- FindStat

Identifier

Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,0,0,0,0] => ([],5) => ([],5)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 890 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => ([],6)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => ([],7) => ([],7)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(3,7),(7,2)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)

[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => ([(0,5),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,4),(3,7),(4,6),(6,5),(7,6)],8)

[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => ([(0,6),(4,7),(5,2),(5,3),(5,7),(6,1),(6,4),(6,5)],8) => ([(0,7),(1,6),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)

[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => ([(0,6),(4,7),(5,3),(5,7),(6,1),(6,2),(6,4),(6,5)],8) => ([(0,7),(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)

[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2),(7,3)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(6,2),(7,2)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,1),(6,7)],8) => ([(0,7),(1,7),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => ([(2,7),(3,7),(4,7),(5,6),(5,7)],8) => ([(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,4),(3,5),(3,6),(3,7)],8)

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => ([(0,6),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(6,5)],8)

[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)

[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)

[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(4,5),(4,6)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7)],8)

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)

[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => ([(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => ([(2,7),(3,7),(4,5),(4,6),(4,7)],8) => ([(2,7),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => ([(4,7),(5,7),(6,7)],8) => ([(4,5),(4,6),(4,7)],8)

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => ([(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => ([(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => ([(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => ([(4,6),(4,7),(5,6),(5,7)],8) => ([(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => ([(3,7),(4,5),(4,6),(4,7)],8) => ([(3,7),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => ([(4,7),(5,6),(5,7)],8) => ([(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => ([(5,7),(6,7)],8) => ([(5,6),(5,7)],8)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => ([(3,4),(3,5),(3,6),(3,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => ([(4,5),(4,6),(4,7)],8) => ([(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => ([(5,6),(5,7)],8) => ([(5,7),(6,7)],8)

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => ([(6,7)],8) => ([(6,7)],8)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => ([],8) => ([],8)

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8)],9)

[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(8,1)],9)

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9)],10)

[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(8,1),(8,2)],9)

[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(9,1)],10)

[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10)],11)

[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(8,7)],9) => ([(0,8),(8,1),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7)],9)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(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)

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => ([(7,8)],9) => ([(7,8)],9)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => ([],9) => ([],9)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(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)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(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)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(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)

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,8),(1,7),(1,8),(3,6),(3,7),(4,2),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => ([(0,4),(1,5),(1,7),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3),(5,8),(6,7),(6,8)],9)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(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)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(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)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(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)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,8),(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9) => ([(0,7),(4,6),(5,4),(6,8),(7,5),(8,1),(8,2),(8,3)],9)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(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)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(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)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(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)

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => ([],10) => ([],10)

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => ([(8,9)],10) => ([(8,9)],10)

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,8),(1,5),(1,8),(2,5),(2,7),(5,6),(6,3),(6,4),(7,3),(7,4),(8,6),(8,7)],9) => ([(0,6),(0,8),(1,6),(1,8),(2,4),(2,5),(5,3),(6,2),(6,7),(7,3),(7,4),(8,5),(8,7)],9)

Map

Hessenberg poset

Description

The Hessenberg poset of a Dyck path.
Let

$D$ be a Dyck path of semilength

$n$ , regarded as a subdiagonal path from

$(0,0)$ to

$(n,n)$ , and let

$\boldsymbol{m}_i$ be the

$x$ -coordinate of the

$i$ -th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to

$D$ has elements

$\{1,\dots,n\}$ with

$i < j$ if

$j < \boldsymbol{m}_i$ .

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

$y \leq x$ .