,8),(4,3),(5,3),(6,7),(7,4),(7,5),(8,4),(8,5)],9) => ([(0,2),(0,3),(1,4),(1,5),(2,7),(2,8),(3,7),(3,8),(6,5),(7,1),(7,6),(8,4),(8,6)],9)

[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => ([(0,8),(1,2),(1,8),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7)],9) => ([(0,2),(0,3),(2,7),(2,8),(3,7),(3,8),(5,4),(6,1),(6,4),(7,5),(7,6),(8,5),(8,6)],9)

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => ([(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,2),(0,3),(2,8),(2,9),(3,8),(3,9),(5,1),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,9,6,8,10] => ([(0,2),(0,9),(1,8),(1,9),(2,7),(2,8),(4,5),(5,3),(6,3),(7,5),(7,6),(8,4),(8,6),(9,4),(9,7)],10) => ([(0,1),(0,3),(1,2),(1,7),(2,8),(2,9),(3,7),(3,8),(6,5),(7,6),(7,9),(8,4),(8,6),(9,4),(9,5)],10)

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => ([(0,2),(0,9),(1,8),(1,9),(2,7),(2,8),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6),(9,6),(9,7)],10) => ([(0,2),(0,9),(1,8),(1,9),(2,7),(2,8),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6),(9,6),(9,7)],10)

[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => ([(0,2),(0,9),(1,8),(1,9),(2,5),(2,8),(5,7),(6,3),(6,4),(7,3),(7,4),(8,6),(8,7),(9,5),(9,6)],10) => ([(0,6),(0,9),(1,6),(1,9),(2,5),(2,8),(5,4),(6,2),(6,7),(7,3),(7,5),(8,3),(8,4),(9,7),(9,8)],10)

[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => ([(0,2),(0,5),(1,5),(1,9),(2,8),(2,9),(5,8),(6,3),(6,4),(7,3),(7,4),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,8),(0,9),(1,8),(1,9),(2,3),(2,4),(5,4),(6,2),(6,5),(7,3),(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] => [3,1,4,2,6,5,8,7,10,9] => ([(0,9),(1,2),(1,9),(2,7),(2,8),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6),(9,7),(9,8)],10) => ([(0,8),(0,9),(1,8),(1,9),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => ([(0,4),(1,3),(3,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,8)],10) => ([(0,8),(3,5),(4,3),(5,9),(6,2),(7,1),(8,4),(9,6),(9,7)],10)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => ([(0,9),(1,8),(4,5),(5,7),(6,4),(7,3),(8,6),(9,2)],10) => ([(0,9),(1,8),(4,5),(5,7),(6,4),(7,3),(8,6),(9,2)],10)

[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => ([(0,9),(1,3),(1,9),(3,4),(3,6),(4,5),(4,8),(5,2),(5,7),(6,8),(8,7),(9,6)],10) => ([(0,9),(1,3),(1,9),(3,4),(3,6),(4,5),(4,8),(5,2),(5,7),(6,8),(8,7),(9,6)],10)

[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => ([(0,9),(1,3),(1,9),(3,4),(3,6),(4,5),(4,8),(5,2),(5,7),(6,8),(8,7),(9,6)],10) => ([(0,9),(1,3),(1,9),(3,4),(3,6),(4,5),(4,8),(5,2),(5,7),(6,8),(8,7),(9,6)],10)

[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => ([(0,11),(1,3),(1,11),(3,5),(3,7),(4,6),(4,9),(5,4),(5,10),(6,2),(6,8),(7,10),(9,8),(10,9),(11,7)],12) => ([(0,11),(1,3),(1,11),(3,5),(3,7),(4,6),(4,9),(5,4),(5,10),(6,2),(6,8),(7,10),(9,8),(10,9),(11,7)],12)

[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => ([(0,11),(1,3),(1,11),(3,5),(3,7),(4,6),(4,9),(5,4),(5,10),(6,2),(6,8),(7,10),(9,8),(10,9),(11,7)],12) => ([(0,11),(1,3),(1,11),(3,5),(3,7),(4,6),(4,9),(5,4),(5,10),(6,2),(6,8),(7,10),(9,8),(10,9),(11,7)],12)

[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [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) => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)

[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => ([(0,11),(1,3),(3,11),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8),(11,10)],12) => ([(0,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,11),(9,1),(10,7),(11,2),(11,9)],12)

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => ([(0,9),(1,8),(4,6),(5,7),(6,2),(7,3),(8,4),(9,5)],10) => ([(0,9),(1,8),(4,6),(5,7),(6,2),(7,3),(8,4),(9,5)],10)

[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,7,8,9,10,1,2,4,5,6] => ([(0,4),(1,8),(1,9),(4,9),(5,6),(6,2),(7,3),(8,5),(9,7)],10) => ([(0,7),(1,8),(3,9),(4,3),(5,2),(6,5),(6,9),(7,4),(8,6)],10)

[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => ([(0,9),(1,3),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10) => ([(0,9),(1,3),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)

[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => ([(0,8),(1,9),(4,6),(5,4),(6,3),(7,2),(8,7),(9,5)],10) => ([(0,8),(1,9),(4,6),(5,4),(6,3),(7,2),(8,7),(9,5)],10)

[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => ([(0,9),(1,8),(4,5),(5,7),(6,4),(7,3),(8,6),(9,2)],10) => ([(0,9),(1,8),(4,5),(5,7),(6,4),(7,3),(8,6),(9,2)],10)

[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => ([(0,8),(1,7),(2,9),(3,9),(5,2),(6,3),(7,5),(8,6),(9,4)],10) => ([(0,9),(3,7),(4,8),(5,3),(6,4),(7,2),(8,1),(9,5),(9,6)],10)

[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => ([(0,8),(1,7),(3,9),(4,9),(5,2),(6,5),(7,3),(8,4),(9,6)],10) => ([(0,8),(3,9),(4,6),(5,7),(6,2),(7,1),(8,3),(9,4),(9,5)],10)

[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => ([(0,7),(1,8),(1,9),(3,9),(4,6),(5,3),(6,2),(7,5),(8,4)],10) => ([(0,7),(1,8),(1,9),(3,9),(4,6),(5,3),(6,2),(7,5),(8,4)],10)

[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => ([(0,7),(1,8),(1,9),(3,9),(5,6),(6,2),(7,3),(8,5),(9,4)],10) => ([(0,8),(1,7),(3,9),(4,6),(5,3),(6,2),(7,5),(8,4),(8,9)],10)

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => ([(0,7),(1,8),(3,9),(4,6),(5,3),(6,2),(6,9),(7,4),(8,5)],10) => ([(0,9),(1,7),(1,9),(4,5),(5,2),(6,3),(7,4),(8,6),(9,8)],10)

[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,9] => ([(0,7),(1,2),(1,7),(2,3),(2,8),(3,5),(3,6),(5,4),(6,4),(7,8),(8,5),(8,6)],9) => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(4,7),(5,8),(6,4),(6,8),(8,7)],9)

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => ([(0,1),(0,2),(1,8),(2,3),(2,8),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7)],9) => ([(0,7),(0,8),(1,7),(1,8),(2,3),(4,5),(5,3),(6,2),(6,5),(7,4),(7,6),(8,4),(8,6)],9)

[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => ([(0,8),(1,2),(1,8),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7)],9) => ([(0,2),(0,3),(2,7),(2,8),(3,7),(3,8),(5,4),(6,1),(6,4),(7,5),(7,6),(8,5),(8,6)],9)

[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => ([(0,2),(0,9),(1,8),(1,9),(2,7),(2,8),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6),(9,6),(9,7)],10) => ([(0,2),(0,9),(1,8),(1,9),(2,7),(2,8),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6),(9,6),(9,7)],10)

[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => ([(0,6),(1,3),(3,7),(4,5),(4,9),(5,2),(5,8),(6,4),(6,7),(7,9),(9,8)],10) => ([(0,9),(1,6),(1,9),(4,5),(4,8),(5,2),(6,4),(6,7),(7,8),(8,3),(9,7)],10)

[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => ([(0,2),(0,9),(1,8),(1,9),(2,8),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,2),(0,3),(1,5),(2,8),(2,9),(3,8),(3,9),(6,1),(6,4),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8] => ([(0,1),(0,2),(1,8),(2,3),(2,8),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7)],9) => ([(0,7),(0,8),(1,7),(1,8),(2,3),(4,5),(5,3),(6,2),(6,5),(7,4),(7,6),(8,4),(8,6)],9)

[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => ([(0,2),(0,8),(1,7),(1,8),(2,6),(2,7),(4,3),(5,3),(6,4),(7,4),(7,5),(8,5),(8,6)],9) => ([(0,1),(0,3),(1,2),(1,7),(2,6),(2,8),(3,7),(3,8),(6,5),(7,4),(7,6),(8,4),(8,5)],9)

[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => ([(0,7),(1,8),(3,9),(5,2),(6,5),(6,9),(7,6),(8,3),(9,4)],10) => ([(0,8),(1,4),(4,9),(5,6),(6,2),(7,3),(8,5),(8,9),(9,7)],10)

[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => ([(0,8),(1,7),(3,9),(5,6),(6,2),(7,3),(8,5),(8,9),(9,4)],10) => ([(0,8),(1,7),(3,9),(5,6),(6,2),(7,3),(8,5),(8,9),(9,4)],10)

[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => ([(0,2),(0,6),(1,6),(1,8),(2,7),(2,8),(4,3),(5,3),(6,7),(7,4),(7,5),(8,4),(8,5)],9) => ([(0,2),(0,3),(1,4),(1,5),(2,7),(2,8),(3,7),(3,8),(6,5),(7,1),(7,6),(8,4),(8,6)],9)

[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => ([(0,2),(0,8),(1,7),(1,8),(2,7),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9) => ([(0,7),(0,8),(1,7),(1,8),(2,4),(5,2),(5,3),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6)],9)

[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => ([(0,9),(1,2),(1,9),(2,7),(2,8),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6),(8,5),(8,6),(9,7),(9,8)],10) => ([(0,8),(0,9),(1,8),(1,9),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,8,9,10,1,3,4,5,7] => ([(0,9),(1,7),(1,9),(3,8),(4,6),(5,3),(6,2),(7,4),(7,8),(9,5)],10) => ([(0,7),(1,6),(1,9),(3,9),(4,5),(5,2),(5,8),(6,4),(7,3),(9,8)],10)

[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,11,12,1,3,4,5,6,7] => ([(0,11),(1,9),(1,11),(4,7),(5,4),(6,8),(7,2),(8,3),(9,5),(10,6),(11,10)],12) => ([(0,9),(1,10),(3,11),(4,8),(5,3),(6,4),(7,5),(8,2),(8,11),(9,6),(10,7)],12)

Map

to 321-avoiding permutation (Billey-Jockusch-Stanley)

Description

The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$

Map

dual poset

Description

The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.